A simplified fluid relaxation method for dynamic multiple flexible job-shop scheduling

Abstract

The present invention discloses a simplified fluid relaxation method for dynamic multiple flexible job shop scheduling, which specifically includes the following steps: Step 1: Obtain order arrival according to the scheduling time point, and obtain the number of all unprocessed tasks in the actual scheduling system at time ; Step 2: Determine whether there is an order arrival at the time ; If an order arrives at time , the number of unfinished tasks at time and subsequent time points is obtained by solving a simplified fluid relaxation model, that is, the fluid level at time ; If no order arrives at time , the unfinished fluid level at time and subsequent time points is calculated; Step 3: By updating the simplified fluid relaxation model in real time, and dynamically updating the fluid level, the optimal scheduling scheme is finally obtained. The present invention solves the problem that traditional scheduling methods are difficult to deal with under dynamic multiple constraint environments, and can effectively balance machine workloads and dynamically adapt to real-time changes in tasks.

Description

Technical Field

[0001] The invention relates to the technical field of workshop scheduling, and in particular to a simplified fluid relaxation method for dynamic multiple flexible job shop scheduling. Background Art

[0002] In a flexible job shop, the manufacturing system may need to process different types of workpieces. For example, type A requires high-precision milling and polishing, while type B involves cutting, welding, and assembly. Each workpiece type may require specific machine settings, different process sequences, or different resource constraints. These workpieces differ in complexity, processing sequence, and priority, which makes the scheduling problem more complicated. In addition, the manufacturing system not only needs to optimize resource utilization, but also needs to deal with uncertainties such as random workpiece arrival, random order insertion, and equipment failure. For random order insertion, since the arrival time and quantity of all workpieces cannot be determined in advance, the scheduling plan is often disrupted, which reduces its reliability and requires the scheduling system to be constantly adjusted. This significantly increases the complexity of scheduling.

[0003] The model proposed by Bertsimas et al. (Bertsimas, D., Sethuraman, J. From fluid relaxations topractical algorithms for job shop scheduling: the makespan objective. Math. Program. 92, 61–102 (2002) ) failed to solve the scheduling problem dynamically and lacked adaptability in handling the dynamic arrival of orders.

[0004] Although the model proposed by Ding et al. (Ding, L., Guan, Z., Zhang, Z. (2021). A Fast and EfficientFluid Relaxation Algorithm for Large-Scale Re-entrant Flexible Job ShopScheduling. In: Dolgui, A., Bernard, A., Lemoine, D., von Cieminski, G., Romero, D. (eds) Advances in Production Management Systems. ArtificialIntelligence for Sustainable and Resilient Production Systems. APMS 2021. IFIP Advances in Information and Communication Technology, vol 634. Springer, Cham. ) has certain dynamic processing capabilities, the formula is complex and the derivation process is cumbersome, which is not conducive to practical implementation.

[0005] Based on the above analysis, the present invention studies the dynamic multiple flexible job shop scheduling problem. In this context, the problem becomes more complicated due to dynamic factors and multiple constraints. Faced with large-scale and complex dynamic multiple flexible job shop scheduling problems, we face many challenges, such as how to process large-scale workpieces in a short time, how to respond to the dynamic arrival of orders in real time, how to reduce the workload of adjusting tasks, and how to make the proposed algorithm have generalization capabilities. However, few studies have considered designing corresponding methods for this problem to reduce the time complexity of solving the target value. Therefore, it is a problem with important practical significance and needs to be solved urgently. Summary of the invention

[0006] In order to address the shortcomings of existing local search techniques, the present invention uses a simplified fluid relaxation model to simplify the complexity of the dynamic multiple flexible job shop scheduling problem. The dynamic analysis of the system is simplified by treating a single entity as a continuous flow. This method allows the use of continuous mathematical tools (such as differential equations) to approximate and asymptotically describe the behavior of the system. Compared with discrete models, the simplified fluid relaxation model is more feasible in dealing with large-scale and complex dynamic multiple flexible job shop scheduling problems. Since it deals with continuous variables rather than a large number of discrete states, the computational burden can be significantly reduced.

