Product manufacturing intelligent scheduling method and device

Abstract

The application provides a product manufacturing intelligent scheduling method and device, and relates to the technical field of intelligent manufacturing. The method comprises the following steps: acquiring an original workpiece set and a newly-arrived workpiece set, wherein the original workpiece set comprises original workpieces, the newly-arrived workpiece set comprises newly-arrived workpieces, and there is an initial optimal scheduling scheme corresponding to the original workpiece set; setting an optional processing strategy for each newly-arrived workpiece; limiting the absolute value of the difference between the completion time of the original workpiece in a new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme to be not more than a preset threshold value, and obtaining a maximum completion time deviation constraint; constructing a target function according to a weighted total completion time, a maximum completion time deviation cost, a compression cost and a rejection cost; and based on the target function and the maximum completion time deviation constraint, a mixed integer programming model is established, so that the global optimal or approximate optimal total cost is realized while the new order is accepted and the stability of the original plan is ensured.

Description

Technical Field

[0001] This application relates to the field of intelligent manufacturing technology, and more specifically, to a method and apparatus for intelligent scheduling of product manufacturing. Background Technology

[0002] In smart manufacturing environments, production scheduling systems often face the challenge of dynamic disturbances. Traditional static scheduling models typically assume a stable production environment, fully known order information, and no sudden changes. Therefore, they struggle to adapt to the uncertainties that frequently occur in actual manufacturing processes, such as order insertions, equipment failures, delivery date adjustments, or resource shortages. When new orders (such as urgent customer orders) arrive, directly inserting them into the existing schedule can significantly shift the completion time of existing workpieces, impacting customer satisfaction and production stability. Conversely, completely rejecting new orders can lead to wasted capacity or lost business opportunities.

[0003] Related research has proposed various rescheduling strategies, mainly including: interruption models (allowing partial interruption of the original plan), rejectable scheduling (rejecting some orders by paying penalty costs), and controllable processing time models (compressing workpiece processing time by investing additional resources). How to achieve globally optimal or near-optimal total cost while accepting new orders and ensuring the stability of the original plan has become a pressing technical challenge. Summary of the Invention

[0004] The problem addressed in this application is how to achieve the global optimum or near-optimal total cost while ensuring the stability of the original plan, and while accepting new orders.

[0005] To address the aforementioned issues, this application provides a method and apparatus for intelligent scheduling of product manufacturing.

[0006] Firstly, this application provides a product manufacturing intelligent scheduling method, including:

[0007] Obtain the original set of jobs and the newly arrived set of jobs, wherein the original set of jobs includes the original jobs and the newly arrived set of jobs includes the newly arrived jobs, and for the original set of jobs, there is an initial optimal scheduling scheme.

[0008] For each newly arriving workpiece, an optional processing strategy is set, wherein the optional processing strategy includes accepting and reducing processing time, or rejecting and paying rejection costs;

[0009] The absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme is limited to not exceeding a preset threshold, thereby obtaining the maximum completion time deviation constraint.

[0010] Construct an objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost;

[0011] Based on the objective function and the maximum completion time deviation constraint, a mixed integer programming model is established.

[0012] Optionally, the newly arriving set of jobs includes schedulable jobs and emergency jobs;

[0013] When the newly arrived workpiece is a schedulable workpiece, the processing time is compressed upon acceptance by resource allocation.

[0014] When the newly arrived workpiece is an urgent workpiece, the urgent workpiece is scheduled for processing according to a fixed time when accepted, and the urgent cost is borne when rejected.

[0015] Optionally, the optional processing strategy is to accept and compress processing time.

[0016] The actual processing time of the newly arrived workpiece is determined by the product of the difference between the normal processing time and the compression rate and the amount of resources invested, wherein the amount of resources invested does not exceed the maximum available resources corresponding to the newly arrived workpiece.

[0017] Optionally, the constraint that the absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme does not exceed a preset threshold, thereby obtaining the maximum completion time deviation constraint, includes:

[0018] A linear inequality is constructed by the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time in the initial optimal scheduling scheme, wherein the linear inequality is used to characterize the advance and delay of the completion time of each original workpiece.

[0019] Using the linear inequality, the deviation measurement variable is defined as the larger of the original workpiece lead time and delay.

[0020] The maximum deviation variable is constructed using the deviation measurement variables of all original workpieces, and the maximum deviation variable is used as the upper bound of all deviation measurement variables;

[0021] The maximum completion time deviation constraint is constructed using the preset threshold, limiting the maximum deviation variable to not exceed the preset threshold.

[0022] Optionally, constructing the objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost includes:

[0023] The weighted total completion time is determined by summing the completion times of all accepted workpieces and using a first weighting coefficient.

[0024] The maximum completion time deviation cost is determined by using the maximum deviation variable and the second weighting coefficient.

[0025] The compression cost is determined by summing the products of the unit compression cost and the resource input for each schedulable workpiece.

[0026] The rejection cost is determined by summing the unit rejection costs of each rejected workpiece.

[0027] Optionally, the maximum completion time deviation constraint consists of a deviation measurement variable and a maximum deviation variable, wherein the maximum deviation variable is not greater than a preset deviation threshold.

[0028] Optionally, establishing a mixed-integer programming model based on the objective function and the maximum completion time deviation constraint includes:

[0029] The last original workpiece is designated as the critical workpiece. The scheduling sequence before the critical workpiece is divided into the left scheduling segment, and the scheduling sequence after the critical workpiece is divided into the right scheduling segment.

