Container terminal external truck reservation management and yard resource allocation integrated optimization method, device, computer equipment and storage medium

Abstract

Embodiments of the present application relate to the field of container yard resource optimization, and provide a container terminal truck reservation management and yard resource allocation integrated optimization method and device, computer equipment and storage medium, the method comprising: respectively constructing an external container truck arrival demand translation submodel, a yard dynamic queuing submodel, a yard throughput envelope submodel and a yard resource allocation submodel, according to the data flow and logical association rules, the submodel integrated optimization processing is carried out, and the integrated optimization model is constructed; based on the preset integrated optimization iterative solution algorithm, the integrated optimization model is solved, and the solution output data corresponding to the integrated optimization model is obtained. The implementation of the method improves the container terminal truck reservation management efficiency and yard resource allocation efficiency.

Description

Technical Field

[0001] This application relates to the field of container yard resource optimization technology, and in particular to an integrated optimization method, apparatus, computer equipment, and storage medium for container terminal off-site truck reservation management and yard resource allocation. Background Technology

[0002] In the field of container yard resource optimization technology, container terminals, as core hubs of the global freight network, undertake the main cargo transshipment tasks in international trade. The efficiency of terminal operations largely depends on the prediction and control of service demand. However, the uncertainty of cargo transportation demand restricts production efficiency.

[0003] Inside the terminal, the container yard is a crucial transfer area for containers to flow between container ships and external trucks. The number of external trucks arriving at the port at different times is highly random, which can easily cause them to accumulate in the container yard, leading to severe traffic congestion and reducing the overall throughput capacity of the terminal.

[0004] Therefore, traditional container yard resource optimization technologies suffer from low efficiency in external truck management and yard resource allocation. Summary of the Invention

[0005] This application provides an integrated optimization method, apparatus, computer equipment, and storage medium for container terminal external truck reservation management and yard resource allocation. More specifically, this application provides an integrated optimization method, apparatus, computer equipment, computer storage medium, and computer program product for container terminal external truck reservation management and yard resource allocation, thereby improving the efficiency of container terminal external truck reservation management and yard resource allocation.

[0006] In a first aspect, embodiments of this application provide an integrated optimization method for container terminal off-site truck reservation management and yard resource allocation, including:

[0007] Based on the principle of mixed integer programming modeling, a sub-model for the translation of external truck arrival demand is constructed;

[0008] Based on the principles of stochastic process modeling and fluid approximation mechanism, a dynamic queuing sub-model for the stockyard is constructed.

[0009] Based on historical external truck service records and yard resource templates, a sub-model of yard throughput envelope is constructed;

[0010] Based on the principle of resource allocation decision transformation and the logic of service rate composition, a sub-model of yard resource allocation is constructed.

[0011] Based on the data flow and logical association rules of the external truck arrival demand translation sub-model, the yard dynamic queuing sub-model, the yard throughput envelope sub-model, and the yard resource allocation sub-model, the sub-models are integrated and optimized to construct an integrated optimization model.

[0012] Based on a preset integrated optimization iterative solution algorithm, the integrated optimization model is solved to obtain the solution output data corresponding to the integrated optimization model.

[0013] Optionally, in some embodiments of this application, the step of constructing the external truck arrival demand translation sub-model based on the mixed-integer programming modeling principle includes:

[0014] The construction principle of the external card arrival demand management model based on mixed integer programming determines the set and parameter definition results;

[0015] Based on the mathematical relationships of demand shift, determine the decision logic for demand shift;

[0016] Based on the defined set and parameters and the decision logic of the demand shift, determine the performance evaluation index of the intervention amount and the constraints of the external truck arrival demand shift sub-model.

[0017] Based on the performance evaluation index of the intervention amount and the constraints of the external truck arrival demand translation sub-model, the external truck arrival demand translation sub-model is determined.

[0018] Optionally, in some embodiments of this application, the mathematical relationship of the demand shift is: the deviation between the original arrival demand and the planned arrival volume is represented by the sum of the positive and negative shifts.

[0019] Optionally, in some embodiments of this application, determining the intervention performance evaluation index and the constraints of the external truck arrival demand shift sub-model based on the set and parameter definition results and the demand shift decision logic includes:

[0020] Determine the maximum intervention level to measure the highest level of intervention undertaken across all truck types;

[0021] Determine the total intervention amount used to measure the overall scale of intervention received by all trucks during the planning period;

[0022] Based on the maximum intervention amount and the total intervention amount, determine the intervention amount performance evaluation index.

[0023] Optionally, in some embodiments of this application, determining the intervention performance evaluation index based on the maximum intervention amount and the total intervention amount includes:

[0024] The maximum intervention amount and the total intervention amount are used as initial performance evaluation indicators;

[0025] The initial performance evaluation index is linearized, and the absolute value term is replaced by linear constraints to obtain the intervention quantity performance evaluation index.

[0026] Optionally, in some embodiments of this application, determining the intervention performance evaluation index and the constraints of the external truck arrival demand shift sub-model based on the set and parameter definition results and the demand shift decision logic includes:

[0027] The demand conservation constraint and the variable nonnegativity constraint are constructed.

[0028] The demand conservation constraint and the variable nonnegativity constraint are used as constraints for the external truck arrival demand translation sub-model.

[0029] Optionally, in some embodiments of this application, the step of constructing a dynamic queuing sub-model for the stockyard based on the principles of stochastic process modeling and fluid approximation mechanisms includes:

[0030] The trucking operations at import and export yards are abstracted into a pre-defined queuing system with Poisson arrival and Irish distribution service times.

[0031] The preset queuing system is subjected to fluid approximation processing to obtain a fluid approximation model;

[0032] The logic for the flow and coupling of multiple types of trucks is constructed, and the calculation rules for capacity utilization are determined.

[0033] Based on the fluid approximation model, the multi-type truck flow and coupling logic, and the capacity utilization calculation rules, the dynamic queuing sub-model of the storage yard is determined.

[0034] Optionally, in some embodiments of this application, the step of performing fluid approximation processing on the preset queuing system to obtain a fluid approximation model includes:

[0035] The preset queuing model is dynamically approximated to obtain the first approximation result;

[0036] A flow balance formula is established using the conservation law. Based on the flow balance formula, the first approximate result is approximated by flow balance to obtain a second approximate result.

[0037] Based on the data relationship of the actual outflow, the characteristics of random queuing are coupled into the deterministic equation of the second approximation result to obtain the final form of the fluid approximation model.

[0038] Optionally, in some embodiments of this application, the construction of multi-type card transfer and coupling logic includes:

[0039] Various types of truck dynamic equations and corresponding dual-task flow correlation equations are constructed.

[0040] Based on the coupling equation set consisting of the dynamic equations of the various types of trucks and the dual-task flow association equations, the multi-type truck flow and coupling logic is determined.

[0041] Optionally, in some embodiments of this application, the calculation rule for determining capacity utilization includes:

[0042] Based on the nonlinear function rule of capacity utilization rate and the number of cards in the initial stage of a time period, the nonlinear characterization result of the capacity utilization rate is determined;

[0043] The nonlinear characterization result is linearized based on the piecewise linear approximation function to obtain the linearized characterization result.

[0044] The calculation rules for the capacity utilization rate are determined based on the linearization characterization results.

[0045] Optionally, in some embodiments of this application, the linearization transformation of the nonlinear characterization result to obtain a linearized characterization result includes:

[0046] Discrete points are sampled based on data sampling technology, and the original utilization rate corresponding to each discrete point is calculated according to the original nonlinear function to construct a preset dataset.

[0047] Based on the curvature characteristics of the original curve, determine the critical point information;

[0048] A preset optimization problem is constructed based on the preset dataset and the critical point information;

[0049] The preset optimization problem is solved to obtain the final calibration formula;

[0050] The linearization characterization result is determined based on the final calibration formula.

[0051] Optionally, in some embodiments of this application, determining the linearization characterization result based on the final calibration formula includes:

[0052] Determine the goodness of fit of the calibrated function corresponding to the final calibration formula;

[0053] If the goodness of fit of the calibrated function meets the preset accuracy condition, the linearization characterization result is determined according to the final calibration formula.

[0054] Optionally, in some embodiments of this application, the step of constructing a yard throughput envelope sub-model based on historical external truck service records and yard resource templates includes:

[0055] Based on the historical external truck service records and the yard resource template, throughput envelope data reflecting different resource configuration levels is generated by piecewise linear fitting.

[0056] Based on the throughput envelope data and the decision logic of the yard throughput envelope sub-model, the yard throughput envelope sub-model is determined;

[0057] The decision logic of the yard throughput envelope sub-model is as follows: select the import and export service rate combination on the target envelope of the given throughput envelope data.

[0058] Optionally, in some embodiments of this application, the step of generating throughput envelope data reflecting different resource configuration levels through piecewise linear fitting based on the historical external truck service records and the yard resource template includes:

[0059] The historical external card service records are cleaned to obtain cleaned data;

[0060] The cleaned data is grouped according to the stockpile resource template to obtain grouped data.

[0061] The grouped data are subjected to concave piecewise linear fitting to construct the fitting problem;

[0062] Based on the fitting objective function and fitting constraints corresponding to the fitting problem, the fitting problem is solved to obtain the fitting solution result;

[0063] The throughput envelope data is determined based on the fitting solution results.

[0064] Optionally, in some embodiments of this application, the method further includes:

[0065] The following constraints are constructed: the slope is monotonically decreasing, the slope is decreasing, and the intercept is decreasing.

[0066] The monotonically decreasing slope constraint condition of the adjacent segments, the slope constraint condition, and the intercept constraint condition are used as the fitting constraint conditions.

[0067] Optionally, in some embodiments of this application, the step of constructing a yard resource allocation sub-model based on the resource allocation decision transformation principle and service rate composition logic includes:

[0068] The principle of resource allocation decision transformation is to select the optimal inbound truck service rate and outbound truck service rate on a given throughput envelope.

[0069] The service rate is determined based on the mathematical relationship between the service rate of a single-export truck and the service rate of a dual-task truck that has not completed its export task.

[0070] A binary variable is introduced to characterize the selection of envelope line segments to determine the constraints of the yard resource allocation sub-model;

[0071] The yard resource allocation sub-model is determined based on the constraints of the yard resource allocation sub-model, the resource allocation decision transformation principle, and the service rate composition logic.

[0072] Optionally, in some embodiments of this application, the step of introducing a binary variable to characterize the selection of envelope segments to determine the constraints of the yard resource allocation sub-model includes:

[0073] The line segment uniqueness constraint, service rate association constraint, and service rate range constraint are determined based on the binary variables.

[0074] Determine the non-negativity constraint of the service rate, and use the non-negativity constraint of the service rate, the uniqueness constraint of the line segment, the service rate correlation constraint, and the service rate range constraint as the constraint conditions of the yard resource allocation sub-model.

[0075] Optionally, in some embodiments of this application, the data flow direction and logical association rules are as follows:

[0076] The external container truck arrival demand translation sub-model is used to output performance evaluation indicators of planned arrival volume and intervention volume based on the original arrival demand;

[0077] The yard dynamic queuing sub-model is used to output queue length data based on the planned arrival volume, service rate data, and capacity utilization rate; and to output yard congestion index based on the queue length data.

[0078] The yard throughput envelope sub-model is used to output throughput envelope data based on historical external truck service records and yard resource templates;

[0079] The yard resource allocation sub-model is used to output the service rate data based on the throughput envelope data.

[0080] Optionally, in some embodiments of this application, the step of performing sub-model ensemble optimization processing to construct an ensemble optimization model includes:

[0081] The lexicographical objective function of the integrated optimization model is determined based on the performance evaluation index of the intervention quantity;

[0082] The upper limit constraint of the yard congestion cost of the integrated optimization model is determined based on the yard congestion index.

[0083] The integrated optimization model is determined based on the lexicographical objective function and the upper limit constraint of the yard congestion cost.

[0084] Optionally, in some embodiments of this application, the step of solving the ensemble optimization model based on a preset ensemble optimization iterative solution algorithm to obtain the solution output data corresponding to the ensemble optimization model includes:

[0085] The original demand, congestion threshold, and step size are determined as the input data for the algorithm.

[0086] The algorithm is initialized based on the input data, and the initialization result is obtained.

[0087] Based on the initialization results, a loop iteration step is executed to determine the solution output data.

[0088] Optionally, in some embodiments of this application, the algorithm initialization based on the algorithm input data includes:

[0089] Initialize the set of feasible service rate options, control parameters, and iteration count;

[0090] The main problem is solved using the original requirements as input to obtain initial resource options, and the set of feasible service rate options is updated based on the resource options.

[0091] Optionally, in some embodiments of this application, the step of performing a loop iteration includes:

[0092] Solving the main problem yields the arrival options and the current congestion costs;

[0093] If the congestion cost exceeds the congestion threshold, a preset sub-loop iteration step is executed;

[0094] The preset sub-loop iteration steps include:

[0095] Update the iteration count and tighten the control parameters;

[0096] Calculate the feasibility threshold for the current set;

[0097] If the control parameter is less than the feasibility threshold, the process terminates and reports that no feasible solution exists.

