High-end equipment supply chain double-agent cooperative scheduling method based on flexible production line opening

Abstract

The invention provides a high-end equipment supply chain double-agent cooperative scheduling method based on flexible production line opening, and relates to the technical field of production scheduling. The scheduling method comprises the following steps: setting input parameters and operation parameters, constructing an initial solution set on the premise of preferentially satisfying an agent 2, and selecting an optimal solution as an initial solution x0; carrying out Shaking operation on the initial solution x0 to obtain a new solution x1, carrying out local search on the x1 to obtain a new solution x2, judging whether the fitness value of the x2 is superior to the fitness value of the x1 or not, if so, continuing iteration by taking the x2 as the initial solution until a global optimal solution xbest is searched, assigning supplier production tasks according to a scheme provided by the xbest, and if not, assigning the supplier production tasks according to the scheme provided by the xbest. The resource utilization efficiency and the operation efficiency of high-end equipment manufacturing enterprises are improved to the maximum extent, and the total cost of a supply chain is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of production scheduling, and in particular to a dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation. Background Art

[0002] In recent years, the high-end equipment market has shown a rapid growth trend. With the continuous expansion of the market and the intensification of competition, the efficiency and quality requirements for batch production and operation and maintenance in the high-end equipment supply chain are getting higher and higher. In the process of ensuring the normal delivery of operation and maintenance spare parts, the total cost of batch production parts can be reduced to the greatest extent, which is of great value to the company's supply chain. Due to the development of a new generation of information technology, high-end equipment manufacturing companies are paying more and more attention to the convenience and richness of dual agents. Dual agent scheduling can be divided into single-stage dual agent scheduling problems and multi-stage agent scheduling problems according to the processing stage. In the field of high-end equipment manufacturing, production and manufacturing is a vital link.

[0003] Taking the aviation industry as an example, large aviation companies rely on suppliers to produce batches of parts, such as batch parts A and B, which are an indispensable basis for aircraft manufacturing. At the same time, in order to ensure the continued safe operation of aircraft, maintenance spare parts such as C are also crucial. When two agents are involved, each agent has a specific role and task. Agent 1 is mainly responsible for the production of batch parts A and B to ensure the smooth progress of the aircraft manufacturing process. Agent 2 focuses on the production of maintenance spare part C to provide support for the subsequent maintenance and operation of the aircraft. Such a dual-agent scheduling problem is of great significance in high-end equipment manufacturing. It requires enterprises to be able to effectively coordinate and manage production activities between different agents to ensure the smoothness and efficiency of the entire manufacturing process.

[0004] In the above context, high-end equipment manufacturing companies set strict time windows for suppliers to deliver batch parts. Once the latest completion deadline is exceeded, the delay penalty cost will be triggered, which is an economic constraint on the supplier's ability to deliver on time. For operation and maintenance spare parts, the urgency is even more significant, and they must be completed unconditionally within the specified time to ensure the continuity and safety of aircraft operations. Therefore, when formulating production plans, companies need to minimize the total delay penalty cost on the basis of meeting the urgent needs of operation and maintenance spare parts, while reasonably controlling the startup cost of the production line to achieve cost-effectiveness optimization. In actual operation, the batch parts of agent 1 and the operation and maintenance spare parts of agent 2 share the supplier's flexible production line resources. This flexible production mode requires highly accurate scheduling and coordination. According to the dynamic changes in the number of workpieces, suppliers need to flexibly adjust the number of production lines to ensure the optimal allocation of resources. However, this adjustment is not unlimited. It is subject to the physical limitation of the total number of production lines of the supplier, requiring the scheduling strategy to consider the actual production capacity boundary while pursuing efficiency.

[0005] In summary, when facing the dual-agent scheduling problem, high-end equipment manufacturing companies need to comprehensively consider multiple dimensions such as time, cost, and resources to formulate an optimal production plan that not only meets production needs but also meets economic benefits. This is not only a test of the supplier's management capabilities, but also the key to improving the overall competitiveness of the company.