[0007] The present invention provides a simplified fluid relaxation method for dynamic multiple flexible job shop scheduling, comprising the following steps:

[0008] Step 1: Get the order arrival status according to the scheduling time point and get the time The number of all unprocessed tasks in the actual scheduling system;

[0009] Step 2: Determine the time Whether there are orders arriving at the time;

[0010] If the time When an order arrives, the time is obtained by solving the simplified fluid relaxation model and subsequent time points The number of unfinished tasks, that is, the number of and Fluid levels;

[0011] If the time No order arrives at this time, and the time is calculated and subsequent time points unfinished fluid levels;

[0012] Step 3: finally obtaining an optimal scheduling solution by updating the simplified fluid relaxation model in real time and dynamically updating the fluid level;

[0013] In time time and subsequent time The fluid level at is calculated as follows:

[0014] ;

[0015] In the formula, Number the machine. is the number of machines, and the machine set is represented by , Artifact type, For the process, For in time The raw data in the actual scheduling system The number of tasks, including Indicates the task, For in time The unfinished simplified fluid relaxation model Number of tasks, For the task In the machine Processing rate on For in time The maximum completion time of the entire schedule is All machine processing tasks Total processing time; , , , .

[0016] Furthermore, at the time point In case of dynamic order arrival:

[0017] For the task In the machine The processing time on , ;

[0018] In time When an order arrives, first get the unprocessed order in the actual scheduling system. Number of tasks ;

[0019] According to the Solving the simplified fluid relaxation model, we obtain The maximum completion time of the entire schedule and all machine processing tasks Total processing time ;

[0020] According to the , And in the machine Processing rate Get in time time and subsequent time The fluid level at and ;

[0021] If there are tasks that can be processed and machines that can be selected, the processing is scheduled; if there are no tasks that can be processed and machines that can be selected, the time point is moved to the earliest time point where the machine is available and tasks can be selected for processing at this time;

[0022] Repeat the above steps, update the simplified fluid relaxation model and dynamically update the task fluid level in real time, and finally obtain the optimal scheduling solution ( ).

[0023] Furthermore, the time When an order arrives, first get the unprocessed order in the actual scheduling system. Number of tasks The calculation method is:

[0024] ;

[0025] in, Indicates all new orders Number of tasks, Indicates all the unfinished processing of the previous order before the new order arrives. Number of tasks.

[0026] Further, the obtained The maximum completion time of the entire schedule and all machine processing tasks Total processing time The objectives, model constraints and explanations are as follows:

[0027] ;

[0028] ;

[0029] ;

[0030] The objective function achieves the reduction of the overall scheduling completion time by balancing and optimizing the workload of all machines; secondly, by ensuring that all available machines In time right The total workload completed must be proportional to the time The total number of unprocessed tasks is fully matched to ensure that the total demand of each process is equal to the processing capacity of the machine, and the specified allocation to the machine implement Processing time Must be non-negative.

[0031] Furthermore, at the time point No order dynamic arrival situation:

[0032] For the task In the machine The processing time on , ;

[0033] In time When no order arrives, first get the unprocessed orders in the actual scheduling system. Number of tasks ;

[0034] According to the number of unprocessed tasks, the time time and subsequent time The fluid level at and ;

[0035] If there are tasks that can be processed and machines that can be selected, the processing is scheduled. If there are no tasks that can be processed and machines that can be selected, the time point is moved to the earliest time point where the machine is available and tasks can be selected for processing at this time;

[0036] Repeat the above steps, update the simplified fluid relaxation model and dynamically update the task fluid level in real time, and finally obtain the optimal scheduling solution ( ).

[0037] The simplified fluid relaxation method for dynamic multiple flexible job shop scheduling provided by the present invention has the following technical effects:

[0038] Method level:

[0039] (1) The present invention transforms the discrete tasks in the dynamic multiple flexible job shop scheduling problem into continuous flow by introducing a simplified fluid relaxation model, which greatly simplifies the calculation process of dynamic analysis and state transfer and reduces the complexity of high-dimensional discrete state space.

[0040] (2) Through mathematical modeling of continuous variables, the present invention avoids the high-overhead operation of solving large-scale task states one by one in the traditional discrete scheduling model, effectively reducing the complexity of solving the scheduling problem;

[0041] (3) During the scheduling process, the fluid level and machine working time of the task are recorded in real time, so that the system can quickly respond to the dynamic arrival of orders and real-time changes in tasks, ensuring that the scheduling system has high real-time and robustness;

[0042] (4) Based on the optimal scheduling framework of the simplified fluid relaxation model, the goal of minimizing the maximum completion time is solved through continuous mathematical tools, which further improves the computational efficiency and the optimization quality of the scheduling solution.