[0098] If the control parameter is greater than or equal to the feasibility threshold, the main problem is solved again to update the arrival plan and the congestion cost;

[0099] Using the latest arrival plan as input, solve the subproblem, update the resource options, and update the set of feasible service rate options.

[0100] Optionally, in some embodiments of this application, the main problem is: to perform demand shifting by adjusting the arrival demand of external trucks, and to find the optimal shifting strategy that can meet the control parameters; the sub-problem is: to receive the arrival scheme generated by the main problem, and to search for new resource options that can minimize congestion costs on the complete throughput envelope.

[0101] Secondly, embodiments of this application provide an integrated optimization device for container terminal external truck reservation management and yard resource allocation, which has the function of implementing the integrated optimization method for container terminal external truck reservation management and yard resource allocation provided in the first aspect above. The function can be implemented by hardware or by hardware executing corresponding software. The hardware or software includes one or more modules corresponding to the above function, and the modules can be software and / or hardware.

[0102] In one possible design, the device includes:

[0103] The module for constructing the external truck arrival demand translation sub-model is used to construct the external truck arrival demand translation sub-model based on the principle of mixed integer programming.

[0104] The dynamic queuing sub-model building module for the stockyard is used to construct a dynamic queuing sub-model for the stockyard based on the principles of stochastic process modeling and fluid approximation mechanism.

[0105] The yard throughput envelope sub-model building module is used to build a yard throughput envelope sub-model based on historical external truck service records and yard resource templates.

[0106] The yard resource allocation sub-model construction module is used to construct the yard resource allocation sub-model based on the resource allocation decision transformation principle and service rate composition logic.

[0107] The integration and optimization module is used to perform sub-model integration and optimization processing based on the data flow direction and logical association rules of the external truck arrival demand translation sub-model, the yard dynamic queuing sub-model, the yard throughput envelope sub-model, and the yard resource allocation sub-model, and to construct an integrated optimization model.

[0108] The solution module is used to solve the ensemble optimization model based on a preset ensemble optimization iterative solution algorithm, and obtain the solution output data corresponding to the ensemble optimization model.

[0109] In another aspect, this application provides a computer device including at least one connected processor and a memory, wherein the memory is used to store program code, and the processor is used to call the program code in the memory to execute the methods described in the above aspects.

[0110] In another aspect, embodiments of this application provide a computer storage medium including instructions that, when executed on a computer, cause the computer to perform the methods described in the above aspects.

[0111] In another aspect, this application provides a computer program product containing instructions that, when run on a computer, cause the computer to perform the methods described in the above aspects.

[0112] Compared to traditional technologies, the technical solution of this application innovatively constructs a collaborative optimization framework for the demand and supply sides, integrating two decision-making processes. Through joint optimization of intervention costs and congestion levels, it significantly improves the global optimality of the decision-making process. A data-driven yard throughput envelope sub-model is developed, improving model tractability, reducing model complexity, and enhancing the adaptability and scalability of the technical solution. A yard dynamic congestion evaluation technology based on non-stationary queuing theory is proposed, accurately predicting the evolution of queue length during peak hours, considering the flow logic of dual-task trucks, and improving the accuracy of congestion mitigation. An efficient iterative solution algorithm and decomposition strategy are designed, improving computational efficiency and ensuring the real-time nature of the decision-making scheme. Therefore, the overall efficiency of container terminal external truck reservation management and yard resource allocation is improved. Attached Figure Description

[0113] Figure 1 This is a flowchart of one embodiment.

[0114] Figure 2 This is a schematic diagram of a dynamic queuing sub-model for a storage yard.

[0115] Figure 3 This is a schematic diagram of the stockpile envelope.

[0116] Figure 4 This is a schematic diagram of the yard resource allocation sub-model.

[0117] Figure 5 This is a schematic diagram of the integrated framework.

[0118] Figure 6 This is a schematic diagram illustrating the effect of the integrated optimization model.

[0119] Figure 7 This is a diagram showing the distribution of truck arrival demand over different number of days.

[0120] Figure 8 This is a structural block diagram of a device in one embodiment.

[0121] Figure 9 This is an internal structural diagram of a computer device in one embodiment.

[0122] Figure 10 This is a diagram of the internal structure of a computer device in another embodiment. Detailed Implementation

[0123] The terms "first," "second," etc., used in the embodiments of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or modules is not necessarily limited to those steps or modules explicitly listed, but may include other steps or modules not explicitly listed or inherent to these processes, methods, products, or devices. The division of modules appearing in the embodiments of this application is only a logical division. In actual applications, there may be other division methods. For example, multiple modules may be combined or integrated into another system, or some features may be ignored or not performed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be through some interface, and the indirect coupling or communication connection between modules may be electrical or other similar forms. None of these are limited in the embodiments of this application. Furthermore, the modules or sub-modules described as separate components may or may not be physically separated, may or may not be physical modules, or may be distributed among multiple circuit modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the embodiments of this application.

[0124] Figure 1 This is a flowchart illustrating one embodiment, such as... Figure 2 As shown in the embodiments of this application, the integrated optimization method for container terminal external truck reservation management and yard resource allocation includes:

[0125] S1100, based on the principle of mixed integer programming modeling, constructs a translation sub-model of external truck arrival demand.

[0126] Among them, the modeling principle of Mixed Integer Programming (MIP) refers to an optimization modeling method that combines integer and continuous variables.

[0127] Among them, the external truck arrival demand shifting sub-model refers to the optimization sub-model for controlling the arrival time of trucks at the port.

[0128] S1200, based on the principles of stochastic process modeling and fluid approximation mechanism, constructs a dynamic queuing sub-model for the stockyard.

[0129] Among them, the principle of stochastic process modeling refers to using probability statistics to describe the dynamic changes in queue arrival and service; the fluid approximation mechanism refers to approximating discrete queues as continuous fluids to simplify dynamic calculations.

[0130] Among them, the dynamic queuing sub-model of the storage yard refers to the dynamic analysis model that describes the changes in storage yard congestion.

[0131] S1300 constructs a sub-model of the yard throughput envelope based on historical external truck service records and yard resource templates.

[0132] Historical external truck service records refer to the actual operational data of trucks entering and leaving the yard in the past. For example, the historical external truck service records of a large container terminal are the operational data for a certain period of time. Yard resource templates refer to the resource combination forms under different equipment and manpower configurations.

[0133] Among them, the yard throughput envelope sub-model refers to the model that describes the boundary of the maximum service capacity of the yard.

[0134] S1400, based on the principle of resource allocation decision transformation and service rate composition logic, constructs a sub-model for yard resource allocation.

[0135] Among them, the principle of resource allocation decision transformation refers to the rule of transforming resource allocation into service rate selection; the service rate composition logic refers to the partial composition logic of the total service rate of the exit.

[0136] Among them, the yard resource allocation sub-model refers to the resource scheduling model that determines the optimal service rate.

[0137] S1500, based on the data flow and logical association rules of the external truck arrival demand translation sub-model, the yard dynamic queuing sub-model, the yard throughput envelope sub-model, and the yard resource allocation sub-model, performs sub-model integration and optimization processing to construct an integrated optimization model.

[0138] Among them, data flow and logical association rules refer to the transmission relationship between input and output, and the coupling relationship between constraints and variables among the sub-models; sub-model integration optimization processing refers to the process of unifying multiple sub-models into a whole model.

[0139] Among them, the integrated optimization model refers to the overall optimization model that integrates the four sub-models in steps S1100 to S1400.

[0140] S1600, based on a preset ensemble optimization iterative solution algorithm, solves the ensemble optimization model and obtains the solution output data corresponding to the ensemble optimization model.

[0141] Among them, the integrated optimization iterative solution algorithm refers to the solution method of alternating iterative solving of the main problem and sub-problems; the solution output data refers to the decision results and performance indicators obtained by the algorithm.

[0142] Compared to traditional technologies, this application embodiment constructs four sub-models: an external truck arrival demand shift sub-model, a yard dynamic queuing sub-model, a yard throughput envelope sub-model, and a yard resource allocation sub-model. Then, based on the data flow and logical association rules of the four sub-models, sub-model integration and optimization processing is performed to construct an integrated optimization model. Finally, based on a preset integrated optimization iterative solution algorithm, the integrated optimization model is solved to obtain the corresponding solution output data. The technical solution of this application embodiment innovatively constructs a collaborative optimization framework for the demand side and the supply side, integrating two decision-making processes, and by considering the intervention cost and... Joint optimization of congestion levels significantly improves the global optimality of decision-making; a data-driven sub-model of yard throughput envelope was developed, improving model tractability, reducing model complexity, and enhancing the adaptability and scalability of technical solutions; a dynamic congestion evaluation technique for yards based on non-stationary queuing theory was proposed, accurately predicting the evolution of queue length during peak hours, considering the flow logic of dual-task trucks, and improving the accuracy of congestion mitigation; an efficient iterative solution algorithm and decomposition strategy were designed, improving computational efficiency and ensuring the real-time nature of decision-making solutions; thus, the overall efficiency of container terminal external truck reservation management and yard resource allocation has been improved.

[0143] For example, the model input / output and model usage of the external truck arrival demand translation sub-model are as follows.

[0144] The model input is: original arrival demand. .

[0145] The model output is: planned arrival volume. Maximum intervention amount Total intervention amount .

[0146] Model Purpose: To provide smoothed demand input for the "Dockyard Dynamic Queuing Sub-model" and "Dockyard Resource Allocation Sub-model," and to provide performance evaluation indicators for intervention (maximum intervention amount). Total intervention amount This is used to measure the magnitude of demand adjustments.

[0147] The construction process of the external truck arrival demand translation sub-model is as follows.

[0148] A mixed integer programming (MIP)-based external truck arrival demand management model is established. Its core objective is to rationally determine the planned arrival volume for each time period while minimizing intervention in the original demand.

[0149] (1) Regarding the definition of sets and parameters:

[0150] set up Let be a set of consecutive time periods within the planning period; This is a collection of external card types.

[0151] in This refers to single-transaction inbound trucks, among which... This refers to Single-transaction Outbound Trucks. This represents dual transaction trucks. (During the time period...) Inside, The original arrival demand of type trucks is expressed as .

[0152] (2) Regarding decision-making logic and variables:

[0153] The model determines the permitted entry points to the pier at different times. The number of trucks of each type is denoted as the planned arrival volume. Original requirements Compared with planned arrival volume The deviation between these values ​​is defined as "demand shifting". This application introduces a positive shift amount. and negative translation To adjust the distribution of arrivals at ports, the mathematical relationship satisfies: .

[0154] (3) Regarding performance evaluation:

[0155] Since the forced shift of arrival demand can interfere with transportation efficiency, the model establishes the following two key indicators (intervention performance evaluation indicators) to assess service levels: Maximum Intervention. Total Intervention .

[0156] Maximum intervention amount This measures the highest level of intervention across all truck types, used to ensure fairness among different business types. The expression is: .

[0157] Total intervention amount The overall scale of intervention received by all trucks during the planning period is measured by the following expression: .

[0158] (4) Regarding constraints and model simplification:

[0159] Demand conservation constraint: Equation Ensure that the total planned demand equals the total original demand during the planning period, that is, ensure that all trucks can eventually obtain service.

[0160] Non-negativity constraint for variables: .

[0161] Linearization (Lemma Explanation): Considering that the objective function contains absolute value terms, this embodiment uses a lemma to prove that linearization is achieved in solving... and At that time, variables and They will not all take positive values ​​simultaneously within the same time period. Therefore, to improve solution efficiency, the intervention indicators in the model can be replaced by the following linear constraints: ; By introducing a pair of mutually exclusive non-negative auxiliary variables (positive shift amount) / Negative translation amount We use the method to decompose the absolute value and utilize the minimization property of the objective function to ensure that the two values ​​will not both take positive values ​​at the same time under the optimal solution, thus mathematically transforming the nonlinear index into an efficient linear sum.

[0162] The container truck arrival demand shift sub-model, through the above constraints (demand conservation constraints, variable non-negativity constraints) and indicators (intervention quantity performance evaluation indicators), achieves precise reshaping of external container truck traffic in the time dimension, laying the foundation for demand-side management for subsequent yard congestion relief.

[0163] Optionally, in some embodiments of this application, a sub-model for the transfer of demand for external trucks arriving at ports is constructed based on the principle of mixed-integer programming modeling. This includes: determining the set and parameter definition results based on the construction principle of the external truck arrival demand management model using mixed-integer programming; determining the decision logic for demand transfer based on the mathematical relationship of demand transfer; determining the performance evaluation index of intervention quantity and the constraints of the external truck arrival demand transfer sub-model based on the set and parameter definition results and the decision logic of demand transfer; and determining the external truck arrival demand transfer sub-model based on the performance evaluation index of intervention quantity and the constraints of the external truck arrival demand transfer sub-model.