[0030] By sorting all accepted workpieces according to their actual processing time in the left and right scheduling segments respectively, a local shortest processing time priority structure is constructed. The mixed integer programming model is established based on the objective function and the maximum completion time deviation constraint. The local shortest processing time priority structure is used to represent the sorting property of the optimal scheduling scheme corresponding to the mixed integer programming model.

[0031] Optionally, after establishing the mixed-integer programming model based on the objective function and the maximum completion time deviation constraint, the method further includes:

[0032] A multidimensional box set is constructed by dividing the state space of the mixed integer programming model into equal intervals.

[0033] By mapping some schedules with similar state values ​​to the same set of boxes, state clustering results are obtained;

[0034] A compressed state space is constructed by retaining only the scheduling states with the minimum disturbance in each set of boxes. The compressed state space is used to reserve a larger time margin for subsequent workpieces while satisfying the maximum completion time deviation constraint.

[0035] Optionally, the intelligent scheduling method for product manufacturing further includes:

[0036] A scaling factor is constructed using preset approximate accuracy parameters and the total number of workpieces, wherein the scaling factor is used to control the fineness of state space discretization.

[0037] Secondly, this application provides a product manufacturing intelligent scheduling device, comprising:

[0038] The acquisition module is used to acquire the original set of workpieces and the newly arrived set of workpieces, wherein the original set of workpieces includes the original workpieces, the newly arrived set of workpieces includes the newly arrived workpieces, and there is an initial optimal scheduling scheme for the original set of workpieces.

[0039] A setting module is used to set optional processing strategies for each newly arriving workpiece, wherein the optional processing strategies include accepting and reducing processing time, or rejecting and paying rejection costs;

[0040] The constraint module is used to limit the absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme to not exceed a preset threshold, thereby obtaining the maximum completion time deviation constraint.

[0041] The objective function module is used to construct an objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost;

[0042] The modeling module is used to establish a mixed integer programming model based on the objective function and the maximum completion time deviation constraint.

[0043] The beneficial effects of the intelligent scheduling method for product manufacturing in this application are:

[0044] By acquiring the original set of workpieces, its initial optimal scheduling scheme, and the set of newly arriving workpieces, a rescheduling framework closely resembling real-world production dynamic disturbances was constructed, providing a foundation for subsequent disturbance control and flexible decision-making. Optional processing strategies were set for each newly arriving workpiece, endowing the scheduling model with autonomous discretion and improving adaptability and economic rationality. The introduction of a maximum completion time deviation constraint quantifies the degree of disturbance to the original plan as a hard constraint, ensuring the fulfillment of original production commitments and the continuity of production rhythm. Based on an objective function constructed from weighted total completion time, maximum completion time deviation cost, compression cost, and rejection cost, multi-dimensional management objectives were unified, guiding scheduling decisions to make global trade-offs between efficiency, stability, resource input, and order acceptance. A mixed-integer programming model based on the objective function and the maximum completion time deviation constraint provides a rigorous mathematical optimization framework, enabling efficient solutions for high-quality scheduling schemes. The final scheduling scheme not only possesses responsiveness, stability, and economy but is also particularly suitable for manufacturing environments with high disturbance and high reliability requirements, effectively balancing the relationship between dynamic response and plan robustness. Attached Figure Description

[0045] Figure 1This is a flowchart illustrating the intelligent scheduling method for product manufacturing according to an embodiment of this application.

[0046] Figure 2 This is an example diagram of an electronic device according to an embodiment of this application. Detailed Implementation

[0047] To make the above-mentioned objects, features, and advantages of this application more apparent and understandable, specific embodiments of this application are described in detail below with reference to the accompanying drawings. Although some embodiments of this application are shown in the drawings, it should be understood that this application can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this application. It should be understood that the accompanying drawings and embodiments of this application are for illustrative purposes only and are not intended to limit the scope of protection of this application.

[0048] It should be understood that the steps described in the method embodiments of this application may be performed in different orders and / or in parallel. Furthermore, the method embodiments may include additional steps and / or omit the steps shown. The scope of this application is not limited in this respect.

[0049] The term "comprising" and its variations as used herein are open-ended, meaning "including but not limited to"; the term "based on" means "at least partially based on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one additional embodiment"; the term "some embodiments" means "at least some embodiments"; and the term "optionally" means "optional embodiments". Definitions of other terms will be given in the description below. It should be noted that the concepts of "first," "second," etc., mentioned in this application are used only to distinguish different devices, modules, or units, and are not intended to limit the order of functions performed by these devices, modules, or units or their interdependencies.

[0050] It should be noted that the terms "one" and "more" used in this application are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise expressly indicated in the context, they should be understood as "one or more".

[0051] The names of messages or information exchanged between multiple devices in the embodiments of this application are for illustrative purposes only and are not intended to limit the scope of these messages or information.

[0052] like Figure 1 As shown in the embodiment of this application, a product manufacturing intelligent scheduling method includes:

[0053] Step S100: Obtain the original workpiece set and the newly arrived workpiece set, wherein the original workpiece set includes the original workpieces and the newly arrived workpiece set includes the newly arrived workpieces, and for the original workpiece set, there is an initial optimal scheduling scheme.

