A port container intelligent scheduling method and system

Abstract

The present application relates to the technical field of port logistics scheduling, and discloses a kind of port container intelligent scheduling method and system, wherein the method comprises: generating container level extraction time probability distribution set using kernel density estimation;Based on resource load rate and window urgency index, calculate dynamic decay coefficient, generate task associated directed graph with dynamic decay coefficient;Along the directed graph, propagate disturbance delay, generate probability-corrected dynamic disturbance influence domain;Convolution modeling is carried out on the transfer box task chain in the influence domain, and a list of probabilistic window default risk chains is generated;Calculate the minimum time compression amount and generate a set of rescheduling constraints;Constrained satisfaction optimization is solved, and the output fusion scheduling scheme is obtained.

Description

Technical Field

[0001] This invention relates to the field of port logistics scheduling technology, specifically to a port container intelligent scheduling method and system. Background Technology

[0002] In tidal-constrained ports, the berthing and unberthing operations of large vessels must be completed within a specific tidal time window, and the cutoff time of the tidal window is rigid and cannot be extended. The retrieval time of a large number of transshipment containers depends on the actual arrival time of the connecting outbound vessels, which is subject to probabilistic fluctuations due to factors such as upstream port congestion, shipping route delays, and weather.

[0003] Existing scheduling methods treat the arrival time of connecting vessels as a deterministic single-point value and optimize the stacking structure according to a fixed time sequence. When a disturbance event occurs, the existing method uses a fixed attenuation coefficient to propagate the delay along the task-associated directed graph to determine the boundary of the influence domain, and then performs local rescheduling of tasks within the influence domain.

[0004] The above approach has the following problems. First, when the actual sailing schedules of multiple connecting routes overlap and drift, the number of containers stacked in a deterministic time sequence increases due to changes in the actual retrieval order. Second, the fixed attenuation coefficient cannot reflect the characteristics of delays being amplified and propagated during periods of intense resource competition as the tidal window approaches its end, leading to an underestimation of the impact domain and the violation of hard constraints on tidal window rules by task chains not included in rescheduling. Third, when disturbances propagate to task chains involving transshipment containers, the combined impact of disturbance delays and the probabilistic arrival times of connecting vessels, as well as the increased risk of stacking and container turnover caused by resource reallocation after the disturbance, are treated separately. Summary of the Invention

[0005] This invention provides a port container intelligent scheduling method and system, which solves the technical problems in related technologies such as the inability to effectively quantify the uncertainty of the arrival time of connecting vessels, insufficient accuracy in assessing the scope of disturbance impact, and difficulty in probabilistically representing the risk of default during tidal window in the port container scheduling process.

[0006] This invention discloses a port container intelligent scheduling method, comprising: Obtain historical arrival deviation records and vessel dynamic data for each connecting and departing vessel, and generate a container-level extraction time probability distribution set. A task-association directed graph is generated based on the task dependencies and resource sharing relationships in the global scheduling plan, and the dynamic decay coefficient of each directed edge is calculated based on the resource load rate and window urgency index. The disturbance delay is propagated along the task-associated directed graph. For task nodes involving transit containers, the specified quantile value of the extracted time probability distribution is used as the effective time relaxation amount estimate for propagation termination judgment, and a dynamic disturbance influence domain after probability correction is generated. Convolutional modeling is performed on the transfer box task chain within the dynamic disturbance influence domain to calculate the probability of the task completion time at the end of the chain exceeding the tidal window deadline, and a probabilistic window default risk chain list is generated. Based on the risk chain list, a set of rescheduling constraints is generated, and constraint satisfaction optimization is performed to output the task execution sequence.

[0007] Further, the generation of the container-level extraction time probability distribution set includes: fitting the historical arrival deviation samples of each connecting vessel using the kernel density estimation method to generate the arrival time probability density function of each connecting vessel; mapping each transshipment container to its corresponding connecting vessel schedule probability density function, and calculating the extraction time probability density function of each transshipment container by combining the loading priority offset of the container on the corresponding vessel; wherein, the loading priority offset is the unloading time deviation of different containers on the same connecting vessel due to differences in loading position, and the extraction time probability density function of each transshipment container is the result of shifting the arrival time probability density function of its corresponding connecting vessel along the time axis by the container loading priority offset.

[0008] Furthermore, the dynamic attenuation coefficient is calculated according to the following formula: in, For a moment Directed edge The dynamic attenuation coefficient; The reference attenuation coefficient; For a moment Directed edge The allocated load rate of the associated shared resources, ranging from 0 to 1; For nodes The remaining time until the expiration time of its nearest associated tidal window; For nodes The total duration of the associated tidal window; and This is a non-negative weighting parameter; when the allocated load rate of the shared resource is high and the remaining time is short, If the value exceeds 1, the delay is amplified and propagated when passing through the directed edge.