[0006] At present, most of the dual-agent collaborative scheduling problems for high-end equipment batch production parts and maintenance spare parts are solved by precise algorithms, heuristic methods or artificial intelligence algorithms. However, when considering the condition that one of the dual agents is an agent for two or more workpieces, the complexity of the problem will be greatly increased, and it will be impossible to find the optimal solution in a short time, which will affect the dual-agent collaborative scheduling of high-end equipment batch production parts and maintenance spare parts. Summary of the invention

[0007] In view of the shortcomings of the prior art, the present invention provides a dual-agent collaborative scheduling method for the high-end equipment supply chain based on the opening of flexible production lines, which solves the problem that the existing collaborative scheduling technology for batch production parts and operation and maintenance accessories of high-end equipment in the production stage cannot quickly and accurately obtain the optimal solution while considering multiple workpiece agents.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solutions:

[0009] A dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line activation, the scheduling method comprises the following steps:

[0010] S1. Setting input parameters based on variable neighborhood search algorithm according to data generated in the production process of high-end equipment;

[0011] S2. Set the operating parameters of the variable neighborhood search algorithm. The operating parameters include: the maximum number of iterations k of the variable neighborhood search algorithm max ; Number of neighborhood structures N s ; Initialize the number of iterations k = 0; Initialize the neighborhood structure s = 1; Variable neighborhood search algorithm local search neighborhood structure initial weight

[0012] S3, encode the high-end equipment production tasks based on the variable neighborhood search algorithm, and randomly generate the initial solution x0 based on the priority of satisfying the maintenance spare parts product C of agent 2;

[0013] S4, based on the variable neighborhood search algorithm, the initial solution x0 is shaken, and the individual population is obtained in the neighborhood structure. The best individual in the individual population is obtained by the greedy algorithm, and the initial solution is updated by the best individual to obtain the new solution x1;

[0014] S5, based on the roulette probability selection to obtain the local search neighborhood structure, in the selected neighborhood N sPerform local search to obtain the local optimal solution x2;

[0015] S6. Compare the fitness value f(x1) of the new solution x1 with the fitness value f(x2) of the local optimal solution x2. If f(x2)≤f(x1), assign the value of x2 to x1, and continue to perform local search based on the current neighborhood structure to obtain the local optimal solution; if not, set s=s+1 and execute S7.

[0016] S7. Determine s≤N s Is it true? If true, return to S5; if not, set k=k+1 and go to S8;

[0017] S8. Determine k≤k max Is it established? If yes, go to S4; if not, go to S9;

[0018] S9, the algorithm terminates and outputs the global optimal solution x best , for x best Decode and output the set PN l , PN l Represents the set of artifact sequence numbers of all artifacts of agent 1 and agent 2 on production line l.

[0019] Preferably, in S1, the input parameters include:

[0020] The number of workpieces n of product A of agent 1 in the production phase A , the number of workpieces of product B n B , the number of workpieces n of product C of agent 2 C ; Total number of workpieces N = n A +n B +n C ; Maximum number of production lines L in the production phase; Production line startup cost sc; Product X workpiece processing time The set of artifacts for product X is

[0021] Preferably, S3 specifically includes the following steps:

[0022] S3.1. Based on the constraints of the high-end equipment production stage, the processing of workpiece C of agent 2 is given priority; on this basis, the code of the production stage is randomly generated, and all initial solutions x are added to the initial solution set X;

[0023] S3.2, determine whether the number of initial solutions in the initial solution set X is greater than the number of initial solutions N0 in the initial solution set. If not, return to S3.1 to continue producing initial solutions, otherwise output the initial solution set X;

[0024] S3.3. Calculate the fitness value of each solution in the initial solution set X, and select the solution with the smallest fitness value as the initial solution x0.

[0025] Preferably, the fitness value calculation formula in S3.3 is expressed as follows:

[0026]

[0027] in,

[0028] Among them, F min It means that the total cost is minimized;

[0029] D A represents the deadline time of product A in agent 1;

[0030] D B Indicates the deadline time of product B in agent 1;

[0031] α and β are the delay penalty cost coefficients of product A and product B respectively;

[0032] sc represents the setup cost of starting a production line;

[0033] represents the maximum completion time of job X, X∈{A, B, C};

[0034] Q C represents the latest completion time of agent 2;

[0035] represents the production time of the process of high-end equipment product X at the i-th position on production line l, X∈{A, B, C};

[0036] It represents the production time of the process of high-end equipment product X at the last process position j on production line l, X∈{A, B, C}.

[0037] Preferably, the S4 specifically includes the following steps:

[0038] S4.1. Define variables i, j, g = 1, obtain input x0, and the current iteration number is k;

[0039] S4.2, randomly generate two integers in the interval [1, N] and assign them to variables i and j;

[0040] S4.3. Select the i-th and j-th elements in x0, swap them, and get a new solution x1.

[0041] S4.4. Let \(g = g + 1\), and determine whether \(g\leq k\) holds. If it holds, return to S4.2; otherwise, execute step S4.5.