[0054] The initial set of jobs represents a group of jobs that, before the disturbance event occurs, are determined to be processed on a single machine. Each job in this set is called an initial job. For the initial set of jobs, there exists an initial optimal scheduling scheme, which is typically generated based on classical scheduling rules, such as the shortest processing time priority rule, to optimize classical scheduling objectives such as total completion time. The initial optimal scheduling scheme provides a benchmark for subsequent rescheduling.

[0055] The newly arrived workpiece set refers to a group of workpieces added to the production schedule due to changes in external demand, before the original workpieces have even begun processing or are in the process of processing. Each workpiece in the set is called a newly arrived workpiece. Not all newly arrived workpieces need to be included in the production plan; their handling is flexible.

[0056] Step S200: For each newly arrived workpiece, set an optional processing strategy, wherein the optional processing strategy includes accepting and reducing processing time, or rejecting and paying rejection costs.

[0057] For each newly arrived workpiece, one of two processing strategies can be chosen: one is to accept it and reduce processing time, i.e., shorten its actual processing time by investing additional resources such as manpower, energy, or specialized equipment; the other is to reject it, i.e., not to schedule its processing and to bear the corresponding rejection costs. This dual-mode decision-making mechanism enables the scheduling scheme to be dynamically adjusted according to cost-effectiveness, avoiding a decline in overall efficiency due to forcibly accepting all new orders.

[0058] These two strategies constitute a flexible decision-making mechanism, enabling the scheduling model to autonomously select the optimal processing method based on the processing characteristics, cost parameters, and current disturbance tolerance of each newly arriving workpiece. While controlling disturbances to the original plan, this effectively balances production revenue, resource consumption, and customer service levels, enhancing the adaptability and economy of the manufacturing process in dynamic environments.

[0059] Step S300: Limit the absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme to no more than a preset threshold, thereby obtaining the maximum completion time deviation constraint.

[0060] The maximum completion time deviation constraint represents a restriction imposed on the difference between the completion time of an original job in the new scheduling scheme and its completion time in the initial optimal scheduling scheme. Specifically, the maximum completion time deviation constraint requires that the completion time offset (i.e., the absolute value of the difference between the two) of any original job after rescheduling must not exceed a pre-given value, which is called the preset threshold K.

[0061] The significance of maximum completion time deviation constraints lies in quantifying and controlling the degree of disruption to existing production plans caused by rescheduling. In real-world manufacturing scenarios, original workpieces typically correspond to delivery schedules already promised to customers. Drastic changes in their completion times can lead to issues such as delivery delays, inventory imbalances, or disruptions in the connection between upstream and downstream processes. By introducing maximum completion time deviation constraints, such disturbances can be limited to an acceptable range, maintaining the basic stability of the original production rhythm.

[0062] Its role is to provide a clear stability boundary for scheduling optimization: while accepting new arriving workpieces, adjusting the processing sequence or compressing processing time, it prevents uncontrollable time delays or advances for the original workpieces, thus balancing the continuity of the plan and the flexibility of scheduling.

[0063] Step S400: Construct an objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost.

[0064] The objective function represents a comprehensive evaluation index for measuring the quality of a scheduling scheme. It is composed of a weighted combination of four cost items, including: weighted total completion time, maximum completion time deviation cost, compression cost, and rejection cost.

[0065] Among them, the weighted total completion time reflects the cumulative effect of the processing time of all accepted workpieces (including original workpieces and newly arrived workpieces), reflecting production efficiency and work-in-process turnover level; the maximum completion time deviation cost represents the stability cost caused by the deviation of the original workpiece completion time due to rescheduling, and its magnitude is proportional to the maximum deviation; the compression cost corresponds to the economic expenditure formed by the additional resources invested to shorten the processing time of newly arrived workpieces; the rejection cost represents the commercial or contractual cost incurred for rejecting some newly arrived workpieces.

[0066] Incorporating these four costs into the objective function establishes a multi-dimensional optimization criterion, avoiding the one-sidedness of decision-making under a single objective. This objective function guides the scheduling scheme to achieve a balance between efficiency, stability, resource consumption, and order acceptance, ensuring that the final result neither excessively sacrifices the reliability of the original plan nor blindly accepts all new orders, leading to resource waste or uncontrolled disruption.

[0067] Step S500: Based on the objective function and the maximum completion time deviation constraint, establish a mixed integer programming model.

[0068] Mixed-integer programming models represent mathematical optimization models built around the objective function and the maximum completion time deviation constraint. This model includes both continuous variables (such as completion time and resource input) and 0-1 integer variables (such as whether a job is accepted and the adjacency order between jobs), used to formally describe the decision logic and constraints in rescheduling problems.

[0069] The foundation lies in unifying the various decisions made in actual manufacturing scheduling, including accepting or rejecting newly arriving workpieces, the degree of compression of processing time, the order of workpiece arrangement, and the tolerance limit for disturbances to the original plan, into a computable mathematical expression. The objective function provides the direction of optimization, while the maximum completion time deviation constraint defines the boundary of feasible solutions; together, they define the solution space of the model.

[0070] This transforms complex dynamic scheduling problems into a standard operations research framework, giving multi-objective, multi-constraint decision-making processes a rigorous mathematical structure. It provides clear and consistent problem input for subsequent solution algorithms, avoiding suboptimal or unreproducible results caused by relying on heuristic rules.