[0009] Furthermore, the propagation termination judgment includes: for task nodes not involving transshipment container operations, propagation terminates on the path when the propagation delay is less than the deterministic time relaxation of the task node; for task nodes involving transshipment container operations, the extraction time probability density function corresponding to the transshipment container in the set of container-level extraction time probability distributions is obtained, and the high quantile value of the extraction time probability density function is extracted as an effective time relaxation estimate; when the propagation delay is less than the effective time relaxation estimate, propagation terminates on the path; after traversing all reachable paths, the set of task nodes covered by all non-terminating paths is marked as the probability-corrected dynamic disturbance influence domain.

[0010] Furthermore, the convolutional modeling of the transit container task chain within the dynamic disturbance influence domain includes: for each transit container task node in each transit container task chain, modeling the completion time of the task as a convolutional distribution of the disturbance delay reaching the task node after propagation and the probability distribution of the extraction time of the transit container; accumulating the completion time probability distribution of each node level by level along the transit container task chain direction to generate the completion time probability distribution of the task at the end of the chain; marking transit container task chains with an over-limit probability higher than a risk threshold as probabilistic window default risk chains, where the risk threshold is a pre-set probability threshold value.

[0011] Further, the step of generating a rescheduling constraint set based on the risk chain list includes: for each probabilistic window default risk chain in the probabilistic window default risk chain list, calculating the critical completion time value corresponding to the default probability equal to the acceptable level on the completion time probability distribution of the tasks at the end of the chain; the difference between the critical completion time value and the tidal window deadline is the minimum time compression amount; allocating the minimum time compression amount to each task node according to the proportion of the execution time of each task to the total execution time of the probabilistic window default risk chain, transforming it into an upper bound constraint for the execution time of each task; and writing the upper bound constraint for the execution time of each task, together with the tidal window boundary constraint and the resource capacity constraint, into the rescheduling constraint set.

[0012] Furthermore, the constraint satisfies that the optimization solution takes the minimum total completion time of tasks within the influence domain of the dynamic disturbance as the objective function. The objective function is the sum of the completion times of all tasks within the influence domain of the dynamic disturbance. The time of the disturbance is taken as the time origin, and the completion time of each task is expressed as a time offset relative to the origin.

[0013] Furthermore, after outputting the task execution sequence, the method further includes: based on the reallocation of yard bridge resources in the task execution sequence, obtaining the updated reachability time of each transit container in the affected yard area; for each pair of transit containers in the same stack within the affected yard area, based on their respective updated extraction time probability distribution and yard bridge reachability time, calculating the probability that their actual extraction order will be reversed relative to the current stacking order, and generating a pair-by-pair reversal probability matrix; marking stacking pairs with reversal probabilities exceeding a preset threshold as pre-positioning targets; wherein, the reversal probability is calculated according to the following formula: in, For containers and The probability of reversal between them; for The extraction time probability density function; for The cumulative distribution function of extraction time; For integration time; For stacking located in The containers above.

[0014] Furthermore, after marking the pre-positioning target, the method further includes: merging the positioning task of the pre-positioning target with the task execution sequence, inserting pre-positioning instructions during the idle period of the yard bridge, and outputting a fusion scheduling scheme that simultaneously satisfies the probabilistic constraints of the tidal window and the risk control of stacking and overturning containers.

[0015] This invention discloses a port container intelligent scheduling system, comprising: The probability distribution generation module is used to obtain historical arrival deviation records and vessel dynamic data of each connecting and departing vessel, and generate a set of container-level extraction time probability distributions. The task association graph generation module is used to generate a directed graph of task associations based on the dependency and resource sharing relationships of tasks in the global scheduling plan, and to calculate the dynamic decay coefficient of each directed edge based on the resource load rate and window urgency index. The disturbance influence domain calculation module is used to propagate the disturbance delay along the task-associated directed graph, determine the propagation termination based on the specified quantile value of the extracted time probability distribution, and generate a dynamic disturbance influence domain after probability correction. The risk chain identification module is used to perform convolutional modeling on the transfer box task chain within the dynamic disturbance influence domain, calculate the probability of the chain end task completion time exceeding the tidal window deadline, and generate a probabilistic window default risk chain list. The constraint generation module is used to calculate the minimum time compression based on the default probability of each probabilistic window default risk chain in the risk chain list, and generate a set of rescheduling constraints that includes upper bound constraints on execution time. The scheduling solution module is used to perform constraint-satisfaction optimization on the rescheduling subproblem within the influence domain of the dynamic disturbance, and output the task execution sequence that satisfies the probabilistic window default constraint.

[0016] The present invention has the following beneficial effects: By utilizing kernel density estimation, the timing of transshipment container retrieval is extended from deterministic single-point values ​​to a probability density function of retrieval time. The high-quantile values ​​of this probability density function are then incorporated into the termination criteria for disturbance propagation. These high-quantile values ​​are more conservative than deterministic relaxations, extending the boundary of the dynamic disturbance influence domain downstream after probability correction. This avoids the problem of deterministic relaxations underestimating the disturbance propagation range and missing critical tasks in the transshipment container task chain.