[0042] S4.5. Calculate the fitness value, and determine whether the solution \(x1\) is better than \(x0\). If so, output \(x1\); otherwise, let \(x1 = x0\).

[0043] Preferably, the specific steps of S5 are as follows:

[0044] S5.1. When initially setting the algorithm parameters, due to the unknown structural effectiveness of the local search neighborhood, the initial neighborhood structure weights are default set to be equal; the set of local search neighborhood structures of the variable neighborhood search algorithm is \(N\) s , \(s = 1, 2, 3,\cdots s\) max , where the initial weights corresponding to each neighborhood structure are

[0045] S5.2. Combine the probability formula of roulette wheel to calculate the probabilities of each neighborhood structure

[0046] S5.3. Calculate the cumulative probability of each neighborhood structure That is, the sum of the selection probabilities of all the neighborhood structures before each neighborhood structure;

[0047] S5.4. Define a variable \(r\), randomly generate a number between \((0, 1)\) and assign it to the variable \(r\). If \(Q\) s-1 \(< r < Q\) s , then select the neighborhood structure \(N\) s for local search.

[0048] Preferably, the neighborhood structure includes:

[0049] Neighborhood Structure 1: Define variables \(x1\), \(x2\), \(y1\), \(y2\). For the production line sequence coding, randomly select two integers in the interval \([1, L]\) and assign them to \(x1\) and \(x2\) with \(x1 < x2\), and take the average of the numbers at the \(x1\)-th position and the \(x2\)-th position in the encoding of the current solution; for the workpiece sequence coding, randomly select two integers in the interval \([1, N]\) and assign them to \(y1\) and \(y2\) with \(y1 < y2\), and swap the numbers before the \(y1\)-th position and after the \(y2\)-th position in the encoding of the current solution;

[0050] Neighborhood Structure 2: Define variables x1, x2, y1, y2. For the production line sequence encoding, randomly select two integers within the interval [1, L], assign them to x1 and x2 with x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers within the interval [1, N], assign them to y1 and y2 with y1 < y2, and reverse the production line position numbers corresponding to the positions between the y1-th and y2-th positions in the encoding of the current solution.

[0051] Neighborhood Structure 3: Define variables x1, x2, x3, y1, y2. For the production line sequence encoding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3 with x1 < x2 < x3, and take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers within the interval [1, N], assign them to y1 and y2 with y1 < y2, exchange the production line position numbers corresponding to the y1-th and y2-th positions in the encoding of the current solution, and exchange the production line position numbers before the y1-th position with the production line position numbers between the y1-th and y2-th positions.

[0052] Neighborhood Structure 4: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers within the interval [1, L], assign them to x1 and x2 with x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3 with y1 < y2 < y3, and exchange the production line position numbers between the y1-th and y2-th positions with the production line position numbers between the y2-th and y3-th positions in the encoding of the current solution.

[0053] Neighborhood Structure 5: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers within the interval [1, L], assign them to x1 and x2 with x1 < x2, and take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3 with y1 < y2 < y3, exchange the left side of the y1-th position with the production line position numbers between the y1-th and y2-th positions in the encoding of the current solution, and then exchange the production line position numbers corresponding to the y2-th and y3-th positions.

[0054] Neighborhood Structure 6: Define variables x1, x2, y1, y2, y3, z. For the production line sequence encoding, randomly select two integers within the interval [1, L], assign them to x1 and x2, and x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3, and y1 < y2 < y3. Swap the production line position numbers on the left side of the y1-th position and on the right side of the y3-th position in the encoding of the current solution, assign the production line position number at the y1-th position to z, then assign the production line position number at the y3-th position to the y1-th position, assign the production line position number at the y2-th position to the y3-th position, and assign z to the y2-th position;

[0055] Neighborhood Structure 7: Define variables x1, x2, x3, y1, y2, z. For the production line sequence encoding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3, and x1 < x2 < x3. Take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers within the interval [1, N], assign them to y1 and y2. Assign the encoding of the current solution to form 2 solutions. Swap the two sides of the y1-th position in the encoding of one solution, and then swap the two sides of the y2-th position in the encoding of the other solution. Randomly select an integer within the interval [1, N], assign it to z. Combine the production line position encodings on the left side of the z-th position (including the z-th position) in the encoding of the first solution and on the right side of the z-th position in the encoding of the second solution to form a new solution;

[0056] Neighborhood Structure 8: Define variables x1, x2, x3, y1, y2, y3, y4. For the production line sequence encoding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3, and x1 < x2 < x3. Take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution; for the workpiece sequence encoding, randomly select four integers within the interval [1, N], assign them to y1, y2, y3, and y4, and y1 < y2 < y3 < y4. Swap the y1-th and y2-th positions in the encoding of the current solution, swap the y3-th and y4-th positions in the encoding of the current solution, and then swap the production line position numbers between the y1-th and y2-th positions and the production line position numbers between the y3-th and y4-th positions.

