Product optimization scheduling method based on limited production resources

Abstract

The invention discloses a product optimization scheduling method based on limited production resources. The method comprises the following steps: constructing a multi-target flexible job shop optimization production scheduling model by taking the minimum total tardiness and the minimum total cost as targets; on the basis of the DRCFJSP mathematical model, the specific number of workers with different technical levels is newly added as decision variables, and an objective function is set as the total cost to construct an optimized production scheduling model with human resource configuration constraints; wherein the total cost comprises workpiece tardiness punishment cost and worker cost in the form of basic salary and performance salary; and constructing a flexible job shop optimized production scheduling model with batch processing constraints by minimizing the total completion time of products with an optimization target. According to the product optimization scheduling method, the requirements of enterprises on delivery cycle, production cost, energy conservation and consumption reduction are met.

Description

Technical Field

[0001] The present invention relates to the technical field of workshop scheduling, and in particular to a product optimization scheduling method based on limited production resources. Background Art

[0002] At present, highly discrete manufacturing enterprises are characterized by a high degree of product personalization, frequent production according to customer order requirements, and a production scale of single-piece small batch production, with large changes in parts. In this case, its production organization becomes more complicated due to the frequent changes in the process. It is basically organized by setting up manufacturing units according to process requirements, and the organization of production resources needs to be effectively matched with the dynamically changing product production. The main differences between this type of manufacturing enterprise and the above-mentioned large-scale, rhythmic manufacturing enterprises are:

[0003] (1) Due to the single-piece small batch production, the product process is long, the process changes quickly, and the process is unstable, which makes it difficult to control the product manufacturing process and to reasonably allocate production resources;

[0004] (2) The contradiction between the complex and changing process and high process requirements and backward processing methods has caused prominent problems in product quality reliability and quality consistency;

[0005] (3) The production process is unstable. Abnormal events that affect production, including orders, equipment, quality, tooling, materials, etc., occur frequently. The random factors that interfere with product production are complex, resulting in a low execution rate of the actual production plan, long product delivery time and a large number of work-in-progress products. Summary of the invention

[0006] The purpose of the present invention is to provide a product optimization scheduling model based on limited production resources, which can scientifically and rationally organize various production resources to meet the needs of enterprises in terms of delivery cycle, production cost, energy saving and consumption reduction.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] A product optimization scheduling method based on limited production resources of the present invention comprises:

[0009] A multi-objective flexible job shop optimization scheduling model is constructed with the goal of minimizing total delay and total cost.

[0010] On the basis of the DRCFJSP mathematical model, the specific number of workers with different technical levels is added as a decision variable, and the objective function is set as the total cost to construct an optimal production scheduling model with human resource allocation constraints; the total cost includes the penalty cost of workpiece delay and the worker cost in the form of basic salary plus performance salary;

[0011] A flexible job shop scheduling model with batch constraints is constructed with the optimization goal of minimizing the total completion time of the product.

[0012] Furthermore, the objective function of the multi-objective flexible job shop optimization scheduling model is as follows:

[0013] Min{Maxc i ,i=1,2,...,n} (1)

[0014]

[0015] Among them, formula (1) and formula (2) are the two objective functions of minimizing total delay and minimizing total cost respectively. i For workpiece J i The completion time, C i1 For workpiece J i The processing cost, C i2 For workpiece J i The cost of early completion or delayed delivery, t ijlk For process O ijl In optional machine M k Processing time on, cm k For machine M k The unit time cost of processing, w1 is the penalty value for early completion of parts, w2 is the penalty value for delayed delivery of parts, d i For workpiece J i The delivery time is C i1 The weight of C i2 The weight of

[0016]

[0017] The constraints of the multi-objective flexible job shop optimization scheduling model are as follows:

[0018]