[0017] A dynamic attenuation coefficient is calculated based on the resource allocation load rate and window urgency indicators, causing the delay propagation intensity to change dynamically with the degree of resource competition and window proximity. During periods when resource queuing effects are significant and the remaining time of the tidal window is limited, a dynamic attenuation coefficient exceeding 1 leads to amplified delay propagation. This overcomes the shortcomings of underestimating the impact domain and violating the hard constraints of the tidal window in task chains not included in rescheduling under the fixed attenuation coefficient assumption.

[0018] By convolving the disturbance delay with the probability density function of the docking schedule to generate the probability distribution of task completion time, the default determination of the tidal window is transformed from a comparison of deterministic time points to an assessment of the probability of exceeding limits. The probability of exceeding limits can quantify the default risk under the superposition of dual uncertainties, so that the coverage of the rescheduling constraint set matches the actual risk level.

[0019] The results of the resource reallocation after the disturbance are fed back to the pairwise reversal probability matrix update, and pre-positioning instructions are inserted during the idle periods of the yard cranes. Resource reallocation changes the reachability time of the yard cranes, thereby changing the actual extraction order of transshipment containers. Reversal risks are identified directly based on the updated extraction time probability density function, and pre-positioning is performed, avoiding the problem of a sudden increase in container turnover caused by ignoring the correlation between resource changes and stacking turnover risks. Attached Figure Description

[0020] Figure 1 This is a flowchart of the intelligent port container scheduling method provided in the embodiments of the present invention; Figure 2 This is a schematic diagram comparing the probability distribution parameters of transit container retrieval time provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of the dynamic decay coefficient of the key edge of the task-associated directed graph provided in the embodiment of the present invention; Figure 4 This is a schematic diagram of the node-by-node propagation process of the disturbance delay provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of the probabilistic window default risk assessment of the transit container task chain provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the allocation of rescheduling constraint set compression amount provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of the comparison before and after the stacking pair reversal probability update (stacking block Z1) provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of the timing Gantt chart of key tasks in the fusion scheduling scheme provided in this embodiment of the invention; Figure 9 This is a schematic diagram illustrating the relationship between the remaining time of each target node and the dynamic decay coefficient provided in an embodiment of the present invention. Detailed Implementation

[0021] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0022] At least one embodiment of the present invention discloses a port container intelligent scheduling method, see Figure 1 This includes the following steps: Step 1: Obtain arrival data of connecting vessels and generate a set of container-level extraction time probability distributions.

[0023] Obtain historical arrival deviation records and current AIS vessel dynamic data for each connecting vessel. Use kernel density estimation to fit the historical arrival deviation samples of each connecting vessel, generating an arrival time probability density function for each vessel. Map each transshipment container to its corresponding transshipment schedule probability density function. Combine this with the stowage priority offset of that container on the corresponding vessel, calculate the extraction time probability density function for each transshipment container. Aggregate the extraction time probability density functions of all transshipment containers to generate a set of container-level extraction time probability distributions.

[0024] It should be noted that the aforementioned loading priority offset refers to the deviation in unloading time caused by the different loading positions of different containers on the same connecting vessel. Containers located on the upper deck or near the hatch are unloaded first, and their loading priority offset is taken as a smaller value; containers located on the bottom deck or deep inside the hold are unloaded later, and their loading priority offset is taken as a larger value. The extraction time probability density function of each transshipment container is the result of shifting the arrival time probability density function of its corresponding connecting vessel along the time axis by the container's loading priority offset.

[0025] Step 2: Obtain task dependency and resource constraint data, and generate a directed graph of task association with dynamic decay coefficient.

[0026] Retrieve the dependencies, resource sharing relationships, and time constraints of all tasks in the current global scheduling plan. Abstract each task as a node, and the dependencies and constraints between tasks as directed edges, generating a directed graph of task associations. Obtain the opening and closing times of each tidal window. For each task node, calculate the remaining time until the closing time of the nearest associated tidal window, and mark this remaining time as the window urgency index for that task node. Obtain the allocated load rate of various shared resources in future time periods at the time of the disturbance.

[0027] For each directed edge in the task-associated directed graph, calculate the dynamic decay coefficient of the edge based on the resource load rate associated with that edge and the window urgency index of the target node. The dynamic decay coefficient is calculated using the following formula: in, For a moment Directed edge The dynamic attenuation coefficient, The current moment; The reference attenuation coefficient; For a moment Directed edge The allocated load rate of the associated shared resources, ranging from 0 to 1; For nodes The remaining time until the expiration time of its nearest associated tidal window; For nodes The total duration of the associated tidal window; and These are non-negative weight parameters; Let be the source node number of the directed edge. Number the target node of the directed edge.

[0028] It should be noted that the dynamic attenuation coefficient mentioned above can be greater than 1. When the allocated load rate of the shared resource is high and the remaining time is short, A value greater than 1 indicates that the delay is amplified and propagated when passing through the directed edge. This characteristic reflects the objective process of small delays being amplified step by step under resource queuing and waiting effects. When the resource load is low and there is ample remaining time, Approaching The delay decreases as usual.