[0164] Among them, the set and parameter definition results refer to the standard definition of objects, constants and variables in the model.

[0165] In this context, the mathematical relationship of demand shift refers to the expression representing the deviation between the original demand and the planned demand. Correspondingly, the decision logic of demand shift refers to the logic of adjusting truck arrival times as represented in the mathematical relationship of demand shift.

[0166] Among them, the intervention quantity performance evaluation index refers to the evaluation index that measures the degree of scheduling intervention; the constraint conditions of the external truck arrival demand translation sub-model refer to the restrictions that the model must meet.

[0167] Optionally, in some embodiments of this application, the mathematical relationship of demand shift is: the sum of the positive and negative shifts represents the deviation between the original arrival demand and the planned arrival.

[0168] Among them, positive shift refers to the number of truck arrival times that are adjusted backward; negative shift refers to the number of truck arrival times that are adjusted forward; original arrival demand refers to the number of trucks originally planned to arrive at the port; and planned arrival volume refers to the number of trucks that have been optimized and adjusted.

[0169] Specifically, the mathematical relationship of demand shift refers to the introduction of a positive shift. and negative translation To represent the original demand Compared with planned arrival volume The deviation between them. More specifically, the mathematical relationship for demand shift is: .

[0170] Optionally, in some embodiments of this application, based on the set and parameter definition results and the decision logic of demand shift, the intervention performance evaluation index and the constraints of the external truck arrival demand shift sub-model are determined, including: determining the maximum intervention amount used to measure the highest level of intervention undertaken among all truck types; determining the total intervention amount used to measure the overall scale of intervention received by all trucks during the planning period; and determining the intervention performance evaluation index based on the maximum intervention amount and the total intervention amount.

[0171] Among them, the intervention volume performance evaluation index is used to characterize the fairness and overall cost of scheduling interventions, including the maximum intervention volume. and total intervention amount .

[0172] Specifically, the maximum intervention level is used to measure the highest level of intervention undertaken across all truck types, ensuring fairness among different business types. Its mathematical expression is: Total intervention amount is used to measure the overall scale of intervention received by all trucks during the planning period, and its mathematical expression is: .

[0173] In this embodiment, scheduling fairness is improved by setting dual intervention indicators.

[0174] Optionally, in some embodiments of this application, determining the intervention performance evaluation index based on the maximum intervention amount and the total intervention amount includes: using the maximum intervention amount and the total intervention amount as initial performance evaluation indexes; linearizing the initial performance evaluation indexes and replacing the absolute value terms with linear constraints to obtain the intervention performance evaluation indexes.

[0175] The initial performance evaluation index refers to the unprocessed original intervention evaluation index; linearization refers to the operation of transforming nonlinear terms into linear expressions.

[0176] For example, the maximum intervention amount after linearization is: The total intervention amount after linearization is: .

[0177] In this embodiment, the linearization of the index improves the solvability of the model, which facilitates faster computation and reduces optimization complexity.

[0178] Optionally, in some embodiments of this application, based on the set and parameter definition results and the decision logic of demand shift, the performance evaluation index of intervention quantity and the constraints of the external truck arrival demand shift sub-model are determined, including: constructing demand conservation constraints and variable non-negativity constraints; and using the demand conservation constraints and variable non-negativity constraints as the constraints of the external truck arrival demand shift sub-model.

[0179] The demand conservation constraint refers to the restriction that aggregate demand remains unchanged before and after the shift, and its mathematical expression can be: The non-negativity constraint refers to the restriction that variables such as translation amounts cannot be negative. Its mathematical expression can be: .

[0180] In this embodiment, by setting basic constraints, the feasibility of the model is improved, and the effectiveness of the decision-making is ensured.

[0181] For example, the model inputs and outputs and the model uses of the dynamic queuing sub-model for the storage yard are as follows.

[0182] Model inputs: Planned arrival volume for each time period (planned arrival volume output by the "External Truck Arrival Demand Shift Sub-model"), currently selected service rate (service rate data output by the "Dock Resource Allocation Sub-model"), and capacity utilization rate.

[0183] Model output: The number of backlogged trucks in the system at the end of each time period (also known as queue length data).

[0184] Model Purpose: To quantitatively assess yard congestion status in real time, calculate new capacity utilization, and serve as the core basis for calculating total congestion cost in the "integrated optimization model". Congestion cost, also known as the weighted queuing total number of trucks, yard congestion level, or yard congestion index, is measured by the total weighted queuing total number of trucks within the planning period.

[0185] The construction process of the dynamic queuing sub-model of the yard is as follows.

[0186] Figure 2 This is a schematic diagram of a dynamic queuing sub-model for a stockyard. The dynamic queuing sub-model is a descriptive, non-stationary queuing model, such as... Figure 2 As shown, it is used to capture the dynamic evolution of truck queues within the yard, thereby enabling accurate assessment of yard congestion levels.

[0187] (1) Modeling of stochastic processes:

[0188] In external truck operations, arrivals and service operations within each time period can be considered a stochastic process. This application abstracts truck operations at import and export yards as an M / E / 1 queuing system with Poisson Arrivals and Erlang Distributions service times. The arrival rate and service rate of this system change dynamically over time, driven by both reservation demand management and resource allocation decisions.

[0189] (2) Fluid approximation model:

[0190] 1) The original mathematical form of the fluid approximation model: The dynamic queuing system of the storage yard can be regarded as a stochastic process of Poisson arrival and k-order Irish distribution service time. Its instantaneous state is described by differential equations (Chapman-Kolmogorov equations), which are difficult to directly perform large-scale optimization analysis due to their non-stationarity and high dimensionality.

[0191] 2) Approximation Step 1 of the Fluid-based Approximation Model (Deterministic Transformation): To improve computational feasibility, this scheme uses a fluid-based model to approximate the M / E / 1 queuing dynamics. It is assumed that within a very short timeframe (e.g., one hour), the arrival and departure of trucks can be considered as a uniformly flowing "fluid," ignoring the discrete random fluctuations of individual vehicles.

[0192] 3) Approximate step two of the fluid approximation model (flow balance): Using the conservation law, establish the following relationship:

[0193] Current state = Initial state + Inflow - Actual outflow.

[0194] 4) Approximate Step Three of the Fluid Approximation Model (Service Capacity Calibration): Since the system does not always operate at full capacity, the actual outflow is not directly equal to the maximum service rate, but rather the product of the maximum service rate and the capacity utilization rate. Here, a nonlinear mapping is introduced, defining the capacity utilization rate as an equation about the queue length, thereby coupling the characteristics of random queuing into the deterministic equation.

[0195] 5) The final form of the fluid approximation model (fluid balance equations): The estimation of the number of trucks in the system therefore follows the following fluid balance equations:

[0196] ;

[0197] in, Indicates time period The initial number of trucks in the system, , and Represent Arrival rate for the time period (arrival rate here) and planned arrival volume These are different expressions of the same data, with the same meaning (maximum service rate). and capacity utilization (Actual service rate) ).

[0198] (3) Flow and coupling logic of multi-type trucks:

[0199] Since dual-task trucks (D) need to complete their operations in the export and import operation areas sequentially, the departing volume after completing their tasks in the export area will be directly converted into the inflow volume in the import area.

[0200] This embodiment establishes the following set of coupled equations to calculate the truck backlog in the single exit (O), dual task (D), and inlet (IN) areas in real time:

[0201] Export zone O-class truck status: ;

[0202] Export zone D-class truck status: ;

[0203] Import Zone (IN) Truck Status: ;

[0204] Dual task workflow association: ,in express The arrival rate of goods arriving at the import terminal after the export operations are completed within a specified time period.

[0205] The above set of equations ensures that the model can accurately capture the impact of dual-task set cards moving across areas within the yard on the overall system congestion.

[0206] (4) Nonlinear characterization and linearization of capacity utilization:

[0207] For the M / E / 1 system, its capacity utilization rate It is the Irish parameter Number of cards in the first episode of the time period Nonlinear functions: The function is concave. To optimize computational efficiency and adapt it to linear programming solvers, this application uses the following piecewise linear approximation function to estimate... The least squares method is used to find the optimal combination of linear parameters by minimizing the sum of squared errors at discrete sampling points. The calibration method is as follows:

[0208] 1) Data sampling:

[0209] exist 1000 discrete points are uniformly sampled within the range, and the corresponding original utilization rate is calculated based on the original nonlinear function. Build dataset .

[0210] 2) Set preset parameters:

[0211] Based on the curvature characteristics of the original curve, a critical point is pre-set. and To ensure numerical stability, the upper bound of the third segment is set... Set it to 0.994 (approaching 1 gradually).

[0212] 3) Solving the optimization problem:

[0213] Construct and solve the following objective function to determine the slope and intercept:

[0214] ; ;

[0215] ; ; ;

[0216] 4) Output of results:

[0217] After numerical optimization, the final calibration formula was obtained. Experiments show that the calibrated function has a goodness of fit (measured at 0.94) and extremely high approximation accuracy.

[0218] ;

[0219] Among them, parameters , , The linearization is obtained by calibration based on the original concave function. Through this linearization technique, this application significantly enhances the model's tractability in complex decision-making environments while maintaining model accuracy.

[0220] Optionally, in some embodiments of this application, a dynamic queuing sub-model for the yard is constructed based on the principles of stochastic process modeling and fluid approximation mechanisms. This includes: abstracting the truck operation process of the inbound and outbound yards into a preset queuing system with Poisson arrival and Irish distribution service times; performing fluid approximation processing on the preset queuing system to obtain a fluid approximation model; constructing multi-type truck flow and coupling logic, and determining the calculation rules for capacity utilization; and determining the dynamic queuing sub-model for the yard based on the fluid approximation model, the multi-type truck flow and coupling logic, and the calculation rules for capacity utilization.

[0221] Among them, import yard refers to the storage area for inbound containers; export yard refers to the storage area for outbound containers; Poisson arrival refers to the arrival of trucks following a Poisson random distribution; and Irish distribution service time refers to the operating time following an Irish distribution.

[0222] Among them, the preset queuing system refers to the standard service model used to describe the queuing of trucks. The preset queuing system is the M / E / 1 queuing system.

[0223] Among them, fluid approximation refers to the method of approximating discrete queuing as continuous flow; fluid approximation model refers to the dynamic model of queuing after continuousization.

[0224] Among them, the multi-type truck flow and coupling logic refers to the flow relationship of trucks with different tasks; the capacity utilization rate refers to the proportion of yard resources actually used.

[0225] Optionally, in some embodiments of this application, a fluid approximation is performed on a preset queuing system to obtain a fluid approximation model, including: performing dynamic approximation on the preset queuing model to obtain a first approximation result; establishing a flow balance formula using conservation laws, and performing flow balance approximation on the first approximation result based on the flow balance formula to obtain a second approximation result; and coupling the characteristics of random queuing into the deterministic equation of the second approximation result according to the data relationship of the actual outflow to obtain the final form of the fluid approximation model.

[0226] Among them, dynamic approximation processing refers to simplifying and approximating the dynamic changes of queuing, also known as the deterministic transformation process. That is, the process of approximating the M / E / 1 queuing dynamics using a fluid model. The first approximation result is the result after this approximation processing.

[0227] The flow balance formula refers to the equation that maintains a balance between arrivals and outflows. For example, the flow balance formula is: Current state = Initial state + Inflow - Actual outflow. The second approximation refers to the intermediate model after balancing.

[0228] The actual outflow data relationship is as follows: the actual outflow is not directly equal to the maximum service rate, but rather the product of the maximum service rate and the capacity utilization rate. The characteristics of random queuing refer to the random fluctuations in arrivals and services; the deterministic equations refer to deterministic equations that do not contain random terms. The final form of the fluid approximation model refers to a directly usable continuous queuing model; the fluid balance equations corresponding to the final form of the fluid approximation model are: .

[0229] In this embodiment, multi-level approximation processing improves the model's computational efficiency and reduces the difficulty of solving the problem.

[0230] Optionally, in some embodiments of this application, the construction of multi-type truck flow and coupling logic includes: constructing various types of truck dynamic equations and corresponding dual-task flow association equations; and determining the multi-type truck flow and coupling logic based on the coupling equation set composed of various types of truck dynamic equations and dual-task flow association equations.

[0231] Among them, the dynamic equations for each category of container truck refer to the equations describing the changes in the number of container trucks for different tasks; for example, the dynamic equations for each category of container truck include:

[0232] Dynamic equations for Class O container trucks in the export zone: ;

[0233] Dynamic equations for Class D container trucks in the export zone: ;

[0234] Dynamic equations for imported (IN) trucks: .

[0235] The dual-task workflow correlation equation refers to the equation describing the transformation relationship between two task sets. For example, the dual-task workflow correlation equation is: Coupled equations refer to a combination of multiple interrelated dynamic equations.