[0071] In this embodiment, by acquiring the original set of workpieces, its initial optimal scheduling scheme, and the set of newly arriving workpieces, a rescheduling framework closely resembling real-world production dynamic disturbances is constructed, providing a foundation for subsequent disturbance control and flexible decision-making. Optional processing strategies are set for each newly arriving workpiece, endowing the scheduling model with autonomous discretion and improving adaptability and economic rationality. The introduction of a maximum completion time deviation constraint quantifies the degree of disturbance to the original plan as a hard constraint, ensuring the fulfillment of original production commitments and the continuity of production rhythm. Based on an objective function constructed from the weighted total completion time, maximum completion time deviation cost, compression cost, and rejection cost, multi-dimensional management objectives are unified, guiding scheduling decisions to make a global trade-off between efficiency, stability, resource input, and order selection. A mixed-integer programming model based on the objective function and the maximum completion time deviation constraint provides a rigorous mathematical optimization framework, enabling efficient solutions for high-quality scheduling schemes. The final scheduling scheme not only possesses responsiveness, stability, and economy but is also particularly suitable for manufacturing environments with high disturbance and high reliability requirements, effectively balancing the relationship between dynamic response and plan robustness.

[0072] Optionally, the newly arriving set of jobs includes schedulable jobs and emergency jobs;

[0073] When the newly arrived workpiece is a schedulable workpiece, the processing time is compressed upon acceptance by resource allocation.

[0074] When the newly arrived workpiece is an urgent workpiece, the urgent workpiece is scheduled for processing according to a fixed time when accepted, and the urgent cost is borne when rejected.

[0075] The newly arrived job set contains two types of jobs: schedulable jobs and urgent jobs. This reflects the differences in time flexibility and processing priority between new orders in actual production.

[0076] Scheduled jobs are those whose processing time can be reduced by allocating additional resources. When such jobs are accepted, their actual processing time is less than the normal processing time, with the reduction depending on the amount of resources allocated. This mechanism aims to trade resource adjustments for time flexibility, helping to reduce the impact on the original job completion time and lower overall scheduling costs.

[0077] Urgent workpieces refer to those whose processing time is incompressible and must be processed within a fixed timeframe. When such workpieces are accepted, they are directly included in the scheduling sequence with their fixed processing time; if rejected, the associated urgent costs must be borne. This setting aims to reflect the characteristics of high-priority or rigid-delivery orders, whose rejection costs are usually high, thereby guiding the model to prioritize the acceptance of such workpieces within a controllable disturbance range.

[0078] The distinction between these two types of workpieces and their corresponding processing rules enable the scheduling model to adopt differentiated strategies for new orders of different natures. This avoids resource misallocation or uncontrolled disturbances caused by treating all new workpieces equally. In practice, the model automatically applies the corresponding processing time expression and cost calculation method based on the workpiece type, and coordinates them uniformly in the objective function and constraints, ultimately generating a scheduling scheme that balances efficiency, stability, and order characteristics.

[0079] Optionally, the optional processing strategy is to accept and compress processing time.

[0080] The actual processing time of the newly arrived workpiece is determined by the product of the difference between the normal processing time and the compression rate and the amount of resources invested, wherein the amount of resources invested does not exceed the maximum available resources corresponding to the newly arrived workpiece.

[0081] When a new workpiece arrives and a processing strategy of accepting it and reducing processing time is adopted, its actual processing time is determined by subtracting the product of the compression rate and the resource input from the normal processing time. Here, the normal processing time refers to the standard processing time of the workpiece without additional resource input; the compression rate reflects the processing time that can be reduced per unit of resource input and is an inherent technological attribute of the workpiece; and the resource input represents the actual amount of resources allocated to reduce processing time, and its value is a non-negative integer.

[0082] Resource input is limited by the maximum available resources, which is determined by the normal processing time and compression rate of the workpiece. This limit is used to prevent the processing time from being compressed to an unreasonable or infeasible level. The purpose of this limit is to ensure that the actual processing time is always positive and meets the basic requirements of the physical processing procedure.

[0083] The actual processing time for a new workpiece to be accepted is expressed as follows:

[0084] ,

[0085] in, This represents the normal processing time for workpiece j. This represents the compression ratio of workpiece j. This indicates the amount of resources invested.

[0086] The maximum available resource quantity is expressed as:

[0087] ,

[0088] in, This represents the amount of resources allocated to workpiece j, satisfying 0 < < .

[0089] Optionally, the constraint that the absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme does not exceed a preset threshold, thereby obtaining the maximum completion time deviation constraint, includes:

[0090] A linear inequality is constructed by the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time in the initial optimal scheduling scheme, wherein the linear inequality is used to characterize the advance and delay of the completion time of each original workpiece.

[0091] Using the linear inequality, the deviation measurement variable is defined as the larger of the original workpiece lead time and delay.

[0092] The maximum deviation variable is constructed using the deviation measurement variables of all original workpieces, and the maximum deviation variable is used as the upper bound of all deviation measurement variables;

[0093] The maximum completion time deviation constraint is constructed using the preset threshold, limiting the maximum deviation variable to not exceed the preset threshold.

[0094] The completion time of the original job in the new scheduling scheme may be earlier or later than its completion time in the initial optimal scheduling scheme. To quantify this change, two linear inequalities are introduced to describe the earlier and later completion times of each original job, respectively. These two inequalities are achieved through the relationship between the difference in completion times and a non-negative deviation variable, so that both the earlier and later completion times can be represented by non-negative values.

[0095] Based on this, a deviation metric variable is defined, whose value is the larger of the lead time and delay time for the job, thus uniformly reflecting the absolute degree of disturbance experienced by the job during rescheduling. The purpose of this variable is to transform the two-way time offset into a single metric, facilitating subsequent optimization processing.