[0029] Step 3: Propagate the perturbation delay along the task-associated directed graph to generate the probability-corrected dynamic perturbation influence domain.

[0030] The perturbation event is mapped to the directly affected task node in the task-associated directed graph, and the perturbation delay is assigned to that task node. The delay is then propagated downstream along the directed edges. Each time a directed edge is traversed... At that time, the delay is multiplied by the value of the directed edge at the current moment. dynamic attenuation coefficient This gives the propagation delay received by the downstream node.

[0031] For task nodes not involving transshipment container operations, propagation terminates on that path when the propagation delay is less than the deterministic time relaxation of that task node. For task nodes involving transshipment container operations, the extraction time probability density function corresponding to the transshipment container in the container-level extraction time probability distribution set is obtained. A specified quantile value of this extraction time probability density function is extracted as an effective time relaxation estimate, which replaces the deterministic relaxation for propagation termination judgment. Propagation terminates on that path when the propagation delay is less than this effective time relaxation estimate.

[0032] After traversing all reachable paths, mark the set of task nodes covered by all non-terminating paths as the dynamic perturbation influence domain after probability correction.

[0033] It should be noted that the specified quantile value mentioned above refers to the high quantile value for extracting the time probability density function. In one embodiment, this quantile can be the 95th percentile. Using a high quantile value means estimating the effective time slack in a more conservative manner, making the estimated effective time slack smaller than the slack obtained from the planned arrival time in the deterministic calculation. This allows the boundary of the dynamic disturbance influence domain after probability correction to extend downstream, covering task nodes that may be affected by disturbances in probabilistic tail risk scenarios.

[0034] Step 4: Perform probabilistic modeling of the transit container task chain within the influence domain to generate a probabilistic window default risk chain list.

[0035] Within the dynamic disturbance influence domain after probability correction, the transit container task chain associated with the tidal window is extracted. For each transit container task node in each transit container task chain, the completion time of the task is modeled as a convolution distribution of the disturbance delay reaching the task node after propagation and the probability distribution of the extraction time of the transit container. The completion time probability distribution of each node is accumulated level by level along the transit container task chain to generate the completion time probability distribution of the task at the end of the chain.

[0036] Calculate the probability that the completion time of the task at the end of the chain exceeds the deadline of the associated tidal window, i.e., the probability of exceeding the limit. Mark transit box task chains with an excess probability higher than the risk threshold as probabilistic window default risk chains. Aggregate all probabilistic window default risk chains and their corresponding default probabilities to generate a list of probabilistic window default risk chains.

[0037] It should be noted that the convolution distribution mentioned above means: the disturbance delay represents the earliest executable time offset caused by upstream disturbances, and the extraction time probability distribution represents the extractable time range of the transshipment container due to fluctuations in the arrival of connecting vessels. The actual completion time of the task depends on the combined effect of the two. When the two are independent, the probability distribution of the completion time is the convolution result of their respective distributions. Both the disturbance delay and the extraction time probability distribution are time-based and can be directly convolved.

[0038] It should be noted that the above risk thresholds are pre-set probability thresholds used to distinguish between acceptable default risk and unacceptable default risk. Their values ​​are determined based on the port's tolerance for tidal window defaults.

[0039] Step 5: Generate a set of rescheduling constraints based on the risk chain default probability.

[0040] For each probabilistic window default risk chain in the list, calculate the minimum time compression required to reduce the default probability of the task at the end of the chain to an acceptable level. Allocate this minimum time compression to each task node on the probabilistic window default risk chain, transforming it into an upper bound constraint on the execution time of each task. Combine the upper bound constraints on the execution time of each task with the original tidal window boundary constraints and resource capacity constraints, and write them into the constraint set of the local rescheduling subproblem.

[0041] It should be noted that the minimum time compression mentioned above is calculated as follows: Based on the probability distribution of completion times for tasks at the end of the chain, find the critical completion time value that makes the default probability equal to the acceptable level. The difference between this critical completion time value and the tidal window deadline is the required total compression. When there are multiple task nodes on the probabilistic window default risk chain, the total compression is allocated to each node according to the proportion of each task's execution time to the total execution time of the probabilistic window default risk chain.

[0042] Step 6: Solve the rescheduling subproblem by satisfying constraints and output the task execution sequence.

[0043] For the rescheduling subproblem within the influence domain of the probabilistically corrected dynamic disturbance, the objective function is to minimize the total completion time of tasks within this domain. The solution is obtained by optimizing the constraint satisfaction under the rescheduling constraint set. The objective function is the sum of the completion times of all tasks within the influence domain of the probabilistically corrected dynamic disturbance, with the disturbance occurrence time as the time origin. Each task's completion time is represented by a time offset relative to this origin. The output is the task execution sequence that satisfies the probabilistic window violation constraint. This task execution sequence constitutes the scheduling scheme that satisfies the tidal window probabilistic constraint.