[0057] Preferably, S9 specifically includes the following steps:

[0058] S9.1. From solution x bestGenerate a set of workpieces PN assigned to production line l l ;

[0059] S9.2, h l The number of the set of workpieces processed on the lth production line is

[0060] S9.3, for the workpiece number on the first production line Sort by

[0061] S9.4, according to the formula Calculate the manufacturing span CmaxX,X∈{A,B} of product A and product B;

[0062] S9.5, according to the formula Output F min .

[0063] Preferably, the heuristic rule is set in S9.3 as follows:

[0064] S9.3.1, if the workpiece number y i >n A +n B When the workpiece number {n A +n B +1,…,N}, and number this part of the workpiece {n A +n B +1,…,N} are sorted in non-increasing order according to processing time;

[0065] S9.3.2. Find the critical point Q of the processing time of product C on production line l, and set the workpiece number {n A +n B +1,…,N} is placed before the critical point Q;

[0066] S9.3.3, number the remaining workpieces {1,2,…,n A +n B}Sort in non-increasing order by processing time.

[0067] The present invention provides a dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line opening. Compared with the prior art, it has the following beneficial effects:

[0068] In the present invention, input parameters based on the variable neighborhood search algorithm are set according to the data of the high-end equipment production process, and the operating parameters of the variable neighborhood search algorithm are set. Under the premise of giving priority to satisfying agent 2, an initial solution set is constructed, and the optimal solution is selected as the initial solution x0 according to the fitness value of the solution; a shaking operation is performed on the initial solution x0 to obtain a new solution x1, and a local search neighborhood structure is selected based on the roulette probability strategy. A local search is performed on x1 in the neighborhood structure to obtain a new solution x2, and it is determined whether the fitness value of x2 is better than the fitness value of x1. If so, x2 is used as the initial solution and it is continued to be iterated until the global optimal solution x1 is searched. best , according to x best The provided solution assigns production tasks to suppliers to minimize the total delay penalty cost of agent 1 and complete production of agent 2 within the specified time limit; it maximizes the resource utilization efficiency and operation efficiency of high-end equipment manufacturing enterprises and reduces the total cost of the supply chain. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 paying creative work.

[0070] Figure 1 is a flow chart of a scheduling method in an embodiment of the present invention;

[0071] Figure 2 It is a coding schematic diagram in an embodiment of the present invention. DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are clearly and completely described. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0073] The embodiment of the present application solves the problem that the existing collaborative scheduling technology for batch production parts and operation and maintenance accessories of high-end equipment in the production stage cannot quickly and accurately find the optimal solution while considering multiple workpiece agents by providing a dual-agent collaborative scheduling method for the high-end equipment supply chain based on the opening of flexible production lines.

[0074] In order to better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0075] Example:

[0076] like Figure 1 As shown, the present invention provides a dual-agent collaborative scheduling method for a high-end equipment supply chain based on the opening of a flexible production line, and the scheduling method includes the following steps:

[0077] S1. Setting input parameters based on variable neighborhood search algorithm according to data generated in the production process of high-end equipment;

[0078] S2. Set the operating parameters of the variable neighborhood search algorithm, including: the maximum number of iterations k of the variable neighborhood search algorithm max ; Number of neighborhood structures N s ; Initialize the number of iterations k = 0; Initialize the neighborhood structure s = 1; Variable neighborhood search algorithm local search neighborhood structure initial weight

[0079] S3, encode the high-end equipment production tasks based on the variable neighborhood search algorithm, and randomly generate the initial solution x0 based on the priority of satisfying the maintenance spare parts product C of agent 2;

[0080] S4, based on the variable neighborhood search algorithm, the initial solution x0 is shaken, and the individual population is obtained in the neighborhood structure. The best individual in the individual population is obtained by the greedy algorithm, and the initial solution is updated by the best individual to obtain the new solution x1;

[0081] S5, based on the roulette probability selection to obtain the local search neighborhood structure, in the selected neighborhood N s Perform local search to obtain the local optimal solution x2;

[0082] S6. Compare the fitness value f(x1) of the new solution x1 with the fitness value f(x2) of the local optimal solution x2. If f(x2)≤f(x1), assign the value of x2 to x1, and continue to perform local search based on the current neighborhood structure to obtain the local optimal solution; if not, set s=s+1 and execute S7.