[0096] Furthermore, for all original job deviation metrics, a maximum deviation variable is introduced, and a set of inequality constraints ensures that this maximum deviation variable is not less than the deviation metric variable of any original job. Thus, the maximum deviation variable becomes the upper bound of the disturbance level of all original jobs, representing the maximum impact of the entire rescheduling on the original plan.

[0097] Finally, the maximum deviation variable is compared with a preset threshold to form a maximum completion time deviation constraint, requiring that the maximum deviation variable not exceed this threshold. The significance of this constraint lies in transforming the requirement for the stability of the original plan into a hard condition that can be embedded in a mathematical programming model, so that the rescheduling scheme can maintain basic respect for the existing production arrangements while pursuing efficiency.

[0098] In practice, the above variables and inequalities are treated as part of a mixed integer programming model and are processed uniformly by the solver, thereby automatically eliminating scheduling schemes that exceed the limits of disturbance in the feasible solution set.

[0099] The linearized expression for the completion time deviation of each original workpiece is:

[0100] ,

[0101] ,

[0102] in, This indicates the deviation in the completion time of workpiece j. This represents the completion time in the adjusted feasible schedule σ. This indicates the total completion time of the original workpiece and the new workpiece that has been accepted.

[0103] ,

[0104] ,

[0105] in, Indicates the maximum completion time deviation. This indicates a preset threshold.

[0106] Optionally, constructing the objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost includes:

[0107] The weighted total completion time is determined by summing the completion times of all accepted workpieces and using a first weighting coefficient.

[0108] The maximum completion time deviation cost is determined by using the maximum deviation variable and the second weighting coefficient.

[0109] The compression cost is determined by summing the products of the unit compression cost and the resource input for each schedulable workpiece.

[0110] The rejection cost is determined by summing the unit rejection costs of each rejected workpiece.

[0111] The weighted total completion time is obtained by multiplying the sum of the completion times of all accepted workpieces by the first weighting coefficient. It is used to reflect the overall production efficiency and work-in-process turnover level. The weighting coefficient reflects the management preference for sensitivity to completion time.

[0112] The cost of the maximum time deviation is determined by multiplying the maximum deviation variable by the second weighting coefficient. The maximum deviation variable represents the maximum time disturbance caused by rescheduling to the original plan. This cost term is used to quantify the stability loss, and the weighting coefficient reflects the importance attached to the stability of the plan.

[0113] Compression cost is obtained by multiplying the unit compression cost of each schedulable workpiece by its actual resource input and then summing the results. It represents the additional resource cost incurred in shortening processing time, and its magnitude is directly related to the resource input strategy.

[0114] Rejection costs are formed by the sum of the unit rejection costs of each rejected workpiece. They represent the economic or commercial costs incurred for giving up some newly arrived workpieces and are used to balance order acceptance with overall scheduling efficiency.

[0115] The four costs mentioned above together constitute the objective function, which serves as the optimization objective of the mixed-integer programming model in practical implementation. Its significance lies in unifying multi-dimensional management objectives such as efficiency, stability, resource consumption, and order selection into a single optimizable index, enabling the scheduling scheme to minimize overall costs while satisfying disturbance constraints.

[0116] The objective function is expressed as:

[0117] Mi ,

[0118] Where q represents the first weighting coefficient (cost per unit completion time). This represents the set of original workpieces and newly arrived workpieces. This indicates the total completion time of the original workpiece and the new workpiece accepted. This represents the second weighting coefficient (unit disturbance cost). Indicates the maximum completion time deviation. Indicates the newly arrived set of workpieces. This represents the unit compression cost of workpiece j. This represents the amount of resources required for workpiece j. This represents the unit rejection cost of workpiece j. This indicates that the variable is accepted.

[0119] Optionally, the maximum completion time deviation constraint consists of a deviation measurement variable and a maximum deviation variable, wherein the maximum deviation variable is not greater than a preset deviation threshold.

[0120] The deviation metric variable is used to characterize the degree of completion time deviation of each original job in the new scheduling scheme relative to the initial optimal scheduling scheme. Its value is not less than the larger of the advance and delay of the completion time of the job, so as to reflect the absolute magnitude of the disturbance of a single job in a non-negative value.

[0121] The maximum deviation variable is used to characterize the maximum value of the disturbance level among all original workpieces. It is defined as a variable that is not less than the upper bound of any deviation measurement variable. The purpose of this variable is to aggregate the disturbance information scattered across multiple workpieces into a single index, which facilitates overall control.

[0122] The maximum completion time deviation constraint is composed of the two types of variables mentioned above. Its core requirement is that the value of the maximum deviation variable must not exceed the preset deviation threshold. This threshold is the maximum allowable disturbance set by the user based on production stability requirements, representing the upper limit of tolerance for changes to the original plan.

[0123] In practice, this constraint is implemented as part of a mixed-integer programming model through linear inequalities, which enables the solution process to automatically exclude any scheduling schemes that cause the overall disturbance of the original workpiece to exceed a preset threshold.

[0124] Optionally, establishing a mixed-integer programming model based on the objective function and the maximum completion time deviation constraint includes:

[0125] The last original workpiece is designated as the critical workpiece. The scheduling sequence before the critical workpiece is divided into the left scheduling segment, and the scheduling sequence after the critical workpiece is divided into the right scheduling segment.