[0019] (c pqsk ×Z pqsk ×X ps )-(c ijlk ×Z ijlk ×X il )+A(1-X il )+A(1-X ps )+

[0020] A(1-Y ijlpqsk ×Z ijlk ×Z pqsk ×X il ×X ps )≥(tpqsk ×Z pqsk ×X ps ) (4)

[0021]

[0022] Y ijlpqsk ×Z ijlk ×Z pqsk ×X il ×X ps ≤1 (7)

[0023] Y ijlpqsk ×X il ≤Z ijlk ×X il (8)

[0024]

[0025] Among them, formula (3) represents the workpiece process constraint, that is, different processes of a workpiece cannot be processed at the same time; formula (4) and formula (5) represent the machine constraint, that is, a machine can only process one process at a time; formula (6) represents the workpiece J i Only one optional process route can be selected; Formulas (7)-(9) indicate that in a scheduling scheme, two different processes can only have one sequence relationship; Formula (10) indicates that each process can only be processed by one machine; Formula (11) indicates that the completion time of all processes is non-negative;

[0026] Where P uj For machine M j No-load power, t j For machine M j Time in no-load state, G i To represent workpiece J i The number of optional process routes contained, P il For workpiece J i The number of processes in the lth process route, t ijlk For process O ijl In optional machine M k Processing time on ijlk >0,c ijlk For process O ijl In optional machine M k The earliest completion time on

[0027]

[0028] Furthermore, the objective function of the optimization scheduling model with human resource allocation constraints is as follows:

[0029] f=min(TC) (12)

[0030] TC=DC+WC (13)

[0031]

[0032] Among them, formula (12) indicates that the optimization goal is to minimize the total cost; formula (13)-formula (15) respectively represent the total cost, delay penalty cost and worker cost of workshop scheduling;

[0033] In the formula, TC is the total cost, DC is the total delay penalty cost, WC is the total worker cost, α i For workpiece J i The unit delay penalty cost, C i For workpiece J i The completion time, D i For workpiece J i Delivery time, wk s is the number of decisions of workers with the sth technical level, K is the set of workers’ technical levels, JB s is the unit time base cost of workers with the sth skill level, JX s is the performance cost per unit time of workers with the sth skill level, n is the number of workpieces, v i For workpiece J i The number of processes, m is the number of machines, t ijqr For process O ij On machine q, by worker W r Processing time;

[0034] The constraints of the optimal scheduling model with human resource allocation constraints are as follows:

[0035]

[0036] T qr +L×(X ijqr -1)≤S ij (18)

[0037] S gh +L×(1-δ ijghq )≥E ij (19)

[0038] T qr +L×(1-ε q'qr )≥T q'r (20)

[0039]

[0040] 0≤wk s ≤wkm s (twenty two)

[0041]

[0042] S ij ≥0,T qr ≥0,t ijqr ≥0 (25)

[0043] Among them, formula (16) indicates that the processing of the process is not allowed to be preempted; formula (17) indicates that there is a sequence constraint between the processes of the same workpiece; formula (18) indicates that each process can only be started after the corresponding machine and worker are ready; formulas (19) and (20) indicate that at the same time, a worker can only operate one machine to process the process; formula (21) indicates that each process can only select one machine and one worker for processing; formula (22) indicates that the number of decisions made by workers of each technical level should not exceed the given maximum number; formula (23) indicates that the total number of decisions made by workers is the sum of the number of decisions made by workers of various technical levels; formula (24) indicates that for any process, at least one worker meets the processing conditions; formula (25) indicates that at time zero, all workpieces have arrived, workers and machines are all ready, and the processing time is greater than 0.