[0044] In this embodiment of the application, to address the issue of a sudden increase in the risk of container overturning in previously safe stacking operations due to resource reallocation after disturbance, the following processing is included in addition to solving the output task execution sequence in step 6: Based on the reallocation of yard bridge resources in the task execution sequence, the updated reachability time of each transit container in the affected yard area is obtained. For each pair of transit containers in the same stack within the affected yard area, based on their respective updated extraction time probability distribution and yard bridge reachability time, the probability that their actual extraction order will be reversed relative to the current stacking order is calculated, generating a pair-by-pair reversal probability matrix. Stacking pairs with reversal probabilities exceeding a preset threshold are marked as pre-positioning targets.

[0045] It should be noted that the above method for calculating the pairwise inversion probability matrix is ​​as follows: for containers in the same stack... and ,set up Located in the stack The top, i.e., the current stacking order, requires extraction first. .set up and They are respectively and The actual extraction time random variable is obtained by truncating the extraction time probability density function corresponding to the container-level extraction time probability distribution set under the yard bridge reachability time constraint. At this point, the actual extraction order may be reversed from the stacking order, requiring a box-flipping operation. Reversal probability. for The probability of that, i.e.: in, For containers and The probability of reversal between them; for The extraction time probability density function; for The cumulative distribution function of extraction time; For integration time; This refers to the number of the container at the top of the stack. This refers to the number of the container at the bottom of the stack. The unit is the reciprocal of time. For dimensionless probability values, the integral variable is... The unit is time, and the product of the three factors, when integrated, yields a dimensionless probability value. The first pair of pairs of inverted probability matrices... The element has the value .

[0046] In this embodiment of the application, after marking the pre-adjustment target, the following steps are further included: Step 7: Merge the pre-scheduled tasks and rescheduled results, and output the fused scheduling scheme.

[0047] The relocation tasks of pre-positioned targets are merged with the task execution sequence. Pre-positioning instructions are inserted during the idle periods of the yard cranes to complete the stacking relocation operation without affecting the execution of already scheduled tasks. The output is a fusion scheduling scheme that simultaneously satisfies the probabilistic constraints of tidal windows and the risk control of stacking container overturning.

[0048] On the other hand, the present invention also proposes a port container intelligent scheduling system, comprising: The probability distribution generation module is used to obtain historical arrival deviation records and current AIS vessel dynamic data for each connecting vessel, and generate a set of container-level extraction time probability distributions.

[0049] The task association graph generation module is used to obtain the dependency relationships, resource sharing relationships, and time constraint relationships of all tasks in the current global scheduling plan, and generate a directed task association graph with a dynamic decay coefficient.

[0050] The disturbance influence domain calculation module is used to propagate the disturbance delay along the task-related directed graph, determine the propagation termination based on the probabilistic relaxation amount estimation, and generate a dynamic disturbance influence domain after probability correction.

[0051] The risk chain identification module is used to perform convolutional modeling on the transit box task chain within the dynamic disturbance influence domain after probability correction, calculate the probability of exceeding the limit of the task completion time distribution at the end of the chain, and generate a probabilistic window default risk chain list.

[0052] The constraint generation module is used to calculate the minimum time compression based on the default probability of each probabilistic window default risk chain in the probabilistic window default risk chain list, and generate a set of rescheduling constraints that includes upper bound constraints on execution time.

[0053] The scheduling solution module is used to perform constraint-satisfying optimization on the rescheduling subproblem and output the task execution sequence that satisfies the probabilistic window default constraint.

[0054] By way of example, the system proposed in this invention may also include various features and combinations thereof in the method embodiments, which will not be elaborated here.

[0055] This invention extends the timing of transshipment container retrieval from deterministic single-point values ​​to an retrieval time probability density function by utilizing kernel density estimation. Furthermore, it incorporates the high-quantile values ​​of the retrieval time probability density function into the termination judgment of disturbance propagation, enabling the boundary calculation of the dynamic disturbance influence domain after probability correction to cover probabilistic tail risk scenarios. Because high-quantile values ​​are more conservative than deterministic relaxations, the boundary of the dynamic disturbance influence domain after probability correction extends downstream, avoiding the problem of deterministic relaxations underestimating the disturbance propagation range and missing critical tasks in the transshipment container task chain.

[0056] This invention calculates a dynamic attenuation coefficient based on resource allocation load rate and window urgency indicators, causing the delay propagation intensity to dynamically change with the degree of resource competition and window proximity. Because during periods when resource queuing effects are significant and the remaining time of the tidal window is limited, a dynamic attenuation coefficient exceeding 1 leads to amplified delay propagation. Therefore, it overcomes the shortcomings of underestimating the impact domain of dynamic disturbances after probability correction under the fixed attenuation coefficient assumption and the violation of the hard constraint of the tidal window by task chains not included in rescheduling.

[0057] This invention generates a task completion time probability distribution by convolving the disturbance delay with the probability density function of the docking schedule, transforming the determination of tidal window defaults from a deterministic comparison of time points to an assessment of the probability of exceeding limits. Because the probability of exceeding limits can quantify the default risk under the superposition of dual uncertainties, the identification of the probabilistic window default risk chain list can capture tail risk scenarios that deterministic methods cannot perceive, thus matching the coverage of the rescheduling constraint set with the actual risk level.