[0236] In this embodiment, by constructing coupled flow logic, the completeness of descriptions of multiple types of jobs is improved, and the model's realism and applicability are enhanced.

[0237] Optionally, in some embodiments of this application, the calculation rules for capacity utilization include: determining the nonlinear representation result of capacity utilization based on the nonlinear function rule of capacity utilization and the number of cards in the initial period; linearizing the nonlinear representation result according to the piecewise linear approximation function to obtain the linearized representation result; and determining the calculation rules for capacity utilization based on the linearized representation result.

[0238] Here, the nonlinear function rule refers to the nonlinear relationship between utilization rate and the number of trucks; the nonlinear characterization result refers to the utilization rate expressed as a nonlinear function. For example, the nonlinear characterization result is: capacity utilization rate. It is the Irish parameter Number of cards in the first episode of the time period The nonlinear function is as follows: .

[0239] Here, piecewise linear approximation function refers to approximating a nonlinear curve using multiple straight lines; linearization transformation refers to the operation of converting a nonlinear relationship into a linear relationship; and linearization representation result refers to the utilization rate expression form after linearization. For example, the linearization representation result is: .

[0240] In this embodiment, the solveability of the model is improved and the computational complexity is reduced by linearizing the utilization rate.

[0241] Optionally, in some embodiments of this application, the nonlinear characterization result is linearized to obtain a linearized characterization result, including: sampling discrete points based on data sampling technology, calculating the original utilization rate corresponding to each discrete point according to the original nonlinear function to construct a preset dataset; determining critical point information based on the curvature characteristics of the original curve; constructing a preset optimization problem based on the preset dataset and critical point information; solving the preset optimization problem to obtain the final calibration formula; and determining the linearized characterization result based on the final calibration formula.

[0242] Data sampling techniques refer to methods for extracting representative points from raw data; discrete points refer to independent data points obtained through sampling; for example, in 1000 discrete points are uniformly sampled within the range.

[0243] Here, the original nonlinear function refers to the unapproximated utilization function; the original utilization rate... This refers to the utilization rate calculated from the true function; the preset dataset refers to the set of sampled data used for fitting, and the preset dataset is... .

[0244] Among them, critical point information refers to the key points where the curve changes significantly, and the critical point information is a pre-set critical point. and Information.

[0245] The pre-defined optimization problem refers to the optimization model used to fit the piecewise straight line. Specifically, the pre-defined optimization problem is the optimization problem constructed to determine the slope and intercept.

[0246] ; ;

[0247] ; ; .

[0248] The final calibration formula refers to the linearized formula obtained after fitting.

[0249] In this embodiment, data-driven fitting calibration improves the approximation accuracy, ensures the reliability of utilization calculation, and enhances model accuracy.

[0250] Optionally, in some embodiments of this application, determining the linearization characterization result based on the final calibration formula includes: determining the goodness of fit of the calibrated function corresponding to the final calibration formula; and determining the linearization characterization result based on the final calibration formula if the goodness of fit of the calibrated function meets a preset accuracy condition.

[0251] Here, the goodness of fit of the calibrated function refers to the degree of closeness between the approximate function and the original function, while the preset accuracy condition refers to the criterion for judging whether the fitting effect meets the requirements. In the experiment, the measured goodness of fit of the calibrated function of this application can reach 0.94, which has extremely high approximation accuracy. The preset accuracy condition can be dynamically set, for example, the preset accuracy condition can be set to 0.9.

[0252] In this embodiment, the reliability of linearization is improved through precision verification, thus ensuring the accuracy of model calculation.

[0253] For example, the model inputs and outputs and the model uses of the yard throughput envelope sub-model are as follows.

[0254] Model inputs: historical external container truck service records, current yard resource templates.

[0255] Model output: Piecewise linear envelope and its geometric parameters (throughput envelope data).

[0256] Model purpose: To transform limited physical resources (such as yard cranes, container yards, etc.) into computable service capacity boundaries, and to set the decision space (also known as the feasible region) for the "yard resource allocation sub-model".

[0257] The construction process of the yard throughput envelope sub-model is as follows.

[0258] This application introduces a yard throughput envelope sub-model to characterize the impact of limited resource supply on truck service capacity. This model, through a data-driven macroscopic representation method, replaces the complex microscopic crane scheduling decisions, significantly improving the tractability of resource allocation decisions.

[0259] (1) Modeling motivation and principles:

[0260] This application, based on the concept of traffic throughput envelope in airport runway management technology, models the runway's capacity to serve takeoffs and landings as a set of piecewise linear envelopes. Observations of truck operation data at large container terminals reveal that the throughput of import and export trucks within the yard also exhibits piecewise linear envelope characteristics. Compared to existing micro-decision models that rely on strong assumptions such as constant crane productivity and arbitrary space availability, the envelope model proposed in this application implicitly captures operational details through a data-driven approach, providing terminal operators with a decision space to flexibly select import and export service rates based on available resources.

[0261] (2) The process of drawing the envelope:

[0262] The envelope is based on the historical external truck service records of a large container terminal (e.g., operation data from January 1 to December 31, 2023). A set of throughput envelopes reflecting different resource allocation levels is generated through piecewise linear fitting. The specific key steps are as follows.

[0263] 1) Historical operation data collection and cleaning:

[0264] Extract long-term (e.g., a whole year) foreign truck operation records from the Terminal Operating System (TOS). Each data point represents the number of imported trucks actually served by the yard within one hour. and number of export trucks During the statistical process, dual-task container trucks are counted in the corresponding import or export service volume according to their operational stage.

[0265] 2) Data grouping based on Yard Resource Template:

[0266] Since yard service capacity is directly limited by the yard resources deployed (such as the number of yard cranes), this application groups the cleaned data using a yard resource template. First, it utilizes the average service rate of a single yard crane (import...) ,exit Estimate the field bridge investment intensity corresponding to each data point. Those with the same or similar The data points of the value are grouped into one group. Each set of data represents a specific level of yard resource allocation.

[0267] 3) Concave piecewise linear fitting:

[0268] Configure the dataset for each set of resources ,in For the observed export service volume, For the corresponding imported service volume, a concave piecewise linear fitting method is used to draw the corresponding envelope. The goal of the fitting is to generate a function. This makes it possible for any given export throughput Its estimated import throughput Compared with actual observed values The error between them is minimized. The fitting problem is modeled as a least-squares optimization problem, with the objective function being to minimize the sum of squared residuals across all data points. The mathematical expression of the fitting problem is:

[0269]

[0270]

[0271]

[0272]

[0273]

[0274]

[0275] in It is the set of indices for all data points within this resource group, and the core decision variable in the fitting process is the slope of each linear segment. and intercept , This is the number of segments (4 segments are recommended for numerical experiments). The breakpoint parameters are used to determine the turning points of line segments.

[0276] 4) To ensure that the generated envelope conforms to the physical logic of container terminal operations, the fitting process must satisfy the following constraints (fitting constraints):

[0277] 1) It is mandatory that the slope of adjacent segments decreases monotonically, that is... .in The slope variation parameter is preset. This constraint ensures that the envelope exhibits a downward-curving concave shape, reflecting the diminishing marginal efficiency effect when resources are switched between different operations.

[0278] 2) Set all slopes This reflects the competitive relationship in import and export operations under limited resources: that is, with resources constant, increasing the rate of export services will inevitably lead to a decrease in the rate of import services.

[0279] 3) Requirements This ensures that service capacity remains positive under any workload.

[0280] After solving the above model through numerical optimization, this application utilizes the coefficient of determination. The goodness of fit was evaluated. Experimental results show that, under various resource templates, the envelope generated by this method... The values ​​are all between 0.85 and 0.94, demonstrating the extremely high accuracy of this method in capturing yard service capabilities.

[0281] (3) Mathematical structure of the envelope:

[0282] Figure 3 This is a schematic diagram of the yard envelope. Figure 3 This demonstrates typical throughput envelopes and their configurations generated using a concave piecewise linear fitting method. Different colored envelopes directly correspond to different yard resource templates at the terminal. In the coordinate system, the further to the upper right of the curve (away from the origin), the higher the configuration of yard resources deployed during that period. This is because a higher curve implies a higher import service rate at the same export service rate, reflecting an increase in the number of core loading and unloading equipment such as yard cranes. Terminal operators specify a specific yard resource template for each period based on a pre-set yard resource template.

[0283] 1) Segmentation definition: Let... This represents the total number of envelopes obtained. Envelope ( )Depend on It consists of linear segments.

[0284] 2) Geometric parameters: The first line segment ( ) has slope ,intercept and the corresponding export truck service rate range .

[0285] 3) Rate Coordination Relationship: Let... The service rate for export trucks (including single-export trucks and dual-task trucks that have not completed their export tasks). This refers to the service rate of imported container trucks (including single-import container trucks and dual-task container trucks that have completed their export missions). If in The time period selected is the first The first envelope line If there are multiple line segments, then the import and export service rates satisfy the following piecewise linear relationship: ;

[0286] in, and This reflects the competition and trade-off between limited yard resources (such as yard cranes and traffic space) in import and export operations.

[0287] (4) Resource templates and decision-making logic:

[0288] In practice, each time period Available resources are typically determined by a predefined YardResource Template. Therefore, the system assigns a specific throughput envelope for each time period. The terminal operator's decision-making task becomes: selecting an appropriate combination of import and export service rates within a given envelope to achieve optimal truck service efficiency under the existing resource allocation scheme. This approach not only simplifies computation but also allows resource allocation decisions to be directly integrated with the aforementioned queuing assessment model, providing quantitative support for alleviating yard congestion.

[0289] Optionally, in some embodiments of this application, a yard throughput envelope sub-model is constructed based on historical external truck service records and yard resource templates, including: generating throughput envelope data reflecting different resource configuration levels through piecewise linear fitting based on historical external truck service records and yard resource templates; and determining the yard throughput envelope sub-model based on the throughput envelope data and the decision logic of the yard throughput envelope sub-model.

[0290] The decision logic of the yard throughput envelope sub-model is as follows: select the combination of inbound and outbound service rates on the target envelope of the given throughput envelope data. The target envelope refers to the given envelope. For example, the decision logic of the yard throughput envelope sub-model is: select an appropriate combination of inbound and outbound service rates on the given envelope to achieve the optimal truck service efficiency under the existing resource allocation scheme.

[0291] Piecewise linear fitting refers to fitting the capacity boundary curve with multiple straight lines; throughput envelope data refers to data describing the maximum throughput capacity of the yard; different resource configuration levels refer to the resource status under different combinations of equipment and manpower.

[0292] Optionally, in some embodiments of this application, throughput envelope data reflecting different resource configuration levels is generated by piecewise linear fitting based on historical external truck service records and yard resource templates. This includes: cleaning the historical external truck service records to obtain cleaned data; grouping the cleaned data according to the yard resource templates to obtain grouped data; performing concave piecewise linear fitting on the grouped data to construct a fitting problem; solving the fitting problem based on the fitting objective function and fitting constraints to obtain the fitting solution result; and determining the throughput envelope data based on the fitting solution result.

[0293] Data cleaning refers to the preprocessing operation of removing abnormal and invalid data; the cleaned data refers to the filtered and valid historical data. Specifically, long-term foreign truck operation records are extracted from the terminal operating system, with each data point representing the number of imported and exported trucks actually served by the yard within one hour; during the statistical process, dual-task trucks are counted in the corresponding import or export service volume according to their operation stage.

[0294] Data grouping refers to classifying data according to resource configuration categories, specifically data grouping based on yard resource templates. Specifically, it involves estimating the yard crane deployment intensity for each data point using the average service rate of a single yard crane, and grouping data points with the same or similar values ​​together. Each data set represents a specific level of yard resource allocation, and the grouped data refers to datasets divided by resource category.

[0295] Here, concave piecewise linear fitting refers to fitting a convex capability boundary curve; the fitting problem refers to the optimization fitting model used to generate the envelope. Specifically, the process of constructing the fitting problem includes: for each set of resource configuration datasets... The corresponding envelope is drawn using a concave piecewise linear fitting method, and the goal of the fitting is to generate the fitting objective function.

[0296] Here, the fitting objective function refers to the target to be optimized during the fitting process; the fitting constraints refer to the restrictions that must be met during the fitting process; and the fitting solution refers to the piecewise linear parameters obtained from the fitting.

[0297] In this embodiment, by standardizing the data processing and fitting process, the quality of envelope generation is improved and the reliability of capability boundaries is enhanced.

[0298] Optionally, in some embodiments of this application, the method further includes: constructing a monotonically decreasing slope constraint, a slope constraint, and an intercept constraint for adjacent segments; and using the monotonically decreasing slope constraint, a slope constraint, and an intercept constraint for adjacent segments as fitting constraints.

[0299] Among them, the fitting constraints include the constraint that the slope of adjacent segments decreases monotonically. Slope constraints and intercept constraints .