[0044] Furthermore, the objective function of the batch-constrained flexible job shop optimization scheduling model is as follows:

[0045] min C max =min{max(C ik )} (26)

[0046] stmin(S ik )(27)

[0047] S ik ≥S jk +t jk , Z ik =Z jk =1, X ji =1,y k =0 (28)

[0048] S ik' ≥max(C lk ),Z lk =Z ik' =1,Y li =1 (29)

[0049] S i =S j ,C i =C j ,2≤n kw ≤N k ,Z ik =Z jk=1,O i ∈BS kw ,O j ∈BS kw ,y k =1(30)

[0050] in, w=1,2,..., Formula (26) indicates that the optimization goal is to minimize the total completion time of the product; Formula (27) indicates that each process should start processing as early as possible under the constraints of Formulas (28)-(30); Formula (28) indicates that the processes on the same common equipment can only be processed in sequence; Formula (29) indicates that the processing of each process must meet the product process constraints; Formula (30) indicates that the processes in the same batch on the batch processing equipment have the same start time and completion time, and the number of processes in the same batch must be less than the batch processing size.

[0051] Compared with the prior art, the present invention has the following beneficial effects: the present invention uses the integrated optimization scheduling technology of dynamic product production to find various factors affecting its production organization and the coupling change rules between these factors, and then optimizes the design of a product optimization scheduling model that includes a multi-objective flexible job shop optimization scheduling model, an optimization scheduling model with human resource allocation constraints, and a flexible job shop optimization scheduling model with batch processing constraints, so that manufacturing enterprises can scientifically and reasonably organize various production resources, thereby meeting the company's delivery cycle, production cost, energy saving and consumption reduction requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the present invention will be described in detail below in combination with the accompanying drawings and detailed embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative labor. Among them:

[0053] Figure 1 This is a structural diagram of a product optimization scheduling model based on limited production resources in the present invention. DETAILED DESCRIPTION

[0054] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0055] Secondly, the present invention is described in detail with reference to schematic diagrams. When describing the embodiments of the present invention in detail, for the sake of convenience, the cross-sectional diagrams showing the device structure will not be partially enlarged according to the general scale, and the schematic diagrams are only examples, which should not limit the scope of protection of the present invention. In addition, in actual production, the three-dimensional dimensions of length, width and depth should be included.

[0056] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0057] The present invention provides a product optimization scheduling model based on limited production resources, which can scientifically and reasonably organize various production resources to meet the needs of enterprises in terms of delivery cycle, production cost, energy saving and consumption reduction.

[0058] Figure 1 The structure diagram of the product optimization scheduling model based on limited production resources of the present invention is shown in FIG. Figure 1 This product optimization scheduling model based on limited production resources includes a multi-objective flexible job shop optimization scheduling model, an optimization scheduling model with human resource allocation constraints, and a flexible job shop optimization scheduling model with batch processing constraints.

[0059] The following will describe in detail the multi-objective flexible job shop optimization scheduling model, the optimization scheduling model with human resource allocation constraints, and the flexible job shop optimization scheduling model with batch processing constraints.

[0060] (1) Multi-objective flexible job shop optimization scheduling model

[0061] Problem description: The traditional job-shop scheduling problem refers to a scheduling method in which m different machines process n workpieces with unique processing routes, and there is no order constraint between the processes of different workpieces. The flexible job-shop scheduling problem (FJSP) is an extension of JSP, which eliminates the constraint of uniqueness of process routes. Its solution includes two sub-problems: machine allocation and process arrangement. At the same time, in the actual solution process, it is often necessary to coordinate multiple conflicting goals at the same time, which is a complex NP-hard problem. It is necessary to study multi-objective flexible job-shop scheduling.

[0062] Basic assumptions: For flexible process planning, that is, each workpiece has multiple feasible process routes. In order to accurately describe the model, the following assumptions are made:

[0063] ① Each artifact is independent of each other and has no priority difference;

[0064] ② Each device can only process one process at the same time;

[0065] ③Different processes of the same workpiece cannot be processed at the same time;

[0066] ④Once each process of each workpiece begins processing, it cannot be interrupted;

[0067] ⑤The initial state of the device is idle, and at time zero, any task is feasible;

[0068] ⑥After one process of the workpiece is processed, it is immediately transferred to the equipment required for the next process, and the transfer time between them is ignored;

[0069] ⑦ The preparation time of all processes has nothing to do with the processing order and is included in the processing time of the process.