[0058] This invention feeds back the results of resource redistribution after disturbances to the pairwise reversal probability matrix update, and inserts pre-positioning instructions during the idle periods of the yard cranes, forming a closed-loop process from disturbance propagation to stacking risk assessment. Because resource redistribution changes the accessibility time of the yard cranes, thus altering the actual retrieval order of transshipment containers, the reversal risk is directly identified and pre-positioning is performed based on the updated retrieval time probability density function. This avoids the problem of a sudden increase in container turnover caused by ignoring the correlation between resource changes and stacking turnover risk.

[0059] See Figures 2-9 The following application examples are proposed: A port's operational area handles transshipment services for both transoceanic trunk lines and near-ocean feeder lines. The port is subject to semi-diurnal tides, with each tidal window lasting 720 minutes. The afternoon tidal window closed at 17:00. At 10:15 that morning, feeder vessel A from an upstream hub port triggered a disturbance event due to anchorage congestion, with an initial delay of 45 minutes. Three vessels—A, B, and C—were scheduled to depart that day, and several transshipment containers were awaiting loading in the yard. The port's dispatch system immediately activated its intelligent dispatch process.

[0060] The dispatching system retrieves historical arrival deviation records for vessels A, B, and C, and reads current AIS dynamic data. Kernel density estimation is performed on the historical deviation samples for each vessel. Vessel A's historical deviation mean is positive and widely distributed, reflecting its frequent route congestion. Subsequently, the system maps each transshipment container to the probability density function of its corresponding vessel and shifts the distribution along the time axis according to the loading priority offset, obtaining the extraction time probability density function for each container. The mean of the extraction time distribution is equal to the sum of the mean arrival deviation of the corresponding vessel and the loading priority offset. Container 002, located at the bottom of the hold, has the largest loading priority offset, and its mean extraction time distribution is significantly greater than that of container 001.

[0061] Table 1. Probability distribution parameters of transshipment container pickup time The scheduling system reads the global scheduling plan, extracts task dependencies, resource sharing relationships, and time constraints, and generates a directed graph of task associations. The system calculates the remaining time for each task node until the tidal window deadline (17:00) and marks it as a window urgency index. The allocated load rate of each shared resource at the time of the disturbance (10:15). Resource usage is read in real time from the resource usage ledger. For each directed edge, it is calculated according to the formula. Calculate the dynamic attenuation coefficient, where , , , Minutes. The CR1 bridge has a high load rate and the target node is close to the tidal window cutoff time. The dynamic attenuation coefficients of edges A→B and B→C both significantly exceed 1, meaning the delay will be amplified and propagated when passing through these two edges. The attenuation coefficient of edge D→E is close to 1, indicating that the delay propagation intensity in this segment is moderate.

[0062] Table 2 Calculation results of dynamic decay coefficient of key edges in task-associated directed graph An initial disturbance delay of 45 minutes is assigned to source node A. The system propagates layer by layer along directed edges, multiplying the current delay by the corresponding dynamic attenuation coefficient at each edge. For nodes involved in transshipment container operations, the 95th percentile of the extracted time probability density function is used as the effective time relaxation estimate, replacing the deterministic relaxation, and a propagation termination judgment is performed. Nodes C and D involve transshipment container operations, and their effective time relaxation estimates use the 95th percentile of the extracted time probability density function. The propagation delay of node C, 118.06 minutes, is less than the 95th percentile estimate of 134 minutes, so propagation continues; the propagation delay of node D, 149.94 minutes, exceeds the 95th percentile estimate of 94 minutes, so propagation continues. The delay of node E is lower than its deterministic relaxation, so propagation terminates. Finally, nodes A through D are all included in the probability-corrected dynamic disturbance influence domain.

[0063] Table 3. Node-by-node propagation process of disturbance delay Within the dynamic disturbance influence domain after probability correction, the transit container task chain associated with the tidal window of the current day (deadline 17:00) is extracted. For node C (associated container 002) and node D (associated container 001), the propagation delay reaching this node is convolved with the probability distribution of the extraction time of the corresponding container to obtain the completion time probability distribution of each node. This is accumulated level by level along the task chain to generate the completion time probability distribution of the task at the end of the chain, and then the probability of exceeding the limit beyond the tidal window deadline is calculated. The risk threshold is set to 0.20. The probability of exceeding the limit for chains 1 and 2 is higher than the risk threshold of 0.20, and they are marked as probabilistic window default risk chains. The probability of exceeding the limit for chain 3 is lower than the risk threshold and is not included in the default risk chain list.

[0064] Table 4. Result of Probabilistic Window Default Risk Assessment for Transit Container Task Chain For chains 1 and 2, calculate the minimum time compression required to reduce the default probability of the tasks at the end of the chains to below 0.20. On the probability distribution of completion times at the end of the chains, find the critical completion time value corresponding to a default probability of 0.20. The difference between this critical value and the tidal window deadline is the total compression. For each task node on the chain, allocate the compression according to the proportion of its execution time to the total execution time of the chain. This is transformed into an upper bound constraint on the execution time of each task, and together with the tidal window boundary constraint and resource capacity constraint, it is written into the rescheduling constraint set.