[0083] S7. Determine s≤N s Is it true? If true, return to S5; if not, set k=k+1 and go to S8;

[0084] S8. Determine k≤k max Is it established? If yes, go to S4; if not, go to S9;

[0085] S9, the algorithm terminates and outputs the global optimal solution x best , for x best Decode and output the set PNl , PN l Represents the set of artifact sequence numbers of all artifacts of agent 1 and agent 2 on production line l.

[0086] The embodiment of the present invention considers dual-agent scheduling with flexible production lines, that is, one agent is responsible for two batch production parts, and the other agent is responsible for one maintenance spare part, and the production line is flexible in the supplier production stage. In this case, the production process of high-end equipment is coordinated and the approximate optimal solution is obtained, which can effectively assign workpieces to the production line, thereby minimizing the total cost of the supply chain and improving the resource utilization efficiency and collaboration efficiency of high-end equipment manufacturing enterprises.

[0087] The following will describe each step in detail based on the specific content:

[0088] In S1, according to the data of the high-end equipment production process, the input parameters based on the variable neighborhood search algorithm are set, wherein the input parameters include:

[0089] The number of workpieces n of product A of agent 1 in the production phase A , the number of workpieces of product B n B , the number of workpieces n of product C of agent 2 C ; Total number of workpieces N = n A +n B +n C ; Maximum number of production lines L in the production phase; Production line startup cost sc; Product X workpiece processing time The set of artifacts for product X is

[0090] In S3, the high-end equipment production task is encoded based on the variable neighborhood search algorithm, and the initial solution x0 is randomly generated based on the priority of satisfying the maintenance spare parts product C of agent 2, which specifically includes:

[0091] Based on the variable neighborhood search algorithm, the production line problem and product workpieces of the high-end equipment manufacturing process are encoded to obtain the initial solution x0. x0 is composed of two sequences: the production line sequence PL and the workpiece sequence PN. The PL code indicates whether the production line is started and the number of workpieces processed on the started production line, and the PN code indicates the production line assigned to all workpiece numbers. The specific implementation process is as follows:

[0092] The encoding process is as follows:

[0093] Based on the characteristics of the flexible production line, the solution x0 consists of two parts, the production line sequence PL and the workpiece sequence PN, which can be expressed as x0 = {h1,h2,…,h L ; 1,2,…,n A ,n A+1 …,nA +n B ,…,N}. The encoding of the production line sequence PL is {h1,h2,h3,…,h L}, the length of the production line sequence PL is the total number of production lines L, h l Indicates the code of the production line sequence PL. If h l =0, indicating that the lth production line is not started; if h l = m, which means that m workpieces are processed on the lth production line; a total of N workpieces are processed on L production lines, that is The encoding of the workpiece sequence PN is {1,2,…,n A ,n A+1 ,…,n A +n B ,…,N}, the length of the workpiece sequence PN is the total number of workpieces of products A, B, and C, that is, N = n A +n B +n C ,y i Represents the encoding of the workpiece sequence PN, {1,2,…,n A} represents the workpiece number of product A, {n A+1 ,…,n A +n B} represents the workpiece number of product B, {n A +n B +1,…,N} represents the workpiece number of product C.

[0094] Therefore, the initial solution can be expressed as x0 = {h1,h2,h3,…,h L ; 1,2,…,n A ,n A+1 ,…,n A +n B ,…,N},

[0095] like Figure 2 As shown, the solution is encoded using a one-dimensional array. The length of the first part is the number of production lines L, h l represents the number of workpieces processed by the lth production line; the length of the second part is the set of all workpieces of the product N, y i Represents the artifact number of the i-th product artifact.

[0096] The S3 specifically includes the following steps:

[0097] S3.1. Based on the constraints of the high-end equipment production stage, the processing of workpiece C of agent 2 is given priority; on this basis, the code of the production stage is randomly generated, and all initial solutions x are added to the initial solution set X;

[0098] S3.2, determine whether the number of initial solutions in the initial solution set X is greater than the number of initial solutions N0 in the initial solution set. If not, return to S3.1 to continue producing initial solutions, otherwise output the initial solution set X;

[0099] S3.3. Calculate the fitness value of each solution in the initial solution set X, and select the solution with the smallest fitness value as the initial solution x0.