[0070] Model parameters: Before building the model, some symbols used need to be defined and explained as follows:

[0071] J: A collection of artifacts,

[0072] M: a collection of machines,

[0073] d i :Workpiece J i Delivery period;

[0074] P uj :Machine M j No-load power;

[0075] t j :Machine M j Time in no-load state;

[0076] G i :Represents workpiece J i The number of optional process routes included;

[0077] O ijl :Workpiece J i The jth process on the lth process route;

[0078] P il :Workpiece J i The number of processes in the lth process route;

[0079] t ijlk :Process O ijl In optional machine M k Processing time on ijlk >0;

[0080] c ijlk :Process O ijl In optional machine M k The earliest completion time on

[0081] S ijlk :Process O ijl In optional machine M k The start time on

[0082] c i :Workpiece J i completion time;

[0083] T i :Workpiece J i delay;

[0084] cm k :Machine M k Unit time cost of processing;

[0085] w1: penalty value for early completion of parts;

[0086] w2: penalty value for delayed delivery of parts;

[0087] C i1 :Workpiece J i processing costs;

[0088] C i2 :Workpiece J i Costs of early completion or delayed delivery;

[0089] α: C i1 The weight of

[0090] β: C i2 The weight of

[0091]

[0092] Objective function: Assuming that the processing quality of all workpieces meets the requirements, the multi-objective flexible job shop scheduling optimization model for green manufacturing is established as follows:

[0093] (1) The total delay of the workpiece is minimized:

[0094] Min{Maxc i ,i=1,2,...,n} (1)

[0095] (2) Minimum total cost:

[0096]

[0097] The constraints are as follows:

[0098]

[0099] (c pqsk ×Z pqsk ×X ps )-(c ijlk ×Z ijlk ×X il )+A(1-X il )+A(1-Xps )+

[0100] A(1-Y ijlpqsk ×Z ijlk ×Z pqsk ×X il ×X ps )≥(t pqsk ×Z pqsk ×X ps ) (4)

[0101]

[0102] Y ijlpqsk ×Z ijlk ×Z pqsk ×X il ×X ps ≤1 (7)

[0103] Y ijlpqsk ×X il ≤Z ijlk ×X il (8)

[0104]

[0105] In this model, equations (1) and (2) are the two objective functions of minimizing the total delay and minimizing the total cost, respectively. Equation (3) represents the workpiece process constraint, that is, different processes of a workpiece cannot be processed at the same time. Equations (4) and (5) represent the machine constraint, that is, a machine can only process one process at a time. Equation (6) represents the workpiece J i Only one optional process route can be selected; Formulas (7)-(9) indicate that in a scheduling plan, two different processes can only have one sequence relationship; Formula (10) indicates that only one machine can be selected for each process; Formula (11) indicates that the completion time of all processes is non-negative.

[0106] (2) Optimal Scheduling Model with Human Resource Allocation Constraints

[0107] Problem description: There are m (M1, M2, ..., Mm) machines in the flexible workshop, w (W1, W2, ..., Ww) workers can perform the work, and the workers' technical levels can be divided into k (K1, K2, ..., Kk) types, such as: primary, intermediate, and advanced. It is assumed that workers with the same technical level are the same, and workers with different technical levels are different. Now n (J1, J2, ..., Jn) workpieces need to be produced, and each workpiece Ji contains vi (i = 1, 2, ..., n) processes. The set of optional machines for processing each process Oij is Mij, The skill level set of optional workers who can operate machine q (q∈Mij) to complete process Oij is Kijq, Choosing different machines and workers with different technical levels will result in different processing times for the processing process Oij. In addition, the costs of workers with different technical levels are also different. The DRCFJSP considering the optimization of the number of workers is to determine the optimal number of workers configuration plan (i.e. the actual number of workers of each technical level) under the premise of satisfying the process constraints, machine constraints, and worker constraints at the same time, and determine the optimal combination of machines and workers and the optimal start time for each process. The goal of this paper is to minimize the total cost, including the penalty cost for delays and the worker cost, among which the worker cost is composed of the basic wage cost and the performance wage cost.