[0126] By sorting all accepted workpieces according to their actual processing time in the left and right scheduling segments respectively, a local shortest processing time priority structure is constructed. The mixed integer programming model is established based on the objective function and the maximum completion time deviation constraint. The local shortest processing time priority structure is used to represent the sorting property of the optimal scheduling scheme corresponding to the mixed integer programming model.

[0127] In one embodiment, a critical workpiece refers to the last original workpiece in the scheduling sequence ordered by actual processing time. Using this as a dividing point, the scheduling sequence is divided into a left scheduling segment and a right scheduling segment; the former includes the critical workpiece and all workpieces preceding it, while the latter includes all workpieces following the critical workpiece.

[0128] The Local Shortest Processing Time First (LST) structure refers to a system where, within the left and right scheduling segments, all accepted jobs are sorted in a non-decreasing order according to their actual processing times. This structure is not directly incorporated into the model as a hard constraint, but rather reflects the inherent sorting pattern of the optimal solution in a mixed-integer programming model.

[0129] The significance of this ordering property lies in revealing the structural characteristics of the optimal scheduling scheme: although the global order may deviate from the classic SPT rule due to perturbation constraints, the local optimal timing arrangement is still maintained within the two sub-intervals of the critical workpiece division.

[0130] In practical implementation, the mixed-integer programming model itself consists of mathematical expressions such as the objective function, maximum completion time deviation constraint, and scheduling logic constraints; while the local shortest processing time first structure is used to describe the typical form of the optimal solution of the model and guide the construction of efficient solution strategies without changing the basic variables and constraint forms of the model. Its role is to connect the mathematical model with scheduling practice, enhancing the interpretability and solvability of the model.

[0131] In one embodiment, all original workpieces and newly arrived workpieces are pre-sorted according to their actual processing time;

[0132] Using the last original workpiece after sorting as the critical workpiece, the scheduling sequence is divided into a left scheduling segment and a right scheduling segment;

[0133] Based on predefined state variables, all feasible partial scheduling states are recursively generated through state transition rules.

[0134] Under the premise of satisfying the maximum completion time deviation constraint, the state that minimizes the overall cost is selected from the final state, and the acceptance / rejection decision and final arrangement order of the workpiece are determined accordingly.

[0135] In practice, the pre-sorting adopts the shortest processing time priority rule to ensure that the workpiece sequence meets the condition that the actual processing time is not reduced, thus providing a foundation for subsequent utilization of the optimal solution structure. The introduction of critical workpieces is used to reflect the anchoring effect of the original workpieces in the scheduling, and their positions are naturally divided into a left segment that is more strongly influenced by the original plan and a relatively free right segment.

[0136] The state variables include the number of jobs in the left segment, the number of jobs in the right segment, the current maximum completion time deviation, the cumulative resource input, and the cumulative total completion time, which together constitute a five-dimensional state space. The state transition is based on six scenarios derived from theory, covering decision paths such as whether a new job is accepted (inserted into the left or right segment with normal or compressed time) or rejected. Each step ensures scheduling legality and timing consistency.

[0137] All generated states are constrained by the value range of each variable; for example, the maximum completion time deviation does not exceed a preset threshold K. After all jobs have been processed, the state with the smallest objective function value is selected from all final states. This objective function consists of the weighted total completion time, compression cost, and disturbance penalty term. The final scheduling scheme is derived from the partial scheduling reconstructed from the optimal state, explicitly indicating whether each newly arriving job is accepted, the amount of resources invested, and its specific position in the entire sequence.

[0138] Optionally, after establishing the mixed-integer programming model based on the objective function and the maximum completion time deviation constraint, the method further includes:

[0139] A multidimensional box set is constructed by dividing the state space of the mixed integer programming model into equal intervals.

[0140] By mapping some schedules with similar state values ​​to the same set of boxes, state clustering results are obtained;

[0141] A compressed state space is constructed by retaining only the scheduling states with the minimum disturbance in each set of boxes. The compressed state space is used to reserve a larger time margin for subsequent workpieces while satisfying the maximum completion time deviation constraint.

[0142] After establishing the mixed-integer programming model, an approximate modeling mechanism is introduced to improve the solution efficiency. This mechanism processes multiple continuous variables (such as the number of workpieces in the left segment, the number of workpieces in the right segment, the maximum completion time deviation, the total amount of resources invested, and the cumulative completion time) in the state space generated during the dynamic solution of the model.

[0143] Geometric interval partitioning refers to dividing the range of values ​​for each continuous variable into several sub-intervals in a geometric progression, with the boundaries of adjacent intervals increasing at a fixed ratio. This partitioning method constructs a multidimensional set of boxes composed of multiple dimensional sub-intervals, with each box set corresponding to a discretized state region.

[0144] Partial scheduling with similar state values ​​refers to different scheduling fragments generated during the dynamic recursion process whose state variables fall within the same multidimensional box set. These scheduling fragments are mapped to the same box set, forming a state clustering result, thereby achieving a coarse-grained abstraction of the original state space.

[0145] In each set of boxes, only the scheduling states with the smallest maximum completion time deviation are retained, and the rest are discarded. This operation constructs a compressed state space, which is significantly smaller than the original state space.

[0146] The purpose of the compressed state space is to prioritize scheduling paths with less disturbance, while ensuring that the maximum completion time deviation does not exceed a preset threshold. This allows for a larger time margin for the insertion of subsequent workpieces, preventing later infeasibility due to excessive time window occupation by early states. This method effectively reduces computational complexity while controlling approximation errors, achieving a high-quality scheduling scheme in polynomial time.