[0065] Table 5. Results of Rescheduling Constraint Set Generation The scheduling system uses the minimum total completion time of all tasks within the dynamic disturbance influence domain after probability correction as its objective function. It solves this problem under a set of rescheduling constraints and outputs a task execution sequence that satisfies the probabilistic constraints of the tidal window. After solving, the system updates the reachability time of each transit container within the affected yard area based on the redistribution of yard bridge CR1 in the task execution sequence. For container pairs within the same stack, based on the updated extraction time probability density function and the yard bridge reachability time, the system calculates the reachability time according to the formula... Calculate the pairwise reversal probabilities to generate the pairwise reversal probability matrix. Wherein, For the container above The extraction time probability density function, For the container below The cumulative distribution function of extraction time, This is the integral time variable. The preset threshold for the reversal probability is 0.30. After the resource reallocation of the field bridge CR1, the reversal probability of box 001 and box 002 increased from 0.18 to 0.43, exceeding the preset threshold of 0.30, and is marked as a pre-positioning target. The reversal probability of box 003 and box 004 is 0.26, which is lower than the threshold, and pre-positioning is not performed.

[0066] Table 6. Stacking pairwise reversal probability matrix (stacking block Z1) The system inserts the repositioning tasks of container 001 and 002 into the idle period of field bridge CR1, merges them with the task execution sequence, and outputs a fusion scheduling scheme. The T-ADJ pre-positioning task is scheduled in the idle period of field bridge CR1, without affecting the execution of TC and TD. The planned completion time of TE is earlier than the tidal window deadline of 17:00, satisfying the hard constraint.

[0067] Table 7 Key Task Sequence of the Integrated Scheduling Scheme The data coherence of the entire process is reflected in the following aspects. The container-level extraction time probability distribution set generated in step 1 provides the 95th percentile relaxation estimate for nodes involving transit containers in step 3, extending the influence domain boundary downstream to node D; the dynamic attenuation coefficient generated in step 2 drives the delay in step 3 to gradually increase from 45 minutes to 149.94 minutes, ensuring that node D is included in the influence domain; the influence domain determined in step 3 limits the extraction range of the task chain in step 4, and the out-of-limit probability output in step 4 directly determines the calculation of the total compression in step 5; the execution time upper bound constraint generated in step 5 serves as the input for solving in step 6, and the solution output, the field bridge resource reallocation result, is fed back to the reversal probability matrix update, driving the pre-adjustment insertion in step 7. All data, starting from the initial disturbance delay, goes through probability modeling, influence domain expansion, risk identification, constraint generation, optimization solution, and pre-adjustment merging, forming a complete closed loop.

[0068] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method for intelligent scheduling of port containers, characterized in that, include: Obtain historical arrival deviation records and vessel dynamic data for each connecting departing vessel, and generate a container-level extraction time probability distribution set; A task-association directed graph is generated based on the task dependencies and resource sharing relationships in the global scheduling plan, and the dynamic decay coefficient of each directed edge is calculated based on the resource load rate and window urgency index. The disturbance delay is propagated along the task-associated directed graph. For task nodes involving transit containers, the specified quantile value of the extracted time probability distribution is used as the effective time relaxation amount estimate for propagation termination judgment, and a dynamic disturbance influence domain after probability correction is generated. Convolutional modeling is performed on the transfer box task chain within the dynamic disturbance influence domain to calculate the probability of the task completion time at the end of the chain exceeding the tidal window deadline, and a probabilistic window default risk chain list is generated. Based on the risk chain list, a set of rescheduling constraints is generated, and constraint satisfaction optimization is performed to output the task execution sequence.

2. The intelligent port container scheduling method according to claim 1, characterized in that, The set of probability distributions for generating container-level extraction times includes: The kernel density estimation method is used to fit the historical arrival deviation samples of each connecting vessel to generate the arrival time probability density function of each connecting vessel. Each transshipment container is mapped to its corresponding connection vessel schedule probability density function. Combined with the loading priority offset of the container on the vessel corresponding to the connection vessel schedule probability density function, the extraction time probability density function of each transshipment container is calculated. The loading priority offset is the deviation in unloading time of different containers on the same connecting vessel due to differences in loading position. The extraction time probability density function of each transit container is the result of shifting the arrival time probability density function of its corresponding connecting vessel along the time axis by the loading priority offset of that container.

3. The intelligent port container scheduling method according to claim 1, characterized in that, The dynamic attenuation coefficient is calculated using the following formula: in, For a moment Directed edge The dynamic attenuation coefficient; The reference attenuation coefficient; For a moment Directed edge The allocated load rate of the associated shared resources, ranging from 0 to 1; For nodes The remaining time until the expiration time of its nearest associated tidal window; For nodes The total duration of the associated tidal window; and These are non-negative weight parameters; When the allocated load rate of shared resources is high and the remaining time is short, If the value exceeds 1, the delay is amplified and propagated when passing through the directed edge.