[0108] Basic assumptions: ① All workpieces have arrived at time 0, and all machines and workers are ready at time 0;

[0109] ② Each workpiece must be processed strictly according to the process sequence, and there is no restriction on the processing sequence between different workpieces;

[0110] ③ The machine can process more than one process, and the worker can operate more than one machine;

[0111] ④At the same time, a machine can only process one process, and a worker can only operate one machine;

[0112] ⑤ There is no priority between workpieces, and preemption is not allowed during processing;

[0113] ⑥ Preparation time and movement time are included in the processing time and can be ignored;

[0114] ⑦ There is an upper limit on the number of workers at each technical level, that is, the number of workers at a certain technical level cannot exceed the given maximum value;

[0115] ⑧The cost difference of processing a process on different machines is small compared to the difference in delay penalty costs and worker costs caused by different scheduling schemes and can be ignored.

[0116] Model parameters: Based on the common DRCFJSP mathematical model, the specific number of workers with different technical levels is added as a decision variable, and the objective function is set to the total cost, including the penalty cost of delayed workpieces and the worker cost in the form of basic salary plus performance salary. In order to clearly express the constructed mathematical model, the symbols and their meanings are shown in the following table:

[0117]

[0118]

[0119]

[0120] Objective function:

[0121] f=min(TC) (12)

[0122] TC=DC+WC (13)

[0123]

[0124] Formula (12) indicates that the optimization goal is to minimize the total cost; Formula (3) to Formula (15) respectively represent the total cost of workshop scheduling, delay penalty cost, and worker cost.

[0125] Constraints:

[0126]

[0127] T qr +L×(X ijqr -1)≤S ij (18)

[0128] S gh +L×(1-δ ijghq )≥E ij (19)

[0129] T qr +L×(1-ε q'qr )≥T q'r (20)

[0130]

[0131] 0≤wk s ≤wkm s (twenty two)

[0132]

[0133] S ij ≥0,T qr ≥0,t ijqr ≥0 (25)

[0134] Formula (16) indicates that the processing of the process is not allowed to be preempted; Formula (17) indicates that there is a sequence constraint between the processes of the same workpiece; Formula (18) indicates that each process can only be started after the corresponding machine and worker are ready; Formulas (19) and (20) indicate that at the same time, a worker can only operate one machine to process the process; Formula (21) indicates that each process can only select one machine and one worker for processing; Formula (22) indicates that the number of decisions made by workers of each technical level should not exceed the given maximum number; Formula (23) indicates that the total number of decisions made by workers is the sum of the number of decisions made by workers of various technical levels; Formula (24) indicates that for any process, at least one worker meets the processing conditions; Formula (25) indicates that at time zero, all workpieces have arrived, workers and machines are all ready, and the processing time is greater than 0.

[0135] (3) Optimal Scheduling Model for Flexible Job Shops with Batch Constraints

[0136] Problem description: Compared with the general comprehensive scheduling problem, the main difference between the batch comprehensive scheduling problem is that the batch processing constraint is added. Due to the particularity of batch processing equipment, the equipment is divided into two categories: ordinary equipment and batch processing equipment. The problem can be described as: the n processes of the product are processed on m equipment, some of which are batch processing equipment, and the processing equipment and processing time of each process are known. It is necessary to determine the processing order and start time of each process on each equipment to optimize a certain performance indicator.

[0137] Basic assumptions: ① Each common device can only process one process at a time;

[0138] ② Each process can only be processed by one device at the same time;

[0139] ③The processing of the process needs to meet the product process constraint requirements;

[0140] ④ Each batch processing equipment can process multiple processes at the same time;

[0141] ⑤Once the process starts, it cannot be interrupted until the processing is completed;

[0142] ⑥All devices are available at zero time.