[0300] For example, the inputs and outputs of the yard resource allocation sub-model and its purpose are as follows.

[0301] Model input: Selected throughput envelope (throughput envelope data output by the "Dockyard Throughput Envelope Sub-model").

[0302] Model output: Service rate data (including service rates of import yards and service rates of export yards).

[0303] Model Purpose: To dynamically adjust the intensity of import and export operations within the capacity boundary, and the output service rate is directly input into the "yard dynamic queuing sub-model" to achieve supply and demand matching.

[0304] The "yard throughput envelope sub-model" simply generates "multiple envelopes" based on "operational data" and then matches a "selected throughput envelope" corresponding to a specific yard resource based on the selected time period. This "selected throughput envelope" has multiple segments, and each point in each segment corresponds to a sub-scheme. The "yard resource allocation sub-model," based on the "selected throughput envelope," optimizes across these segments and outputs the optimal data for the point corresponding to the "import yard service rate" and "export yard service rate."

[0305] The construction process of the yard resource allocation sub-model is as follows.

[0306] Figure 4 This is a schematic diagram of the yard resource allocation sub-model. For example... Figure 4 As shown, the yard resource allocation sub-model aims to scientifically allocate limited yard service capacity to external trucks of different operation types.

[0307] (1) Resource templates and configuration decisions:

[0308] The total amount of available yard resources in each time period is determined by a preset resource template. This model transforms resource allocation decisions into: given the first time period... On each throughput envelope line, select the optimal service rate for imported container trucks. and export truck service speed .

[0309] (2) Service rate composition logic:

[0310] In the resource allocation process, the total export service rate It consists of two parts: the service rate of single-exit trucks (Category O) Service rates of dual-task trucks (Class D) that have not completed their export missions. Their mathematical relationship satisfies: ;

[0311] in and These are not preset values, but rather decision results automatically generated through model algorithms.

[0312] (3) Mathematical model construction:

[0313] Introducing binary variables (like Time period selection The first envelope line a line segment, then Otherwise The yard resource allocation model is as follows:

[0314] 1) Uniqueness constraint of line segments: This ensures that only one set of capability configurations on the envelope can be selected in each time period.

[0315] 2) Service rate-related constraints: The import service rate is modeled as a linear function of the export service rate under the selected line segment. , Represent Time period The first of the envelope lines The slope and intercept of each linear segment. This indicates the number of segments in the envelope. The constraint uses a summation structure and binary variables to allow it to express different slope intervals of the piecewise function, thus describing the segmented resource boundaries of the storage yard.

[0316] 3) Service rate range constraints: Ensure that the selected service rate point lies within the domain of the corresponding segment of the envelope. Inside. This indicates the left endpoint (lower bound) of the line segment on the export service rate axis, while This represents the right endpoint (upper bound) of the line segment. This constraint strictly limits the range of values ​​for the export service rate to the piecewise linear interval selected in its associated constraints. This ensures consistency. It guarantees that during the solution process of the mathematical model, the value of the service rate and its corresponding linear slope parameter are perfectly matched in physical space, thus ensuring the rigor of the envelope model as a physical boundary constraint.

[0317] 4) Nonnegativity constraint: .

[0318] Overall, the technical advantages of the yard resource allocation sub-model are:

[0319] Enhancing Decision Processability: Unlike traditional models that explicitly specify allocation schemes for each individual crane or other specific equipment, this model quantifies service capacity through a highly aggregated "throughput envelope." This data-driven abstraction approach avoids strong assumptions about micro-parameters such as crane productivity and yard space availability, significantly improving computational efficiency in complex decision-making environments.

[0320] Supports dynamic performance evaluation: The real-time service rate determined by this model can be directly input into the aforementioned "yard dynamic queuing sub-model", enabling the system to monitor and evaluate the impact of different resource allocation schemes on the queue length of external trucks and the level of yard congestion in real time, realizing a quantitative closed loop from resource supply to service performance.

[0321] Optionally, in some embodiments of this application, a yard resource allocation sub-model is constructed based on the resource allocation decision transformation principle and the service rate composition logic, including: determining that the resource allocation decision transformation principle is to select the optimal inbound truck service rate and outbound truck service rate on a given throughput envelope; determining the service rate composition logic based on the mathematical relationship between the service rate of a single outbound truck and the service rate of a dual-task truck that has not completed its outbound task; introducing binary variables to characterize the selection of envelope segments to determine the constraints of the yard resource allocation sub-model; and determining the yard resource allocation sub-model based on the constraints of the yard resource allocation sub-model, the resource allocation decision transformation principle, and the service rate composition logic.

[0322] The principle of resource allocation decision transformation refers to the fact that this model transforms resource allocation decisions into: given the first... On each throughput envelope line, select the optimal service rate for imported container trucks. and export truck service speed .

[0323] Among them, a single-export truck refers to a truck that only performs export tasks, and the service rate of a single-export truck refers to the service rate of a single-export truck (Category O). Dual-task trucks that have not completed their export missions refer to trucks that have both import and export functions but have not completed their export missions. The service rate of dual-task trucks that have not completed their export missions refers to the service rate of dual-task trucks (Category D) that have not completed their export missions. The mathematical relationship between them satisfies: .

[0324] Here, binary variables refer to logical selection variables that take the value of 0 or 1. .

[0325] Optionally, in some embodiments of this application, binary variables are introduced to characterize the selection of envelope line segments to determine the constraints of the yard resource allocation sub-model, including: determining line segment uniqueness constraints, service rate correlation constraints, and service rate range constraints based on binary variables; determining service rate non-negativity constraints, and using service rate non-negativity constraints, line segment uniqueness constraints, service rate correlation constraints, and service rate range constraints as constraints of the yard resource allocation sub-model.

[0326] The constraints of the yard resource allocation sub-model include:

[0327] Line segment uniqueness constraint: ;

[0328] Service rate related constraints: ;

[0329] Service rate range constraints: .

[0330] For example, the process of performing sub-model integration optimization to construct the integrated optimization model is as follows.

[0331] This application constructs four core sub-models consisting of an external truck arrival demand shift sub-model, a yard dynamic queuing sub-model, a yard throughput envelope sub-model, and a yard resource allocation sub-model. It achieves global optimal decision-making through integrated models and customized iterative algorithms. The overall data flow logic is as follows: (1) The "yard throughput envelope sub-model" first constructs the service capacity boundary based on historical data, setting the decision range for the "yard resource allocation sub-model"; (2) The "external truck arrival demand shift sub-model" transforms the original demand into the planned arrival volume, providing deterministic inflow data for the "yard dynamic queuing sub-model"; (3) The "yard resource allocation sub-model" determines the service rate within the capacity boundary, providing outflow parameters for the "yard dynamic queuing sub-model"; (4) The "yard dynamic queuing sub-model" integrates inflow and outflow data, outputs the system queue leader status in real time, and feeds this status back to the yard resource allocation link to dynamically adjust the capacity utilization rate, ultimately achieving integrated optimization of congestion costs and intervention costs.

[0332] The four sub-models proposed in this application do not operate in isolation, but are tightly integrated through mathematical constraints and decision-making logic, forming a closed-loop architecture of "demand-side management—supply-side management—performance feedback." First, the yard throughput envelope sub-model serves as the physical boundary constraint, pre-determining the maximum service rate that the yard can handle under different resource configurations. Then, the external truck arrival demand shift sub-model outputs the planned arrival volume for each time period based on the original preferences, constituting the main input flow of the system. The yard resource allocation sub-model determines the optimal service rate for each time period within the feasible region defined by the envelope, serving as the outflow control parameter. The yard dynamic queuing sub-model receives the inflow and outflow volumes, calculates the queue length within the yard in real time using the fluid balance equation, and converts it into congestion costs.

[0333] This application proposes an integrated optimization model aimed at effectively alleviating yard congestion while maintaining the service level of external trucks by coordinating the management of external truck arrival demand and the allocation of yard resources. This model integrates demand management, supply management, and performance evaluation into a unified decision-making framework.

[0334] (1) Performance Metrics:

[0335] This application mainly considers two levels of performance evaluation in the integrated model: the level of external truck demand intervention and the level of yard congestion.

[0336] 1) External Truck Demand Intervention Indicators (Intervention Quantity Performance Evaluation Indicators): Based on the definition of the "External Truck Arrival Demand Shift Sub-model," this application measures the intervention level through two dimensions: maximum intervention quantity. (Fairness indicators) and total intervention volume (Efficiency metrics). This scheme uses a lexicographic objective function for optimization: ;

[0337] First, minimize the maximum intervention amount. This aims to ensure a fair distribution of demand migration costs among different types of trucks. After achieving optimal fairness, the total intervention amount is then minimized. To optimize overall system efficiency, lexicographical order optimization, compared to the traditional weighted summation method, does not require pre-setting weight parameters and can directly ensure Pareto optimality, making the solution more interpretable and feasible. In actual operation, disproportionately allocating demand intervention to specific types of trucks will severely damage driver satisfaction and weaken the terminal's competitiveness. Therefore, fairness (i.e., controlling the maximum transfer volume) is set as a decision priority over overall efficiency.

[0338] 2) Yard congestion indicators:

[0339] The level of yard congestion is measured by the weighted average number of trucks queuing at the yard during the planning period: ;in, , , The weights are assigned to the queue lengths of import, single export, and dual-task container trucks, respectively. Considering that dual-task container trucks need to complete both export and import operations consecutively, resulting in a long task chain and high sensitivity to delays, the weights set in this application meet the following requirements. This is to give higher service priority to dual-task operations.

[0340] (2) Model Formulation:

[0341] The integrated optimization model M1 (M1 is used to identify the model name) proposed in this application aims to minimize the level of demand intervention, while being subject to the operator's preset upper limit on yard congestion costs. Constraints.

[0342] (3) Trade-off between logic and technical characteristics:

[0343] Model M1 reveals the constraint relationship between demand intervention and congestion mitigation. Optimal intervention level. and All according to congestion threshold The increase is monotonous and does not increase. That is, the port can reduce intervention in the demand for container trucks by appropriately tolerating higher levels of congestion, and vice versa.

[0344] The integrated optimization model of this application, through the rigorous mathematical framework described above, realizes collaborative decision-making throughout the entire process from demand forecasting to performance evaluation, providing an optimal path that balances fairness and efficiency for alleviating port congestion.

[0345] Optionally, in some embodiments of this application, the data flow and logical association rules are as follows: the external truck arrival demand translation sub-model is used to output the planned arrival volume and intervention volume performance evaluation indicators based on the original arrival demand; the yard dynamic queuing sub-model is used to output queue length data based on the planned arrival volume, service rate data, and capacity utilization rate; and output yard congestion indicators based on the queue length data; the yard throughput envelope sub-model is used to output throughput envelope data based on historical external truck service records and yard resource templates; and the yard resource allocation sub-model is used to output service rate data based on the throughput envelope data.

[0346] This embodiment demonstrates the input and output of the four sub-models. For details, please refer to the description in the above embodiment, which will not be repeated here.

[0347] Optionally, in some embodiments of this application, sub-model integration optimization processing is performed to construct an integrated optimization model, including: determining the lexicographical objective function of the integrated optimization model based on the intervention quantity performance evaluation index; determining the yard congestion cost upper limit constraint of the integrated optimization model based on the yard congestion index; and determining the integrated optimization model based on the lexicographical objective function and the yard congestion cost upper limit constraint.

[0348] Among them, the performance evaluation indicators for intervention volume include the maximum intervention volume. (Fairness indicators) and total intervention volume (Efficiency metrics) The lexicographical objective function refers to a multi-objective function that is optimized sequentially according to priority. Specifically, the lexicographical objective function is used for optimization: .

[0349] The yard congestion index is measured by the weighted total number of trucks queuing at the yard during the planning period. The expression for the yard congestion index is as follows: The yard congestion cost ceiling constraint refers to the restriction that congestion costs do not exceed a certain limit. Specifically, the yard congestion cost ceiling constraint is the upper limit of yard congestion costs preset by the operator. Constraints.

[0350] In this embodiment, multi-objective integrated optimization improves scheduling fairness and efficiency, and alleviates yard congestion.

[0351] For example, the iterative solution logic of the preset integrated optimization iterative solution algorithm is as follows.

[0352] Because the ensemble model M1 involves Equal-sized decision variables and nonlinear bilinear terms in queuing dynamics Directly solving this problem is extremely difficult. This application proposes an iterative solution algorithm based on logical decomposition. This algorithm achieves a balance between computational efficiency and solution quality by simplifying the original problem into a "main problem" containing only finite service rate options and combining it with a "subproblem" of finding the optimal resource allocation.

[0353] (1) Model Reformulation:

[0354] To eliminate nonlinear terms, this application transforms the original model into a mixed integer programming (MIP) form (model M2).