[0100] Among them, the fitness value calculation formula in S3.3 is expressed as follows:

[0101]

[0102] in,

[0103] Among them, F min It means that the total cost is minimized;

[0104] D A represents the deadline time of product A in agent 1;

[0105] D B Indicates the deadline time of product B in agent 1;

[0106] α and β are the delay penalty cost coefficients of product A and product B respectively;

[0107] sc represents the setup cost of starting a production line;

[0108] represents the maximum completion time of job X, X∈{A, B, C};

[0109] Q C represents the latest completion time of agent 2;

[0110] represents the production time of the process of high-end equipment product X at the i-th position on production line l, X∈{A, B, C};

[0111] It represents the production time of the process of high-end equipment product X at the last process position j on production line l, X∈{A, B, C}.

[0112] In S4, the initial solution x0 is shaken based on the variable neighborhood search algorithm to obtain an individual population in the neighborhood structure, and the best individual in the individual population is obtained by the greedy algorithm. The initial solution is updated by the best individual to obtain a new solution x1, which specifically includes:

[0113] Select the kth neighborhood structure (initial k = 1), perform a shaking operation on the initial solution x0 obtained in step S3, obtain a population of q individuals, calculate the fitness values ​​of q individuals in the population, and use the greedy algorithm to obtain the optimal individual x in the population. min , and update the new solution x1=x min Before obtaining the individual population through the neighborhood structure, it is necessary to set the neighborhood structure of the algorithm's shaking operation, and set the shaking operation perturbation neighborhood set to N k ,k=1,2,…,k max

[0114] S4.1. Define variables i, j, g = 1, obtain input x0, and the current iteration number is k;

[0115] S4.2, randomly generate two integers in the interval [1, N] and assign them to variables i and j;

[0116] S4.3. Select the i-th and j-th elements in x0, swap them, and get a new solution x1.

[0117] S4.4, let g = g + 1, determine whether g ≤ k is true, if so, return to S4.2; otherwise, execute step S4.5;

[0118] S4.5. Calculate the fitness value and determine whether the solution x1 is better than x0. If so, output x1; otherwise, set x1 = x0.

[0119] The corresponding shaking operation here is to transform the initial solution to another point in the feasible domain according to certain rules. This can avoid the same initial solution from falling into the local optimum under continuous iteration, thereby improving the global search capability of the algorithm.

[0120] In S5, based on the roulette probability selection, a local search neighborhood structure is obtained. In the selected neighborhood N s Perform local search to obtain the local optimal solution x2, including:

[0121] It should be noted that the local search in the variable neighborhood search algorithm is to recycle the neighborhood structure of the local search only when the neighborhood structure searches for a solution that is better than the current solution. In order to search for a more effective neighborhood structure in advance and reduce unnecessary iterations and cycle time, a weight selection strategy is added when selecting the neighborhood structure, that is, roulette probability selection. The specific process is as follows:

[0122] S5.1. When setting the algorithm parameters initially, due to the unknown structural validity of the local search neighborhood, the default setting of the initial neighborhood structure weights is equal; the local search neighborhood structure set of the variable neighborhood search algorithm is N s, s = 1, 2, 3, … s max , where the initial weight corresponding to each neighborhood structure is

[0123] S5.2. Combine the probability formula of roulette wheel to calculate the probability of each neighborhood structure

[0124] S5.3. Calculate the cumulative probability of each neighborhood structure That is, the sum of the selection probabilities of all neighborhood structures before each neighborhood structure;

[0125] S5.4. Define a variable r, randomly generate a number between (0, 1) and assign it to the variable r. If Q s-1 < r < Q s , then select the neighborhood structure N s for local search.

[0126] According to the roulette wheel probability weight strategy, select the neighborhood structure. Due to the characteristics of heavy tasks and complex constraint relationships in high-end equipment manufacturing enterprises, 8 different neighborhood structures are set in the local search algorithm, and the specific situations are as follows:

[0127] Neighborhood structure 1: Define variables x1, x2, y1, y2. For the production line sequence coding, randomly select two integers in the interval [1, L] and assign them to x1 and x2, and x1 < x2. Take the average of the numbers at the x1-th position and the x2-th position in the current solution's coding; for the workpiece sequence coding, randomly select two integers in the interval [1, N] and assign them to y1 and y2, and y1 < y2. Swap the numbers before the y1-th position and after the y2-th position in the current solution's coding.