[0143] In addition to satisfying the above constraints, the batch-constrained scheduling problem studied is also subject to the limitation of the number of simultaneous processing operations of the batch processing equipment on its batch processing volume. The simultaneously processed operations must meet the same start and completion time, and the scheduling goal is still to minimize the total completion time of the product.

[0144] Problem model: Assume that the product has n processes {O i} 1≤i≤n , m devices {M k} 1≤k≤m, C max represents the total completion time; S ik , C ik and t ik Respectively represent process O i On device M k The start time, completion time and processing time on the ji =1 indicates process O j It is process O i The same common equipment is used for the preceding process; li =1 indicates process O l It is process O i The process immediately preceding the process; Z ik =1 indicates process O l On device M k Upper processing; k Is a binary variable. If device M k If it is a batch device, the value is 1, otherwise, the value is 0; when the device M k For batch processing equipment, BS kw Indicates that on device M k The process set of the last w batch; n kw Indicates that on device M k The number of processes in the previous batch w; N k' Indicates device M k Therefore, the mathematical model of the research problem is:

[0145] min C max =min{max(C ik )}(26)

[0146] stmin(S ik )(27)

[0147] S ik ≥S jk +t jk ,Z ik =Z jk =1,X ji =1,y k =0(28)

[0148] S ik' ≥max(C lk ),Z lk =Z ik' =1,Y li =1 (29)

[0149] S i =S j ,C i =C j ,2≤nkw ≤N k ,Z ik =Z jk =1,O i ∈BS kw ,O j ∈BS kw ,y k =1(30)

[0150] in, w=1,2,..., Formula (26) indicates that the optimization goal is to minimize the total completion time of the product; Formula (27) indicates that each process should start processing as early as possible under the constraints of Formulas (28)-(30); Formula (28) indicates that the processes on the same common equipment can only be processed in sequence; Formula (29) indicates that the processing of each process must meet the product process constraints; Formula (30) indicates that the processes in the same batch on the batch processing equipment have the same start time and completion time, and the number of processes in the same batch must be less than the batch processing size.

Claims

1. A product optimization scheduling method based on limited production resources, It is characterized in that The method includes: A multi-objective flexible job shop optimization scheduling model is constructed with the goal of minimizing total delay and total cost. On the basis of the DRCFJSP mathematical model, the specific number of workers with different technical levels is added as a decision variable, and the objective function is set as the total cost to construct an optimal production scheduling model with human resource allocation constraints; the total cost includes the penalty cost of workpiece delay and the worker cost in the form of basic salary plus performance salary; A flexible job shop scheduling model with batch constraints is constructed with the optimization goal of minimizing the total completion time of the product.