[0043] Application level:

[0044] (1) Compared with the traditional discrete model scheduling method, the present invention adopts a simplified continuous variable description of the fluid relaxation model, which significantly reduces the calculation time of large-scale dynamic task scheduling, allowing the system to generate optimization solutions more quickly;

[0045] (2) The present invention can dynamically adapt to the real-time arrival of orders and maintain the continuity and efficiency of production in a complex production environment by quickly adjusting the scheduling plan, thereby reducing idle resources and increased production costs caused by scheduling delays;

[0046] (3) The optimized scheduling scheme effectively reduces the idle time of machines and resources, improves the utilization and reliability of the production system, and avoids bottlenecks caused by unreasonable scheduling in the production process;

[0047] (4) The present invention is applicable to scenarios where dynamic tasks change frequently, and can provide enterprises with efficient and stable scheduling optimization solutions to help improve the overall efficiency of the production line and reduce operating costs.

[0048] Compared with the existing fluid models, the simplified fluid relaxation model proposed in the present invention has significant advantages in dynamic resource allocation and model simplification. The model allows dynamic adjustment of resource allocation in each time interval, thereby optimizing the maximum completion time of the system; at the same time, by refining formulas and simplifying ideas, unnecessary complexity is reduced, which not only reduces the difficulty of implementation, but also improves the efficiency and operability in practical applications. The present invention can effectively cope with complex scenarios such as dynamic order arrival and coexistence of multiple tasks, and provides an efficient and practical solution to the dynamic multi-constrained flexible job shop scheduling problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 The Gantt chart of the dynamic multiple flexible job shop scheduling of the present invention, wherein (a) is the second order A 2 Arrival before the first order A 1 The initial scheduling Gantt chart of (b) is the second order A 2 Complete scheduling Gantt chart upon arrival;

[0050] Figure 2 The simplified fluid relaxation model flow chart provided by the present invention;

[0051] Figure 3 Comparison chart of confidence intervals of the present invention. DETAILED DESCRIPTION

[0052] Embodiments of the present invention will now be described more fully below with reference to the accompanying drawings showing embodiments of the present invention. However, the present invention can be implemented in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and the scope of the present invention will be fully conveyed to those skilled in the art. Throughout the text, the same numerals represent the same elements.

[0053] Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by those of ordinary skill in the art to which the present invention belongs. It will be further understood that, unless expressly defined herein, the terms used herein should be interpreted as having a meaning consistent with the meaning in the context of this specification and the relevant art, and will not be interpreted in an idealized or overly formal sense.

[0054] The present invention is described below with reference to flowcharts and / or block diagrams of methods, systems and computer program products according to embodiments of the present invention. It will be understood that some blocks of the flowchart illustrations and / or block diagrams and combinations of some blocks of the flowchart illustrations and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be stored or implemented in a microcontroller, a microprocessor, a digital signal processor (DSP), a field programmable gate array (FPGA), a state machine, a programmable logic controller (PLC) or other processing circuits, a general-purpose computer, a special-purpose computer. A computer or other programmable data processing device (e.g., a production machine) is used to create a device or block diagram block for implementing the functions / actions specified in the flowchart and / or.

[0055] These computer program instructions may also be stored in a computer-readable memory, which may direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device to implement the functions / actions specified in the flowchart and / or block diagram.

[0056] Computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are performed on a computer or other programmable device to produce a computer-implemented process, thereby making it possible for the instructions executed on the computer or other programmable device. Other programmable devices provide steps for implementing the functions / actions specified in the flow chart and / or block diagram boxes. It should be understood that the functions / actions indicated in the boxes may not occur in the order indicated in the operation diagram. For example, depending on the functions / actions involved, two boxes shown in succession can actually be executed substantially simultaneously, or sometimes these boxes can be executed in the opposite order. Although some figures include arrows on the communication path to show the main direction of communication, it should be understood that communication can occur in the direction opposite to the arrows depicted.

[0057] The specific implementation process of the present invention is as follows:

[0058] Taking parts processing as an example, there are many types of workpieces that need to be processed in the workshop. Each type of workpiece has a fixed processing procedure, which needs to be completed on a specific machine, and the processing time of different machines may be different. First, the workpieces are grouped according to their types, for example, the workpieces are divided into the first type of workpieces (type A) and the second type of workpieces (type B).

[0059] Specifically, the first type of workpiece (Type A): Each workpiece contains multiple processes, such as milling, drilling and polishing operations. Multiple machines can be selected for each process, but the processing time of different machines may vary. The second type of workpiece (Type B): Each workpiece also contains multiple processes, such as cutting, welding and assembly operations. Each process corresponds to a group of available machines, and the processing efficiency and processing time of each machine are different.