[0128] Neighborhood structure 2: Define variables x1, x2, y1, y2. For the production line sequence coding, randomly select two integers in the interval [1, L] and assign them to x1 and x2, and x1 < x2. Take the average of the numbers at the x1-th position and the x2-th position in the current solution's coding; for the workpiece sequence coding, randomly select two integers in the interval [1, N] and assign them to y1 and y2, and y1 < y2. Reverse the production line position numbers corresponding between the y1-th position and the y2-th position in the current solution's coding.

[0129] Neighborhood Structure 3: Define variables x1, x2, x3, y1, y2. For the production line sequence encoding, randomly select three integers in the interval [1, L], and assign them to x1, x2, and x3 with x1 < x2 < x3. Take the average of the numbers at the x1-th, x2-th, and x3-th positions in the encoding of the current solution. For the workpiece sequence encoding, randomly select two integers in the interval [1, N], and assign them to y1 and y2 with y1 < y2. Swap the production line position numbers corresponding to the y1-th and y2-th positions in the encoding of the current solution, and swap the production line position numbers before the y1-th position with the production line position numbers between the y1-th and y2-th positions.

[0130] Neighborhood Structure 4: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers in the interval [1, L], and assign them to x1 and x2 with x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution. For the workpiece sequence encoding, randomly select three integers in the interval [1, N], and assign them to y1, y2, and y3 with y1 < y2 < y3. Swap the production line position numbers between the y1-th and y2-th positions with the production line position numbers between the y2-th and y3-th positions in the encoding of the current solution.

[0131] Neighborhood Structure 5: Define variables x1, x2, y1, y2, y3. For the production line sequence encoding, randomly select two integers in the interval [1, L], and assign them to x1 and x2 with x1 < x2. Take the average of the numbers at the x1-th and x2-th positions in the encoding of the current solution. For the workpiece sequence encoding, randomly select three integers in the interval [1, N], and assign them to y1, y2, and y3 with y1 < y2 < y3. Swap the left side of the y1-th position with the production line position numbers between the y1-th and y2-th positions in the encoding of the current solution, and then swap the y2-th position with the production line position number corresponding to the y3-th position.

[0132] Neighborhood Structure 6: Define variables x1, x2, y1, y2, y3, z. For the production line sequence encoding, randomly select two integers within the interval [1, L], assign them to x1 and x2, and x1 < x2. Take the average of the numbers at the x1-th position and the x2-th position in the encoding of the current solution; for the workpiece sequence encoding, randomly select three integers within the interval [1, N], assign them to y1, y2, and y3, and y1 < y2 < y3. Swap the production line position numbers on the left side of the y1-th position and on the right side of the y3-th position in the encoding of the current solution, assign the production line position number at the y1-th position to z, then assign the production line position number at the y3-th position to the y1-th position, assign the production line position number at the y2-th position to the y3-th position, and assign z to the y2-th position.

[0133] Neighborhood Structure 7: Define variables x1, x2, x3, y1, y2, z. For the production line sequence encoding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3, and x1 < x2 < x3. Take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers within the interval [1, N], assign them to y1 and y2. Assign the encoding of the current solution to form 2 solutions. Swap the two sides of the y1-th position in the encoding of one solution, and then swap the two sides of the y2-th position in the encoding of the other solution. Randomly select an integer within the interval [1, N], assign it to z. Combine the production line position encodings on the left side of the z-th position and including the z-th position in the encoding of the first solution and on the right side of the z-th position in the encoding of the second solution to form a new solution.

[0134] Neighborhood Structure 8: Define variables x1, x2, x3, y1, y2, y3, y4. For the production line sequence encoding, randomly select three integers within the interval [1, L], assign them to x1, x2, and x3, and x1 < x2 < x3. Take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the encoding of the current solution; for the workpiece sequence encoding, randomly select four integers within the interval [1, N], assign them to y1, y2, y3, and y4, and y1 < y2 < y3 < y4. Swap the y1-th position and the y2-th position in the encoding of the current solution, swap the y3-th position and the y4-th position in the encoding of the current solution, and then swap the production line position numbers between the y1-th position and the y2-th position and the production line position numbers between the y3-th position and the y4-th position.

[0135] In the embodiments of the present invention, eight neighborhood structures are designed according to the actual problem background, which improves the ability of the algorithm to globally search for the optimal solution.