[0355] 1) Service rate option set: [Settings to be filled in] This is the set of all feasible service rate options determined based on the yard throughput envelope. Each option Includes the service rate sequence throughout the entire planning period. .

[0356] 2) Linearized representation: Introducing binary variables Indicate whether to use the option By binding the queuing evolution equation to specific service rate options, model M2 (mixed-integer programming form) eliminates product terms between variables. Although The theoretical scale is enormous, but only one option needs to be used in the optimal solution, which provides a basis for iterative search.

[0357] (2) Iterative solution architecture:

[0358] This algorithm approximates the optimal solution by alternately running the main problem and subproblems:

[0359] 1) Master Problem (MP): The master problem is within a limited set of options. The internally controlled congestion control model is responsible for finding the appropriate congestion control parameters from the current resource candidates by adjusting the arrival demand of external trucks (demand shifting). Optimal translation strategy .

[0360] 2) Subproblem (SP): The subproblem receives the destination mode generated by the main problem. Search the entire throughput envelope for new resource allocation options that minimize congestion costs. If a better option is found, add it. To update the main question.

[0361] 3) Control parameter iteration: Introducing step size By continuously tightening congestion control thresholds The algorithm is guided to search for better intervention solutions.

[0362] (3) The complete logical flow of the iterative solution algorithm in this application is introduced using iterative algorithm pseudocode. The iterative algorithm pseudocode is as follows:

[0363] enter:

[0364] Original requirements Congestion threshold Step length .

[0365] initialization:

[0366] Step 1 Setup Control parameters Iteration counting ;

[0367] Step 2: Based on the original requirements Solve the SP as input to obtain the initial resource options. ,make ;

[0368] Loop iteration:

[0369] Step 3: Solve the main problem MP to obtain the arrival solution. and current congestion costs ;

[0370] Step 4 While Do:

[0371] Step 5: Update the iteration count and tighten control parameters ;

[0372] Step 6: Calculate the feasibility threshold for the current set. ;

[0373] Step 7 If Then terminate and report that no feasible solution exists;

[0374] Step 8 Else: Solve MP again and update. and ;

[0375] Step 9 with the latest Solve SP for input to obtain new resource options. Update the candidate option set. ;

[0376] Step 10 End While;

[0377] Output:

[0378] untie and performance indicators and .

[0379] (4) Computation acceleration strategies:

[0380] The main problem addresses the lexicographical order optimization metric. The algorithm decomposes MP into two sequential subproblems: first, minimizing the fairness metric... Then, minimize the total intervention under the optimal fairness constraint. By analyzing the option set Parallel verification significantly reduced the search time.

[0381] The subproblem employs a rolling heuristic acceleration strategy: a time-period optimization approach. This strategy prioritizes the service rate of high-priority dual-task trucks (D), and then determines the optimal balance point between import and export rates through linear programming. Experiments show that this heuristic algorithm can quickly generate high-quality resource allocation options, ensuring that the system can complete industrial-grade solutions within 40 minutes when handling real-world examples involving thousands of trucks.

[0382] Optionally, in some embodiments of this application, the integrated optimization model is solved based on a preset integrated optimization iterative solution algorithm to obtain the solution output data corresponding to the integrated optimization model, including: determining the original demand, congestion threshold and step size as algorithm input data; performing algorithm initialization based on the algorithm input data to obtain initialization results; and performing iterative steps based on the initialization results to determine the solution output data.

[0383] The algorithm input data includes the original requirements. Congestion threshold Step length .

[0384] The steps of initializing the algorithm based on the input data and obtaining the initialization result correspond to steps 1 and 2 in the iterative algorithm pseudocode. The execution of the loop iteration steps refers to steps 3 through 10 in the iterative algorithm pseudocode.

[0385] The solution output data obtained after solving includes: and performance indicators and .

[0386] Optionally, in some embodiments of this application, algorithm initialization is performed based on algorithm input data, including: initial setting of the feasible service rate option set, control parameters, and iteration count; solving the main problem with the original requirements as input to obtain initial resource options; and updating the feasible service rate option set based on the resource options.

[0387] The algorithm initialization process includes: setting a set of feasible service rate options. Control parameters Iteration counting Based on original needs To obtain initial resource options, solve the main problem SP as input. The resource options update set of feasible service rate options makes .

[0388] Optionally, in some embodiments of this application, a loop iteration step is performed, including: solving the main problem to obtain the arrival scheme and the current congestion cost; and performing a preset sub-loop iteration step when the congestion cost is greater than the congestion threshold.

[0389] The preset sub-loop iteration steps include: updating the iteration count and tightening the control parameters; calculating the feasibility threshold under the current set; terminating and reporting no feasible solution if the control parameters are less than the feasibility threshold; solving the main problem again and updating the arrival scheme and congestion cost if the control parameters are greater than or equal to the feasibility threshold; solving the sub-problem with the latest arrival scheme as input and updating the resource options to update the set of feasible service rate options.

[0390] For example, the specific steps of performing the iterative loop are: solving the main problem MP to obtain the arrival solution. and current congestion costs When the cost of congestion exceeds the congestion threshold ( In the case of ), the preset sub-loop iteration steps are executed.

[0391] The preset sub-loop iteration steps refer to steps 5 to 9 in the pseudocode of the iteration algorithm.

[0392] For example, the specific steps of executing the preset sub-loop iteration are as follows:

[0393] Update iteration count and tighten control parameters ; Calculate the feasibility threshold for the current set When the control parameters are less than the feasibility threshold ( If the control parameter is greater than or equal to the feasibility threshold, terminate and report that no feasible solution exists; if the control parameter is greater than or equal to the feasibility threshold, terminate and report that no feasible solution exists. In the case of MP, solve the main problem MP again and update the solution to the port. and congestion costs With the latest arrival plan Update resource options to solve subproblem SP from the input. To update the set of feasible service rate options .

[0394] In this embodiment, a two-layer iteration mechanism is used to improve the solution quality and enhance the optimality and feasibility of the solution.

[0395] Optionally, in some embodiments of this application, the main problem is: to shift demand by adjusting the arrival demand of external trucks and find the optimal shifting strategy that can meet the control parameters; the sub-problem is: to receive the arrival scheme generated by the main problem and search for new resource options that can minimize congestion costs on the complete throughput envelope.

[0396] For example, the main problem is: in a limited set of options The internally controlled congestion control model is responsible for finding the appropriate congestion control parameters from the current resource candidates by adjusting the arrival demand of external trucks (demand shifting). Optimal translation strategy .

[0397] The subproblem is: receiving the arrival mode generated by the main problem. Search the entire throughput envelope for new resource allocation options that minimize congestion costs. If a better option is found, add it. To update the main question.

[0398] In this embodiment, the solution efficiency is improved and the practicality of the solution is enhanced by the division of labor and cooperation between the main problem and sub-problems.

[0399] The technical research process and other technical details of this application are described below with reference to a specific embodiment.

[0400] In traditional technologies, container terminals, as core hubs of global freight networks, undertake the main cargo transshipment tasks. The efficiency of terminal operations largely depends on the prediction and control of service demand. However, global supply chains are highly vulnerable, easily disrupted by trade frictions, energy price fluctuations, and unforeseen public events. These disruptions lead to a high degree of uncertainty in cargo transportation demand, making it difficult to control and execute predetermined terminal operation plans, severely restricting production efficiency.

[0401] Within the terminal, the yard is a crucial transfer area for containers moving between container ships and external trucks. While ship operational needs can be known in advance through shipping schedules, the number of external trucks arriving at the port at different times is highly random, especially during supply chain disruptions. When the terminal's allocated yard resources (such as yard crane equipment and manpower) cannot match the surge in arrival demand during peak hours, external trucks accumulate in the yard, causing severe traffic congestion. This congestion not only delays the execution of individual tasks but also creates a chain reaction, reducing the overall throughput capacity of the terminal. Addressing this common pain point in the industry, effectively alleviating yard congestion has become an urgent need to enhance port competitiveness.

[0402] Currently, the main methods used by academia and industry to alleviate yard congestion are demand-side management and supply-side management.

[0403] On the demand side, the distribution of external truck arrivals is primarily controlled through the implementation of a gate appointment system. This method allows terminal operators to limit the number of arrivals within a specific time period and reallocate appointment quotas as necessary. However, existing models typically assume a fixed yard service rate, neglecting the dynamic impact of supply-side resource allocation on service capacity. This leads to arrival schemes failing in actual operations due to yards being unable to provide the scheduled service rates.

[0404] On the supply side, research often focuses on yard space allocation and yard crane scheduling. While such research can improve equipment utilization, its highly complex micro-decision-making logic (such as considering yard crane movement paths and conflicts between adjacent container positions) often results in excessively high model dimensionality. This makes it difficult for models to assess the complex coupling relationship between the distribution of external container trucks arriving at ports and resource allocation while ensuring computational efficiency.

[0405] In summary, the existing technology has the following significant drawbacks:

[0406] (1) Isolation of decision-making dimension: Existing technologies usually handle external truck reservation requirements or yard service resource allocation separately, lacking a coordination mechanism. Since the combined impact of external truck arrival management and yard service resource allocation is difficult to quantify, terminals find it difficult to maintain optimal operating conditions in uncertain demand environments.

[0407] (2) Insufficient model tractability: Due to overly fine constraints, the micro-scheduling model has extremely high computational costs and cannot quickly respond to the dynamically changing arrival rates of external container trucks at the tactical level. Furthermore, it is difficult to integrate into the macro-level yard congestion evaluation system.

[0408] (3) Lack of trade-off analysis between external truck demand intervention and yard congestion queuing: In actual operation, there is an inherent trade-off between yard congestion (measured by external truck queuing costs) and external truck arrival intervention (measured by the magnitude of the original external truck arrival distribution shift). On the one hand, in order to achieve better yard congestion management, the terminal must implement strong demand management and force a significant shift in truck reservation times, but this will seriously damage the service satisfaction of truck drivers and logistics efficiency. On the other hand, if the arrival preferences of external trucks are fully accommodated (minimizing intervention), the arrival demand during peak hours will far exceed the yard service capacity, causing severe queuing. Currently, there is a lack of an integrated optimization framework that can quantitatively reveal and weigh the costs of external truck demand intervention and yard congestion levels. Due to the inability to quantify the mutual constraints between these two factors, terminal operators find it difficult to make optimal "intervention-efficiency" balance decisions based on current resource conditions.

[0409] (4) Neglect of the flow logic of dual transaction operations for external container trucks: Existing solutions often simply split dual-transaction external container trucks (i.e., simultaneously picking up and delivering containers) into two independent tasks, ignoring the spatiotemporal correlation between them immediately flowing into the import operation area after completing their tasks in the export operation area. This logical omission makes it impossible to accurately capture the continuous impact of dual-transaction container trucks on the overall congestion status of the system when allocating resources.

[0410] To address the problems of isolated decision-making, computational limitations, and lack of trade-offs in current methods for managing container yard congestion, this application provides an integrated optimization method for truck arrival management and yard resource allocation at a container terminal. This method can also be referred to as an integrated optimization method for alleviating container terminal yard congestion, and for ease of description in the embodiments, it can be simply called the optimization method of this application. The details are as follows.

[0411] The optimization method proposed in this application is achieved through the collaborative management of external truck arrival demand on the demand side and yard resource allocation on the supply side. This integrated model consists of three core parts: an arrival demand management model that manages the distribution of truck arrivals; a non-stationary queuing model that captures the dynamic process of truck arrivals and services; and a yard capacity utilization model (including a yard throughput envelope sub-model and a yard resource allocation sub-model) established using a data-driven approach to control yard resource allocation and corresponding import / export truck service rates. This application develops a customized iterative solution algorithm that effectively balances truck throughput and yard congestion levels by decomposing demand and supply decisions. Experimental results show that this method can significantly reduce yard congestion and improve terminal operation efficiency with relatively low demand intervention costs.

[0412] The optimization method presented in this application, by synergistically considering the dynamic coupling characteristics of demand shifting and yard capacity utilization for external trucks arriving at ports, provides a complete integrated optimization decision-making scheme for the differentiated import and export demands and dual-transaction flow logic during external truck operations. Addressing the shortcomings of the aforementioned prior art, the technical advancements, innovations, and multi-dimensional effects achieved by this application are as follows:

[0413] (1) An innovative collaborative optimization framework for demand and supply is constructed: This application proposes and implements for the first time an integrated optimization model that coordinates the management of external truck arrivals and the allocation of yard resources. Unlike existing sequential decision-making methods that only adjust reservation quotas or simply schedule equipment, this method fundamentally solves the problem of spatiotemporal mismatch between demand and supply by integrating two decision-making processes. Through the joint optimization of "intervention cost" and "congestion level", the global optimality of the decision is significantly improved.