[0147] Optionally, it also includes:

[0148] A scaling factor is constructed using preset approximate accuracy parameters and the total number of workpieces, wherein the scaling factor is used to control the fineness of state space discretization.

[0149] The approximate accuracy parameter is a positive number given by the user, used to characterize the maximum relative deviation between the allowed solution and the optimal solution. The total number of workpieces refers to the sum of the original workpieces and the number of newly arrived workpieces, reflecting the problem size.

[0150] The scaling factor is determined by the approximate accuracy parameter and the total number of workpieces, and its typical form is 1+ε / (2n), where ε represents the approximate accuracy parameter and n represents the total number of workpieces. This factor is used to control the fineness of the state space discretization.

[0151] In implementation, the scaling factor, as the common ratio of the equal-ratio partitioning, determines the granularity of the division of the value intervals of each continuous variable. When the scaling factor is closer to 1, the partitioning is finer, more states are retained, and the accuracy of the solution is higher; when the scaling factor is larger, the partitioning is coarser, the number of states is reduced, computational efficiency is improved, but the approximation error increases.

[0152] The significance of this scaling factor lies in establishing a quantitative relationship between approximate accuracy and computational complexity, enabling the state compression process to have adjustable and controllable error boundaries. Discretization guided by this factor allows for a scheduling scheme that meets preset accuracy requirements to be obtained in polynomial time, balancing solution efficiency and solution quality.

[0153] In one embodiment, the Fully Polynomial-Time Approximation Scheme (FPTAS) includes:

[0154] Initialize a set of Boolean items containing the initial state and its associated partial schedule; process each artifact sequentially, and deduce all possible true states for the next stage based on the currently true Boolean item;

[0155] Map the new state to the corresponding multidimensional box set. If the set already contains a state, select the one with the smaller perturbation as the state to be retained.

[0156] Select the state that satisfies the maximum completion time deviation constraint and minimizes the overall cost from all final states, and output its corresponding partial schedule as an approximate optimal solution.

[0157] In practical implementation, Boolean terms are used to characterize whether a certain state is reachable. Their five-dimensional coordinates correspond to the discretized interval indices of the number of tasks in the left segment, the number of tasks in the right segment, the maximum completion time deviation, the total resource input, and the cumulative total completion time. Each Boolean term is associated with a specific continuous state, which represents the complete information of the current partial scheduling.

[0158] When processing the (j+1)th job, according to the state transition rules, all possible new states are generated starting from the current true state. These new states are mapped to a set of boxes consisting of equally divided intervals defined by the scaling factor. If a state already exists in a certain set of boxes, the maximum completion time deviation between the old and new states is compared, and the one with the smaller deviation is retained, thus achieving state compression.

[0159] This process significantly reduces the number of states without substantially lowering the solution quality by discarding redundant states with large disturbances. Finally, among all final states that satisfy the condition that the maximum completion time deviation does not exceed a preset threshold, the state that minimizes the sum of the weighted total completion time, compression cost, and disturbance penalty is selected, and its corresponding partial scheduling is the desired approximate solution.

[0160] This application provides an intelligent scheduling device for product manufacturing, comprising:

[0161] The acquisition module is used to acquire the original set of workpieces and the newly arrived set of workpieces, wherein the original set of workpieces includes the original workpieces, the newly arrived set of workpieces includes the newly arrived workpieces, and there is an initial optimal scheduling scheme for the original set of workpieces.

[0162] A setting module is used to set optional processing strategies for each newly arriving workpiece, wherein the optional processing strategies include accepting and reducing processing time, or rejecting and paying rejection costs;

[0163] The constraint module is used to limit the absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme to not exceed a preset threshold, thereby obtaining the maximum completion time deviation constraint.

[0164] The objective function module is used to construct an objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost;

[0165] The modeling module is used to establish a mixed integer programming model based on the objective function and the maximum completion time deviation constraint.

[0166] like Figure 2 As shown in the embodiment of this application, an electronic device 200 includes a memory 210 and a processor 220; the memory 210 is used to store a computer program; the processor 220 is used to implement the product manufacturing intelligent scheduling method as described above when the computer program is executed.

[0167] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the product manufacturing intelligent scheduling method described above.

[0168] Electronic device 200, which can serve as a server or client in this application, is described below as an example of hardware devices that can be applied to various aspects of this application. Electronic device 200 is intended to represent various forms of digital electronic computer devices, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. Electronic device 200 can also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the application described and / or claimed herein.

[0169] Electronic device 200 includes a computing unit that can perform various appropriate actions and processes based on a computer program stored in read-only memory (ROM) or a computer program loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The computing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0170] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. The storage medium can be a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM), etc. In this application, the units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of this application according to actual needs. Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated units can be implemented in hardware or as software functional units.

[0171] Although the above disclosure is provided, the scope of protection of this application is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of this application, and all such changes and modifications will fall within the scope of protection of this application.