4. The intelligent port container scheduling method according to claim 1, characterized in that, The propagation termination determination includes: For task nodes that do not involve transshipment container operations, propagation terminates on that path when the propagation delay is less than the deterministic time relaxation of that task node. For a task node involving transshipment container operations, obtain the extraction time probability density function corresponding to the transshipment container in the container-level extraction time probability distribution set, extract the high quantile value of the extraction time probability density function as an effective time relaxation estimate, and when the propagation delay is less than the effective time relaxation estimate, the propagation terminates on the path. After traversing all reachable paths, the set of task nodes covered by all unterminated paths is marked as the dynamic disturbance influence domain after probability correction.

5. The intelligent port container scheduling method according to claim 1, characterized in that, The convolutional modeling of the transfer box task chain within the dynamic disturbance influence domain includes: For each transit container task node in each transit container task chain, the completion time of the task is modeled as the convolution distribution of the disturbance delay that propagates to the task node and the probability distribution of the extraction time of the transit container. The completion time probability distribution of each node is accumulated level by level along the task chain of the transit box to generate the completion time probability distribution of the task at the end of the chain. The transit container task chain with an over-limit probability higher than the risk threshold is marked as a probabilistic window default risk chain, where the risk threshold is a pre-set probability threshold value.

6. The intelligent port container scheduling method according to claim 1, characterized in that, The generation of the rescheduling constraint set based on the risk chain list includes: For each probabilistic window default risk chain in the probabilistic window default risk chain list, calculate the critical completion time value that makes the default probability equal to the acceptable level on the completion time probability distribution of the task at the end of the chain. The difference between the critical completion time value and the tidal window deadline is the minimum time compression. The minimum time compression is allocated to each task node according to the proportion of the execution time of each task to the total execution time of the probabilistic window default risk chain, and is transformed into an upper bound constraint on the execution time of each task. The upper bound constraints of the execution time of each task, the tidal window boundary constraints, and the resource capacity constraints are all written into the rescheduling constraint set.

7. The intelligent port container scheduling method according to claim 1, characterized in that, The constraint satisfies that the optimization solution takes the minimum total completion time of tasks within the influence domain of the dynamic disturbance as the objective function. The objective function is the sum of the completion times of all tasks within the influence domain of the dynamic disturbance. The time of the disturbance is taken as the time origin, and the completion time of each task is expressed as a time offset relative to the origin.

8. The intelligent port container scheduling method according to claim 1, characterized in that, After outputting the task execution sequence, the following is also included: Based on the reallocation of yard bridge resources in the task execution sequence, the updated reachability time of each transit container in the affected yard area is obtained; For each pair of transit containers in the same stack within the affected yard area, based on their respective updated extraction time probability distribution and yard crane reachability time, calculate the probability that their actual extraction order will be reversed relative to the current stacking order, and generate a pair-by-pair reversal probability matrix. Stacking pairs with a reversal probability exceeding a preset threshold are marked as pre-adjustment targets; The reversal probability is calculated using the following formula: in, For containers and The probability of reversal between them; for The extraction time probability density function; for The cumulative distribution function of extraction time; For integration time; For stacking located in The containers above.

9. The intelligent port container scheduling method according to claim 8, characterized in that, After marking the pre-adjustment target, the method further includes: The relocation task of the pre-positioned target is merged with the task execution sequence, and the pre-positioning instruction is inserted during the idle period of the yard bridge to output a fusion scheduling scheme that simultaneously satisfies the probabilistic constraints of the tidal window and the risk control of stacking and overturning.

10. A port container intelligent scheduling system, used to execute the port container intelligent scheduling method according to any one of claims 1 to 9, characterized in that, include: The probability distribution generation module is used to obtain historical arrival deviation records and vessel dynamic data of each connecting and departing vessel, and generate a set of container-level extraction time probability distributions. The task association graph generation module is used to generate a directed graph of task associations based on the dependency and resource sharing relationships of tasks in the global scheduling plan, and to calculate the dynamic decay coefficient of each directed edge based on the resource load rate and window urgency index. The disturbance influence domain calculation module is used to propagate the disturbance delay along the task-associated directed graph, determine the propagation termination based on the specified quantile value of the extracted time probability distribution, and generate a dynamic disturbance influence domain after probability correction. The risk chain identification module is used to perform convolutional modeling on the transfer box task chain within the dynamic disturbance influence domain, calculate the probability of the chain end task completion time exceeding the tidal window deadline, and generate a probabilistic window default risk chain list. The constraint generation module is used to calculate the minimum time compression based on the default probability of each probabilistic window default risk chain in the risk chain list, and generate a set of rescheduling constraints that includes upper bound constraints on execution time. The scheduling solution module is used to perform constraint-satisfaction optimization on the rescheduling subproblem within the influence domain of the dynamic disturbance, and output the task execution sequence that satisfies the probabilistic window default constraint.

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