[0060] During the processing, all workpieces exist in the workshop at the same time and must be processed in sequence according to the process sequence of each workpiece. In addition, new orders may be accepted during the processing. After accepting the new order, the workpieces that have not been processed will be scheduled for processing together with all the workpieces in the new order. In this case, the scheduling problem is a dynamic multiple flexible job shop scheduling problem.

[0061] Therefore, the present invention provides a simplified fluid relaxation method for dynamic multiple flexible job shop scheduling, such as Figure 1 As shown in the example, the following steps are included:

[0062] Step 1: Get the order arrival status according to the scheduling time point and get the time The number of all unprocessed tasks in the actual scheduling system;

[0063] Step 2: Determine the time Whether there are orders arriving at the time;

[0064] If the time When an order arrives, the time is obtained by solving the simplified fluid relaxation model and subsequent time points The number of unfinished tasks, that is, the number of and Fluid levels;

[0065] If the time No order arrives at this time, and the time is calculated and subsequent time points unfinished fluid levels;

[0066] Step 3: finally obtaining an optimal scheduling solution by updating the simplified fluid relaxation model in real time and dynamically updating the fluid level;

[0067] In time time and subsequent time The fluid level at is calculated as follows:

[0068] ;

[0069] In the formula, Number the machine. is the number of machines, and the machine set is represented by , Artifact type, For the process, For in time The raw data in the actual scheduling system The number of tasks, including Indicates the task, For in time The unfinished simplified fluid relaxation model Number of tasks, For the task In the machine Processing rate on For in time The maximum completion time of the entire schedule is All machine processing tasks Total processing time; , , , .

[0070] Preferably, the time point In case of dynamic order arrival:

[0071] For the task In the machine The processing time on , ;

[0072] In time When an order arrives, first get the unprocessed order in the actual scheduling system. Number of tasks ;

[0073] According to the Solving the simplified fluid relaxation model, we obtain The maximum completion time of the entire schedule and all machine processing tasks Total processing time ;

[0074] According to the , And in the machine Processing rate Get in time time and subsequent time The fluid level at and ;

[0075] If there are tasks that can be processed and machines that can be selected, the processing is scheduled; if there are no tasks that can be processed and machines that can be selected, the time point is moved to the earliest time point where the machine is available and tasks can be selected for processing at this time;

[0076] Repeat the above steps, update the simplified fluid relaxation model and dynamically update the task fluid level in real time, and finally obtain the optimal scheduling solution ( ).

[0077] Preferably, the time When an order arrives, first get the unprocessed order in the actual scheduling system. Number of tasks The calculation method is:

[0078] ;

[0079] in, Indicates all the new orders Number of tasks, Indicates all the unfinished processing of the previous order before the new order arrives. Number of tasks.

[0080] Preferably, the time The maximum completion time of the entire schedule and all machine processing tasks Total processing time The objectives, model constraints and explanations are as follows:

[0081] ;

[0082] ;

[0083] ;

[0084] The objective function achieves the reduction of the overall scheduling completion time by balancing and optimizing the workload of all machines; secondly, by ensuring that all available machines In time right The total workload completed must be proportional to the time The total number of unprocessed tasks is fully matched to ensure that the total demand of each process is equal to the processing capacity of the machine, and the specified allocation to the machine implement Processing time Must be non-negative.

[0085] Preferably, the time point No order dynamic arrival situation:

[0086] For the task In the machine The processing time on , ;

[0087] In time When no order arrives, first get the unprocessed orders in the actual scheduling system. Number of tasks ;

[0088] According to the number of unprocessed tasks, the time time and subsequent time The fluid level at and ;

[0089] If there are tasks that can be processed and machines that can be selected, the processing is scheduled. If there are no tasks that can be processed and machines that can be selected, the time point is moved to the earliest time point where the machine is available and tasks can be selected for processing at this time;

[0090] Repeat the above steps, update the simplified fluid relaxation model and dynamically update the task fluid level in real time, and finally obtain the optimal scheduling solution ( ).

[0091] By recording the current fluid level of the task and the processing load of the machine in real time, when the maximum completion time needs to be calculated, the target value is directly obtained according to the change of the fluid level of the task and the processing time of the machine By dynamically updating the task quantity and machine allocation status, the time for repeated calculations is reduced, and the efficiency and response speed of workshop scheduling are improved.