Claims

1. A product manufacturing intelligent scheduling method, characterized in that, include: Obtain the original set of jobs and the newly arrived set of jobs, wherein the original set of jobs includes the original jobs and the newly arrived set of jobs includes the newly arrived jobs, and for the original set of jobs, there is an initial optimal scheduling scheme. For each newly arriving workpiece, an optional processing strategy is set, wherein the optional processing strategy includes accepting and reducing processing time, or rejecting and paying rejection costs; The absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme is limited to not exceeding a preset threshold to obtain the maximum completion time deviation constraint, including: A linear inequality is constructed using the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time in the initial optimal scheduling scheme. This linear inequality characterizes the lead time and delay for each original workpiece. A deviation metric variable is defined as the larger of the lead time and delay for the original workpiece using this linear inequality. A maximum deviation variable is constructed using the deviation metric variables for all original workpieces, and this maximum deviation variable serves as the upper bound for all deviation metric variables. Finally, a maximum completion time deviation constraint is constructed using a preset threshold, limiting the maximum deviation variable to not exceed the preset threshold. The objective function is constructed based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost. This includes: determining the weighted total completion time by summing the completion times of all accepted jobs and using a first weighting coefficient; determining the maximum completion time deviation cost by summing the maximum deviation variable and a second weighting coefficient; determining the compression cost by summing the products of the unit compression cost and the resource input for each schedulable job; and determining the rejection cost by summing the unit rejection costs for each rejected job. Based on the objective function and the maximum completion time deviation constraint, a mixed integer programming model is established.

2. The intelligent scheduling method for product manufacturing according to claim 1, characterized in that, The newly arriving set of jobs includes schedulable jobs and emergency jobs; When the newly arrived workpiece is a schedulable workpiece, the processing time is compressed upon acceptance by resource allocation. When the newly arrived workpiece is an urgent workpiece, the urgent workpiece is scheduled for processing according to a fixed time when accepted, and the urgent cost is borne when rejected.

3. The intelligent scheduling method for product manufacturing according to claim 1, characterized in that, The optional processing strategy is to accept and compress processing time. The actual processing time of the newly arrived workpiece is determined by the product of the difference between the normal processing time and the compression rate and the amount of resources invested, wherein the amount of resources invested does not exceed the maximum available resources corresponding to the newly arrived workpiece.

4. The intelligent scheduling method for product manufacturing according to claim 1, characterized in that, The maximum completion time deviation constraint consists of a deviation measurement variable and a maximum deviation variable, wherein the maximum deviation variable is not greater than a preset deviation threshold.

5. The intelligent scheduling method for product manufacturing according to claim 1, characterized in that, The establishment of the mixed-integer programming model based on the objective function and the maximum completion time deviation constraint includes: The last original workpiece is designated as the critical workpiece. The scheduling sequence before the critical workpiece is divided into the left scheduling segment, and the scheduling sequence after the critical workpiece is divided into the right scheduling segment. By sorting all accepted workpieces according to their actual processing time in the left and right scheduling segments respectively, a local shortest processing time priority structure is constructed. The mixed integer programming model is established based on the objective function and the maximum completion time deviation constraint. The local shortest processing time priority structure is used to represent the sorting property of the optimal scheduling scheme corresponding to the mixed integer programming model.

6. The intelligent scheduling method for product manufacturing according to claim 1, characterized in that, After establishing the mixed-integer programming model based on the objective function and the maximum completion time deviation constraint, the method further includes: A multidimensional box set is constructed by dividing the state space of the mixed integer programming model into equal intervals. By mapping some schedules with similar state values ​​to the same set of boxes, state clustering results are obtained; A compressed state space is constructed by retaining only the scheduling states with the minimum disturbance in each set of boxes. The compressed state space is used to reserve a larger time margin for subsequent workpieces while satisfying the maximum completion time deviation constraint.

7. The intelligent scheduling method for product manufacturing according to claim 6, characterized in that, Also includes: A scaling factor is constructed using preset approximate accuracy parameters and the total number of workpieces, wherein the scaling factor is used to control the fineness of state space discretization.

8. A product manufacturing intelligent scheduling device, characterized in that, include: The acquisition module is used to acquire the original set of workpieces and the newly arrived set of workpieces, wherein the original set of workpieces includes the original workpieces, the newly arrived set of workpieces includes the newly arrived workpieces, and there is an initial optimal scheduling scheme for the original set of workpieces. A setting module is used to set optional processing strategies for each newly arriving workpiece, wherein the optional processing strategies include accepting and reducing processing time, or rejecting and paying rejection costs; A constraint module is used to limit the absolute value of the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time of the original workpiece in the initial optimal scheduling scheme to not exceed a preset threshold, thereby obtaining a maximum completion time deviation constraint. This includes: constructing a linear inequality using the difference between the completion time of the original workpiece in the new scheduling scheme and the completion time in the initial optimal scheduling scheme, where the linear inequality characterizes the lead time and delay of each original workpiece; defining a deviation metric variable as the larger of the lead time and delay of the original workpiece using the linear inequality; constructing a maximum deviation variable using the deviation metric variables of all original workpieces, and using the maximum deviation variable as the upper bound of all deviation metric variables; and constructing the maximum completion time deviation constraint using the preset threshold, limiting the maximum deviation variable to not exceed the preset threshold. The objective function module is used to construct an objective function based on the weighted total completion time, the maximum completion time deviation cost, the compression cost, and the rejection cost. This includes: determining the weighted total completion time by summing the completion times of all accepted workpieces and using a first weighting coefficient; determining the maximum completion time deviation cost by using the maximum deviation variable and a second weighting coefficient; determining the compression cost by summing the products of the unit compression cost and the resource input for each schedulable workpiece; and determining the rejection cost by summing the unit rejection costs for each rejected workpiece. The modeling module is used to establish a mixed integer programming model based on the objective function and the maximum completion time deviation constraint.

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