[0414] (2) A data-driven yard throughput envelope model was developed, improving the model's tractability: This application breaks the limitation of traditional research that must rely on extremely fine micro-operations (such as crane paths, container location conflicts, etc.) to evaluate service capacity. By constructing a piecewise linear throughput envelope using historical terminal operation data, this method accurately captures the substitution relationship between resource allocation and import / export service rates at the macro level. This approach significantly reduces model complexity, making large-scale real-time optimization at the tactical planning level possible, and greatly improving the adaptability and scalability of the technical solution.

[0415] (3) A dynamic congestion assessment technology for yards based on non-stationary queuing theory is proposed: This application models the external truck operation process as a non-stationary M / E / 1 queuing system and uses the fluid approximation method to plot the truck queuing dynamics in real time. Compared with the static model that assumes a constant service rate, this application can accurately predict the evolution of queue length during peak hours, and specifically considers the flow logic of dual-task trucks from the exit area to the import area, making the congestion assessment more consistent with the actual operating conditions and improving the accuracy of congestion mitigation.

[0416] (4) An efficient iterative solution algorithm and decomposition strategy were designed: For the nonlinear terms in the ensemble model, this application developed a main problem-sub-problem iterative solution architecture. Through logical decomposition, the main problem optimizes the port arrival mode, and the sub-problems optimize resource allocation. Combined with a rolling time-domain heuristic strategy, this method significantly improves computational efficiency compared to traditional methods when dealing with large-scale instances containing thousands of external trucks, ensuring the real-time performance of the decision-making scheme.

[0417] Figure 5 This is a schematic diagram of the integrated framework, such as... Figure 5 As shown in the figure. This application achieves coordinated optimization of demand-side intervention and supply-side resource allocation by establishing an arrival demand shift model, a non-stationary queuing dynamic model, and a data-driven yard throughput envelope model. While ensuring the service level of trucks, it effectively alleviates yard traffic congestion and improves resource utilization efficiency.

[0418] The core of this application is the construction of a collaborative optimization framework, which integrates external truck arrival demand management, dynamic allocation of yard resources, and congestion performance assessment to achieve the goal of alleviating yard traffic pressure under complex operating conditions.

[0419] Figure 6 A schematic diagram illustrating the effect of the integrated optimization model, such as Figure 6 As shown, on the demand side, the original imbalance in arrival demand (such as...) Figure 6 Part a) is adjusted to a smoother planned arrival volume (e.g., by translation). Figure 6 Part c). On the supply side, the adjusted demand is precisely matched with the dynamic service capacity of the yard (e.g., Figure 6 Part d) addresses the congestion problem caused by a severe mismatch between original demand and service capacity (such as...). Figure 6 (Part b). Ultimately, this will achieve a dynamic balance between supply and demand, eliminating yard congestion.

[0420] The numerical experiments and analysis process of this application are described below.

[0421] This application verifies the effectiveness of the proposed integrated optimization model and iterative algorithm through a series of numerical experiments, mainly including: (1) evaluating the computational efficiency of the iterative algorithm; (2) verifying the effect of demand management and resource coordination in alleviating congestion; (3) exploring the impact of the ratio of dual-task external trucks (D) on system performance; and (4) summarizing the management implications of terminal operation.

[0422] (1) Computational performance and algorithm convergence: The experimental environment used a computer configured with an Intel i7-12700H 2.30 GHz CPU and 16 GB RAM, and Gurobi 11.0 was used as the mixed integer programming solver.

[0423] 1) Improved computational efficiency: The experiment targeted 12 computational examples of different scales (planning period) to Tests were conducted on small to medium-sized computational instances (hours). Results showed that for such instances... The iterative algorithm proposed in this application can obtain the optimal or near-optimal solution in a very short time. For large-scale computational examples (…), When the commercial solver Gurobi cannot find a feasible solution within a 2-hour time limit, this algorithm can obtain a high-quality solution in less than 38 minutes, demonstrating excellent industrial-grade solving capabilities.

[0424] 2) Convergence performance: As the number of iterations increases, the total congestion cost ( It shows a clear downward trend and rapidly approaches the preset threshold. Convergence. Meanwhile, the amount of demand intervention ( , The increase in demand validates the technical logic of achieving a significant reduction in congestion through appropriate demand intervention under limited resources.

[0425] (2) Implications of the results of demand management and resource coordination:

[0426] Figure 7 This is a diagram showing the distribution of truck arrival demand over different number of days. For example... Figure 7 As shown, through experiments on 6 sets of actual operational data with different arrival distributions, this application has obtained the following core technological achievements.

[0427] 1) Significant congestion reduction effect: When the congestion target is set as Compared to the baseline scenario with no demand intervention, this method achieves an average congestion cost reduction of 25.14% and a peak queue length reduction of 18.58%. Achieving this requires only shifting approximately 4.57% of the original arrival demand. This demonstrates that through precise arrival management and resource coordination, significant operational efficiency improvements can be achieved with minor service adjustments.

[0428] 2) Correlation between arrival distribution and intervention intensity: Experiments revealed that the efficiency of congestion mitigation is highly dependent on the distribution characteristics of the initial arrival demand. For scenarios where arrival peaks occur in the early stages of the planning period (such as Day 3 and Day 6), stronger intervention measures (higher thresholds) are required due to the cumulative effect of queuing. , Only by addressing these factors can the goal of alleviating congestion be achieved; while scenarios where peak hours occur later are more easily mitigated through resource allocation.

[0429] (3) Deep impact of dual-transaction external card operations: Sensitivity analysis of the proportion of dual transactions reveals its dual impact on system performance.

[0430] 1) Optimal balance point of resource utilization: Experimental results show that as the proportion of dual tasks increases, the total congestion cost decreases. The trend is upward because dual-task card groups have a higher weight. However, from the perspective of queuing metrics, when the dual-task ratio is 0.75, both the total queue length and the peak queue length reach their lowest values.

[0431] 2) Bottleneck Migration Phenomenon: When the dual-task ratio reaches an extremely high level (e.g., 1.0), due to the highly coupled nature of dual-task operations, the resource pressure in the exit operation area increases dramatically, and the queue length rebounds significantly. This indicates that a moderate dual-task ratio is beneficial to improving the overall resource efficiency of the terminal, but an excessively high ratio will cause the exit operation area to become a system bottleneck.

[0432] (4) Management implications: Based on the above experimental results, this application provides the following decision support suggestions for container terminal operators.

[0433] 1) Quantitative Trade-offs Support Decision Making: Operators should not blindly pursue zero congestion or zero intervention. The "intervention-congestion" trade-off curve provided by this model can help management scientifically set congestion control thresholds based on real-time resource conditions, achieving a balance between driver satisfaction and operating costs.

[0434] 2) Differentiated Priority Strategy: By setting a higher delay penalty coefficient for dual-task trucks in the model, operators can effectively optimize the operational process of dual-task trucks. Experiments have shown that assigning higher service priority to dual-task trucks can guide resources to be tilted towards complex tasks, thereby reducing the average turnaround time of vehicles in the terminal overall.

[0435] 3) Precise control of peak arrival times: Terminals should focus on intervening in arrivals during the early morning or morning peak hours. Experimental data supports the logic of "early intervention, early benefit," and by shifting some demand in advance, the exponential propagation of queues within the linear programming period can be effectively prevented.

[0436] 4) Robustness of the resource envelope: Experiments demonstrate that the proposed 4-segment envelope model achieves an optimal balance between fitting accuracy and computational robustness. This provides operators with a simple and easy-to-use data-driven tool, enabling them to grasp the overall service capabilities without delving into micro-scheduling.

[0437] The advantages of the optimization method in this application are as follows.

[0438] (1) An innovative integrated optimization architecture for demand-side management and supply-side resource allocation is proposed: This application breaks through the limitation of the isolation between the "reservation system (demand management)" and "yard scheduling (supply management)" in the prior art. By integrating the transfer of external truck arrival demand, non-stationary queuing dynamics, and resource allocation decisions, this method can quantitatively reveal and weigh the constraints between "Truck Demand Intervention" and "Yard Congestion". Compared with the traditional decision-making method that presets a fixed service rate, this integrated architecture significantly reduces the peak queue length and total congestion cost of the yard by coordinating the optimization of demand and supply, while ensuring the service level of trucks.

[0439] (2) A data-driven approach to model the throughput envelope of a yard is proposed: This application breaks through the limitation of traditional research that relies on micro-level crane scheduling details (such as yard crane paths and container location conflicts) to assess service capacity. This method innovatively constructs a piecewise linear throughput envelope model using historical operational data, abstracting complex resource allocation into a continuous selection problem of import / export service rates. This model can accurately characterize the substitution relationship of limited resources between import / export operations, improving the scalability and computational tractability of the model while preserving operational characteristics, making large-scale real-time optimization at the tactical planning level possible.

[0440] (3) A non-stationary queuing dynamic evaluation model coupled with dual-transaction flow logic is established: This application proposes a fluid approximation model based on descriptive non-stationary M / E / 1 queuing theory to address the randomness of external truck operations. This model not only captures the dynamic evolution of queue length over time, but also, for the first time, mathematically clarifies the spatiotemporal coupling logic of "dual-transaction trucks" between the export and import operation areas. By introducing piecewise linearization techniques to handle the nonlinear constraints of capacity utilization, this application can accurately evaluate the impact of different arrival modes on yard backlog. Furthermore, by setting differentiated congestion penalty weights for dual-transaction trucks, precise control of high-priority business flows is achieved, with service efficiency superior to static or micro-scheduling methods in existing literature.

[0441] (4) An iterative solution algorithm for the master problem and subproblems based on logical decomposition was developed: To address the bilinear nonlinear terms and large-scale variable characteristics in the ensemble model, this application designed a customized iterative solution architecture. The algorithm decomposes the original problem into a master problem (optimizing the port arrival mode) and a subproblem (searching for the optimal resource allocation). By controlling the congestion cost threshold and employing a rolling heuristic strategy, the algorithm can quickly converge to the global solution in large-scale real-world cases (such as those involving thousands of trucks and a 12-hour planning period), solving the technical bottleneck of insufficient computational efficiency of existing commercial solvers in large-scale ensemble optimization problems.

[0442] It should be noted that any technical feature in any of the above embodiments provided in this application is also applicable to any of the following embodiments provided in this application, and similar details will not be repeated hereafter.

[0443] Figure 8 Here is a structural block diagram of the device in one embodiment, with reference to Figure 8 The integrated optimization device for container terminal external truck reservation management and yard resource allocation includes:

[0444] The external truck arrival demand translation sub-model construction module 801 is used to construct the external truck arrival demand translation sub-model based on the mixed integer programming modeling principle;

[0445] The dynamic queuing sub-model construction module 802 is used to construct the dynamic queuing sub-model of the stockyard based on the principles of stochastic process modeling and fluid approximation mechanism.

[0446] The yard throughput envelope sub-model construction module 803 is used to construct the yard throughput envelope sub-model based on historical external truck service records and yard resource templates.

[0447] The yard resource allocation sub-model construction module 804 is used to construct the yard resource allocation sub-model based on the resource allocation decision transformation principle and service rate composition logic.

[0448] The integration optimization module 805 is used to perform sub-model integration optimization processing based on the data flow direction and logical association rules of the external truck arrival demand translation sub-model, the yard dynamic queuing sub-model, the yard throughput envelope sub-model, and the yard resource allocation sub-model, and to construct the integrated optimization model.

[0449] The solver module 806 is used to solve the ensemble optimization model based on a preset ensemble optimization iterative solver algorithm, and obtain the solution output data corresponding to the ensemble optimization model.

[0450] In this embodiment of the application, based on, as follows Figure 8 The connections between the various modules or units shown in the diagram improve the efficiency of container terminal external truck reservation management and yard resource allocation through the cooperation between these modules or units.

[0451] In another embodiment, a computer device is provided, which may be a server, and its internal structure diagram may be as follows: Figure 9 As shown, it includes a processor, memory, input / output interfaces, and a communication interface. The processor, memory, and input / output interfaces are connected via a system bus, and the communication interface is connected to the system bus via the input / output interfaces. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The database stores relevant data. The input / output interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. The computer program can be executed by the processor to implement the various methods described in the above embodiments.

[0452] In yet another embodiment, a computer device is provided, such as a terminal, whose internal structure diagram may be as follows: Figure 10 As shown, it includes a processor, memory, input / output interface, communication interface, display unit, and input device. The processor, memory, and input / output interface are connected via a system bus, and the communication interface, display unit, and input device are also connected to the system bus via the input / output interface. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The input / output interface is used for exchanging information between the processor and external devices. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, mobile cellular networks, NFC (Near Field Communication), or other technologies. The computer program can be executed by the processor to implement the various methods described in the above embodiments.

[0453] Those skilled in the art will understand that Figure 9 and Figure 10 The structure shown is only a block diagram of a part of the structure related to the present application and does not constitute a limitation on the computer device on which the present application is applied. It may also include more or fewer components than shown in the figure, or combine certain components, or have different component arrangements, in order to realize the function of the computer device.