[0092] Figure 1 (a) and (b) show the Gantt chart of the dynamic multiple flexible job shop scheduling of the present invention, wherein Expressed as No. There are two orders in this example. , , the arrival time of the first order , the arrival time of the second order , the type and quantity of workpieces in each order can be seen from the figure. Figure 1 (a) and (b) show two orders A in detail. 1 , A 2 After they arrived one after another, the scheduling situation of the entire production workshop, Figure 2 A flow chart showing a simplified fluid relaxation model of the present invention is shown, Figure 3is a confidence interval comparison diagram of the present invention, wherein FM applies the proposed simplified fluid relaxation model, and FM_NO does not apply the proposed simplified fluid relaxation model; RPI represents the relative percentage increase as a performance evaluation index, The calculation formula is ,in, represents the maximum completion time obtained when a specific algorithm solves a specific case, and It means the minimum maximum completion time obtained by solving the same example above among all the algorithms used. Specifically, Figure 3 The RPI value shows that the FM The results are obviously better than FM_NO, which shows that the method of the present invention speeds up the calculation time of the target value, makes the model performance fully utilized, and can converge to the best value at a faster convergence speed.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. After reading this application, technical personnel in the relevant field may make various modifications or changes to the present invention with reference to the above embodiments, which are all within the scope of protection claimed in the pending application of the present invention.

Claims

1. A simplified fluid relaxation method for dynamic multiple flexible job shop scheduling, characterized in that: The following steps are involved: Step 1: Get the order arrival status according to the scheduling time point and get the time The number of all unprocessed tasks in the actual scheduling system; Step 2: Determine the time Whether there are orders arriving at the time; If the time When an order arrives, the time is obtained by solving the simplified fluid relaxation model and subsequent time points The number of unfinished tasks, that is, the number of and Fluid levels; If the time No order arrives at this time, calculate the time and subsequent time points unfinished fluid levels; Step 3: finally obtaining an optimal scheduling solution by updating the simplified fluid relaxation model in real time and dynamically updating the fluid level; Among them, at time time and subsequent time The fluid level at is calculated as follows: ； In the formula, Number the machine. is the number of machines, and the machine set is represented by , Artifact type, For the process, For in time The raw data in the actual scheduling system The number of tasks, including Indicates the task, For in time The unfinished simplified fluid relaxation model Number of tasks, For the task In the machine Processing rate on For in time The maximum completion time of the entire schedule is All machine processing tasks Total processing time; , , , .

2. A simplified fluid relaxation method for dynamic multiple flexible job shop scheduling according to claim 1, characterized in that: At the point in time In case of dynamic order arrival: For the task In the machine The processing time on , ; In time When an order arrives, first get the unprocessed order in the actual scheduling system. Number of tasks ; According to the Solving the simplified fluid relaxation model, we obtain The maximum completion time of the entire schedule and all machine processing tasks Total processing time ; According to the , And in the machine Processing rate Get in time time and subsequent time The fluid level at and ; If there are tasks that can be processed and machines that can be selected, the processing is scheduled; if there are no tasks that can be processed and machines that can be selected, the time point is moved to the earliest time point where the machine is available and tasks can be selected for processing at this time; Repeat the above steps, update the simplified fluid relaxation model and dynamically update the task fluid level in real time, and finally obtain the optimal scheduling solution ( ).

3. A simplified fluid relaxation method for dynamic multiple flexible job shop scheduling according to claim 2, characterized in that: Said in time When an order arrives, first get the unprocessed order in the actual scheduling system. Number of tasks The calculation method is: ； in, Indicates all the new orders Number of tasks, Indicates all the unfinished processing of the previous order before the new order arrives. Number of tasks.

4. A simplified fluid relaxation method for dynamic multiple flexible job shop scheduling according to claim 2, characterized in that: The obtained The maximum completion time of the entire schedule and all machine processing tasks Total processing time The objective function is as follows: ； ； 。 5. A simplified fluid relaxation method for dynamic multiple flexible job shop scheduling according to claim 4, characterized in that: All available machines In time right The total workload completed must be proportional to the time The total number of unprocessed tasks when the specified machine is assigned exactly matches implement Processing time is non-negative.

6. A simplified fluid relaxation method for dynamic multiple flexible job shop scheduling according to claim 1, characterized in that: At the point in time No order dynamic arrival: For the task In the machine The processing time on , ; In time When no order arrives, first get the unprocessed orders in the actual scheduling system. Number of tasks ; According to the number of unprocessed tasks, the time time and subsequent time The fluid level at and ; If there are tasks that can be processed and machines that can be selected, the processing is scheduled. If there are no tasks that can be processed and machines that can be selected, the time point is moved to the earliest time point where the machine is available and tasks can be selected for processing at this time; Repeat the above steps, update the simplified fluid relaxation model and dynamically update the task fluid level in real time, and finally obtain the optimal scheduling solution ( ).

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