2. The product optimization scheduling method according to claim 1, It is characterized in that The objective function of the multi-objective flexible job shop optimization scheduling model is as follows: Min{Maxc i ,i=1,2,...,n} (1) Among them, formula (1) and formula (2) are the two objective functions of minimizing total delay and minimizing total cost respectively. i For workpiece J i The completion time, C i1 For workpiece J i The processing cost, C i2 For workpiece J i The cost of early completion or delayed delivery, t ijlk For process O ijl In optional machine M k Processing time on, cm k For machine M k Unit time cost of processing, w 1 is the penalty value for early completion of parts, w 2 is the penalty value for delayed delivery of parts, d i For workpiece J i The delivery time is C i1 The weight of C i2 The weight of The constraints of the multi-objective flexible job shop optimization scheduling model are as follows: AND ijlpqsk ×Z ijlk ×Z pqsk ×X il ×X ps ≤1 (7) AND ijlpqsk ×X il ≤Z ijlk ×X il (8) Among them, formula (3) represents the workpiece process constraint, that is, different processes of a workpiece cannot be processed at the same time; formula (4) and formula (5) represent the machine constraint, that is, a machine can only process one process at a time; formula (6) represents the workpiece J i Only one optional process route can be selected; Formulas (7)-(9) indicate that in a scheduling scheme, two different processes can only have one sequence relationship; Formula (10) indicates that each process can only be processed by one machine; Formula (11) indicates that the completion time of all processes is non-negative; Where P uj For machine M j No-load power, t j For machine M j Time in no-load state, G i To represent workpiece J i The number of optional process routes contained, P il For workpiece J i The number of processes in the lth process route, t ijlk For process O ijl In optional machine M k Processing time on ijlk >0,c ijlk For process O ijl In optional machine M k The earliest completion time on 3. The product optimization scheduling method according to claim 1, It is characterized in that The objective function of the optimal production scheduling model with human resource allocation constraints is as follows: f=min(TC) (12) TC=DC+WC (13) Among them, formula (12) indicates that the optimization goal is to minimize the total cost; formula (13)-formula (15) respectively represent the total cost, delay penalty cost and worker cost of workshop scheduling; In the formula, TC is the total cost, DC is the total delay penalty cost, WC is the total worker cost, α i For workpiece J i The unit delay penalty cost, C i For workpiece J i The completion time, D i For workpiece J i Delivery time, wk s is the number of decisions of workers with the sth technical level, K is the set of workers’ technical levels, JB s is the unit time base cost of workers with the sth skill level, JX s is the performance cost per unit time of workers with the sth skill level, n is the number of workpieces, v i For workpiece J i The number of processes, m is the number of machines, t ijqr For process O ij On machine q, by worker W r Processing time; The constraints of the optimal scheduling model with human resource allocation constraints are as follows: T qr +L×(X ijqr -1)≤S ij (18) S gh +L×(1-δ ijghq )≥E ij (19) T qr +L×(1-e q ' qr )≥T q ' r (20) 0≤wk s ≤wkm s (22) S ij ≥0,T qr ≥0,t ijqr ≥0 (25) Among them, formula (16) indicates that the processing of the process is not allowed to be preempted; formula (17) indicates that there is a sequence constraint between the processes of the same workpiece; formula (18) indicates that each process can only be started after the corresponding machine and worker are ready; formulas (19) and (20) indicate that at the same time, a worker can only operate one machine to process the process; formula (21) indicates that each process can only select one machine and one worker for processing; formula (22) indicates that the number of decisions made by workers of each technical level should not exceed the given maximum number; formula (23) indicates that the total number of decisions made by workers is the sum of the number of decisions made by workers of various technical levels; formula (24) indicates that for any process, at least one worker meets the processing conditions; formula (25) indicates that at time zero, all workpieces have arrived, workers and machines are all ready, and the processing time is greater than 0.

4. The product optimization scheduling method according to claim 1, It is characterized in that The objective function of the flexible job shop optimization scheduling model with batch processing constraints is as follows: my C max =min{max(C ik )} (26) s.t.min(S ik )(27) S ik ≥S jk +t jk , Z ik =Z jk =1, X ji =1,y k =0 (28) Sik ' ≥max(Clk), Zlk=Zik ' =1, Over=1 (29) S i =S j ,C i =C j ,2≤n kw ≤N k ,Z ik =Z jk =1,O i ∈BS kw ,O j ∈BS kw ,y k =1(30) in, w=1,2,..., Formula (26) indicates that the optimization goal is to minimize the total completion time of the product; Formula (27) indicates that each process should start processing as early as possible under the constraints of Formulas (28)-(30); Formula (28) indicates that the processes on the same common equipment can only be processed in sequence; Formula (29) indicates that the processing of each process must meet the product process constraints; Formula (30) indicates that the processes in the same batch on the batch processing equipment have the same start time and completion time, and the number of processes in the same batch must be less than the batch processing size.

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