[0454] In the above embodiments, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0455] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the systems, devices, equipment, modules or units described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0456] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, devices, or methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or modules may be electrical, mechanical, or other forms.

[0457] The modules described as separate components may or may not be physically separate. The components shown as modules may or may not be physical modules; that is, they may be located in one place or distributed across multiple network modules. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0458] Furthermore, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can be stored in a computer-readable storage medium.

[0459] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product.

[0460] The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can store or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium, or a semiconductor medium (e.g., a solid-state drive), etc.

[0461] The technical solutions provided by the embodiments of this application have been described in detail above. Specific examples have been used in the embodiments of this application to illustrate the principles and implementation methods of the embodiments of this application. The description of the above embodiments is only for the purpose of helping to understand the methods and core ideas of the embodiments of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the embodiments of this application. Therefore, the content of this specification should not be construed as a limitation on the embodiments of this application.

Claims

1. An integrated optimization method for container terminal off-site truck reservation management and yard resource allocation, characterized in that, The method includes: Based on the principle of mixed integer programming modeling, a sub-model for the translation of external truck arrival demand is constructed; Based on the principles of stochastic process modeling and fluid approximation mechanism, a dynamic queuing sub-model for the stockyard is constructed. Based on historical external truck service records and yard resource templates, a sub-model of yard throughput envelope is constructed; Based on the principle of resource allocation decision transformation and the logic of service rate composition, a sub-model of yard resource allocation is constructed. Based on the data flow and logical association rules of the external truck arrival demand translation sub-model, the yard dynamic queuing sub-model, the yard throughput envelope sub-model, and the yard resource allocation sub-model, the sub-models are integrated and optimized to construct an integrated optimization model. Based on a preset integrated optimization iterative solution algorithm, the integrated optimization model is solved to obtain the solution output data corresponding to the integrated optimization model.

2. The method according to claim 1, characterized in that, The aforementioned model, based on the principle of mixed-integer programming, constructs a sub-model for the translation of external truck arrival demand, including: The construction principle of the external card arrival demand management model based on mixed integer programming determines the set and parameter definition results; Based on the mathematical relationships of demand shift, determine the decision logic for demand shift; Based on the defined set and parameters and the decision logic of the demand shift, determine the performance evaluation index of the intervention amount and the constraints of the external truck arrival demand shift sub-model. Based on the performance evaluation index of the intervention amount and the constraints of the external truck arrival demand translation sub-model, the external truck arrival demand translation sub-model is determined.

3. The method according to claim 2, characterized in that, The mathematical relationship of the demand shift is: the sum of the positive and negative shifts represents the deviation between the original arrival demand and the planned arrival.

4. The method according to claim 2, characterized in that, The step of determining the intervention performance evaluation index and the constraints of the external truck arrival demand shift sub-model based on the set and parameter definition results and the demand shift decision logic includes: Determine the maximum intervention level to measure the highest level of intervention undertaken across all truck types; Determine the total intervention amount used to measure the overall scale of intervention received by all trucks during the planning period; Based on the maximum intervention amount and the total intervention amount, determine the intervention amount performance evaluation index.

5. The method according to claim 4, characterized in that, The step of determining the intervention performance evaluation index based on the maximum intervention amount and the total intervention amount includes: The maximum intervention amount and the total intervention amount are used as initial performance evaluation indicators; The initial performance evaluation index is linearized, and the absolute value term is replaced by linear constraints to obtain the intervention quantity performance evaluation index.

6. The method according to claim 2, characterized in that, The step of determining the intervention performance evaluation index and the constraints of the external truck arrival demand shift sub-model based on the set and parameter definition results and the demand shift decision logic includes: The demand conservation constraint and the variable nonnegativity constraint are constructed. The demand conservation constraint and the variable nonnegativity constraint are used as constraints for the external truck arrival demand translation sub-model.

7. The method according to claim 1, characterized in that, The dynamic queuing sub-model for the stockyard, constructed based on the principles of stochastic process modeling and fluid approximation mechanisms, includes: The trucking operations at import and export yards are abstracted into a pre-defined queuing system with Poisson arrival and Irish distribution service times. The preset queuing system is subjected to fluid approximation processing to obtain a fluid approximation model; The logic for the flow and coupling of multiple types of trucks is constructed, and the calculation rules for capacity utilization are determined. Based on the fluid approximation model, the multi-type truck flow and coupling logic, and the capacity utilization calculation rules, the dynamic queuing sub-model of the storage yard is determined.

8. The method according to claim 7, characterized in that, The process of performing fluid approximation processing on the preset queuing system to obtain a fluid approximation model includes: The preset queuing model is dynamically approximated to obtain the first approximation result; A flow balance formula is established using the conservation law. Based on the flow balance formula, the first approximate result is approximated by flow balance to obtain a second approximate result. Based on the data relationship of the actual outflow, the characteristics of random queuing are coupled into the deterministic equation of the second approximation result to obtain the final form of the fluid approximation model.

9. The method according to claim 7, characterized in that, The constructed logic yields multi-type card transfer and coupling logic, including: Various types of truck dynamic equations and corresponding dual-task flow correlation equations are constructed. Based on the coupling equation set consisting of the dynamic equations of the various types of trucks and the dual-task flow association equations, the multi-type truck flow and coupling logic is determined.

10. The method according to claim 7, characterized in that, The calculation rules for determining capacity utilization include: Based on the nonlinear function rule of capacity utilization rate and the number of cards in the initial stage of a time period, the nonlinear characterization result of the capacity utilization rate is determined; The nonlinear characterization result is linearized based on the piecewise linear approximation function to obtain the linearized characterization result. The calculation rules for the capacity utilization rate are determined based on the linearization characterization results.

11. The method according to claim 10, characterized in that, The linearization transformation of the nonlinear characterization result to obtain a linear characterization result includes: Discrete points are sampled based on data sampling technology, and the original utilization rate corresponding to each discrete point is calculated according to the original nonlinear function to construct a preset dataset. Based on the curvature characteristics of the original curve, determine the critical point information; A preset optimization problem is constructed based on the preset dataset and the critical point information; The preset optimization problem is solved to obtain the final calibration formula; The linearization characterization result is determined based on the final calibration formula.

12. The method according to claim 11, characterized in that, Determining the linearization characterization result based on the final calibration formula includes: Determine the goodness of fit of the calibrated function corresponding to the final calibration formula; If the goodness of fit of the calibrated function meets the preset accuracy condition, the linearization characterization result is determined according to the final calibration formula.

13. The method according to claim 1, characterized in that, The process of constructing a sub-model of the yard throughput envelope based on historical external truck service records and yard resource templates includes: Based on the historical external truck service records and the yard resource template, throughput envelope data reflecting different resource configuration levels is generated by piecewise linear fitting. Based on the throughput envelope data and the decision logic of the yard throughput envelope sub-model, the yard throughput envelope sub-model is determined; The decision logic of the yard throughput envelope sub-model is as follows: select the import and export service rate combination on the target envelope of the given throughput envelope data.

14. The method according to claim 13, characterized in that, The step of generating throughput envelope data reflecting different resource configuration levels through piecewise linear fitting based on the historical external truck service records and the yard resource template includes: The historical external card service records are cleaned to obtain cleaned data; The cleaned data is grouped according to the stockpile resource template to obtain grouped data. The grouped data are subjected to concave piecewise linear fitting to construct the fitting problem; Based on the fitting objective function and fitting constraints corresponding to the fitting problem, the fitting problem is solved to obtain the fitting solution result; The throughput envelope data is determined based on the fitting solution results.

15. The method according to claim 14, characterized in that, The method further includes: The following constraints are constructed: the slope is monotonically decreasing, the slope is decreasing, and the intercept is decreasing. The monotonically decreasing slope constraint condition of the adjacent segments, the slope constraint condition, and the intercept constraint condition are used as the fitting constraint conditions.

16. The method according to claim 1, characterized in that, The resource allocation decision transformation principle and service rate composition logic are used to construct a yard resource allocation sub-model, which includes: The principle of resource allocation decision transformation is to select the optimal inbound truck service rate and outbound truck service rate on a given throughput envelope. The service rate is determined based on the mathematical relationship between the service rate of a single-export truck and the service rate of a dual-task truck that has not completed its export task. A binary variable is introduced to characterize the selection of envelope line segments to determine the constraints of the yard resource allocation sub-model; The yard resource allocation sub-model is determined based on the constraints of the yard resource allocation sub-model, the resource allocation decision transformation principle, and the service rate composition logic.

17. The method according to claim 16, characterized in that, The introduction of binary variables to characterize the selection of envelope segments to determine the constraints of the yard resource allocation sub-model includes: The line segment uniqueness constraint, service rate association constraint, and service rate range constraint are determined based on the binary variables. Determine the non-negativity constraint of the service rate, and use the non-negativity constraint of the service rate, the uniqueness constraint of the line segment, the service rate correlation constraint, and the service rate range constraint as the constraint conditions of the yard resource allocation sub-model.

18. The method according to claim 1, characterized in that, The data flow and logical association rules are as follows: The external container truck arrival demand translation sub-model is used to output performance evaluation indicators of planned arrival volume and intervention volume based on the original arrival demand; The yard dynamic queuing sub-model is used to output queue length data based on the planned arrival volume, service rate data, and capacity utilization rate. Based on the queue length data, output the yard congestion index; The yard throughput envelope sub-model is used to output throughput envelope data based on historical external truck service records and yard resource templates; The yard resource allocation sub-model is used to output the service rate data based on the throughput envelope data.

19. The method according to claim 1, characterized in that, The sub-model ensemble optimization process is performed to construct an ensemble optimization model, including: The lexicographical objective function of the integrated optimization model is determined based on the performance evaluation index of the intervention quantity; The upper limit constraint of the yard congestion cost of the integrated optimization model is determined based on the yard congestion index. The integrated optimization model is determined based on the lexicographical objective function and the upper limit constraint of the yard congestion cost.

20. The method according to claim 1, characterized in that, The ensemble optimization iterative solution algorithm based on a preset algorithm solves the ensemble optimization model to obtain the solution output data corresponding to the ensemble optimization model, including: The original demand, congestion threshold, and step size are determined as the input data for the algorithm. The algorithm is initialized based on the input data, and the initialization result is obtained. Based on the initialization results, a loop iteration step is executed to determine the solution output data.

21. The method according to claim 20, characterized in that, The algorithm initialization based on the input data includes: Initialize the set of feasible service rate options, control parameters, and iteration count; The main problem is solved using the original requirements as input to obtain initial resource options, and the set of feasible service rate options is updated based on the resource options.

22. The method according to claim 20, characterized in that, The execution of the loop iteration step includes: Solving the main problem yields the arrival options and the current congestion costs; If the congestion cost exceeds the congestion threshold, a preset sub-loop iteration step is executed; The preset sub-loop iteration steps include: Update the iteration count and tighten the control parameters; Calculate the feasibility threshold for the current set; If the control parameter is less than the feasibility threshold, the process terminates and reports that no feasible solution exists. If the control parameter is greater than or equal to the feasibility threshold, the main problem is solved again to update the arrival plan and the congestion cost; Using the latest arrival plan as input, solve the subproblem, update the resource options, and update the set of feasible service rate options.

23. The method according to claim 22, characterized in that, The main problem is: to find the optimal shifting strategy that can meet the control parameters by adjusting the arrival demand of external trucks; the sub-problem is: to receive the arrival plan generated by the main problem and search for new resource options that can minimize congestion costs on the complete throughput envelope.

24. An integrated optimization device for container terminal off-site truck reservation management and yard resource allocation, characterized in that, The device includes: The module for constructing the external truck arrival demand translation sub-model is used to construct the external truck arrival demand translation sub-model based on the principle of mixed integer programming. The dynamic queuing sub-model building module for the stockyard is used to construct a dynamic queuing sub-model for the stockyard based on the principles of stochastic process modeling and fluid approximation mechanism. The yard throughput envelope sub-model building module is used to build a yard throughput envelope sub-model based on historical external truck service records and yard resource templates. The yard resource allocation sub-model construction module is used to construct the yard resource allocation sub-model based on the resource allocation decision transformation principle and service rate composition logic. The integration and optimization module is used to perform sub-model integration and optimization processing based on the data flow direction and logical association rules of the external truck arrival demand translation sub-model, the yard dynamic queuing sub-model, the yard throughput envelope sub-model, and the yard resource allocation sub-model, and to construct an integrated optimization model. The solution module is used to solve the ensemble optimization model based on a preset ensemble optimization iterative solution algorithm, and obtain the solution output data corresponding to the ensemble optimization model.

25. A computer device, characterized in that, The computer device includes: At least one processor and memory; The memory is used to store program code, and the processor is used to call the program code stored in the memory to execute the method as described in any one of claims 1 to 23.

26. A computer storage medium, characterized in that, It includes instructions that, when executed on a computer, cause the computer to perform the method as described in any one of claims 1 to 23.

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