[0136] In S9, for x best The decoding process is to assign all workpieces to the corresponding production lines for processing, and then arrange the processing order of the workpieces based on the heuristic algorithm, calculate the manufacturing span of each product, and finally calculate the total cost of agent 1. The specific operations include the following:

[0137] S9.1, by solving x best Generate a set of workpieces PN assigned to production line l l ;

[0138] S9.2, h l The number of the set of workpieces processed on the lth production line is

[0139] S9.3, for the workpiece number on the first production line To sort, set the following heuristic rules:

[0140] S9.3.1, if the workpiece number y i >n A +n B When the workpiece number {n A +n B +1,…,N}, and number this part of the workpiece {n A +n B +1,…,N} are sorted in non-increasing order according to processing time;

[0141] S9.3.2. Find the critical point Q of the processing time of product C on production line l, and set the workpiece number {n A +n B +1,…,N} is placed before the critical point Q;

[0142] S9.3.3, number the remaining workpieces {1,2,…,n A +n B} Sort in non-increasing order by processing time;

[0143] S9.4, according to the formula Calculate the manufacturing span CmaxX,X∈{A,B} of product A and product B;

[0144] S9.5, according to the formula Output F min .

[0145] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0146] 1. In the embodiment of the present invention, the input parameters of the variable neighborhood search algorithm are set according to the data of the high-end equipment production process, the operating parameters of the variable neighborhood search algorithm are set, and the initial solution set is constructed under the premise of giving priority to satisfying agent 2. According to the fitness value of the solution, the optimal solution is selected as the initial solution x0; the initial solution x0 is shaken to obtain a new solution x1, and a local search neighborhood structure is selected based on the roulette probability strategy. A local search is performed on x1 in the neighborhood structure to obtain a new solution x2, and it is determined whether the fitness value of x2 is better than the fitness value of x1. If so, x2 is used as the initial solution and it is iterated continuously until the global optimal solution x1 is searched. best , according to x best The provided solution assigns production tasks to suppliers to minimize the total delay penalty cost of agent 1 and complete production of agent 2 within the specified time limit; it maximizes the resource utilization efficiency and operation efficiency of high-end equipment manufacturing enterprises and reduces the total cost of the supply chain.

[0147] 2. In the embodiment of the present invention, dual-agent scheduling with flexible production lines is considered, that is, one agent is an agent for two batch production parts, and the other agent is an agent for one operation and maintenance spare part, and the production line is flexible in the supplier's production stage; in this case, the production process of high-end equipment is collaboratively scheduled to obtain an approximate optimal solution, which can effectively assign production lines, thereby minimizing the total cost of the supply chain and improving the resource utilization efficiency and collaboration efficiency of high-end equipment manufacturing enterprises.

[0148] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0149] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A dual-agent collaborative scheduling method for a high-end equipment supply chain based on flexible production line opening, characterized in that: The scheduling method includes the following steps: S1. Set the input parameters based on the variable neighborhood search algorithm according to the data generated in the high-end equipment production process; S2. Set the operating parameters of the variable neighborhood search algorithm. The operating parameters include: the maximum number of iterations k of the variable neighborhood search algorithm max ; Number of neighborhood structures N s ; Initialize the number of iterations k = 0; Initialize the neighborhood structure s = 1; Variable neighborhood search algorithm local search neighborhood structure initial weight S3. Encode the high-end equipment production tasks based on the variable neighborhood search algorithm, and randomly generate an initial solution x0 on the basis of giving priority to meeting the maintenance spare parts product C of Agent 2; S4. Perform a Shaking operation on the initial solution x0 based on the variable neighborhood search algorithm, obtain an individual population within the neighborhood structure, and obtain the optimal individual in the individual population by the greedy algorithm. Update the initial solution through the optimal individual to obtain a new solution x1; S5, based on the roulette probability selection to obtain the local search neighborhood structure, in the selected neighborhood N s Perform local search to obtain the local optimal solution x2; S6. Compare the fitness value f(x1) of the new solution x1 with the fitness value f(x2) of the local optimal solution x2. If f(x2) ≤ f(x1), then assign the value of x2 to x1, and continue to perform local search based on the current neighborhood structure to obtain the local optimal solution; if not, then let s = s + 1 and execute S7; S7. Determine s≤N s Is it true? If true, return to S5; if not, set k=k+1 and go to S8; S8. Determine k≤k max Is it established? If yes, go to S4; if not, go to S9; S9, the algorithm terminates and outputs the global optimal solution x best , for x best Decode and output the set PN l , PN l Represents the set of artifact sequence numbers of all artifacts of agent 1 and agent 2 on production line l.

2. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening according to claim 1 is characterized in that: In S1, the input parameters include: The number of workpieces n of product A of agent 1 in the production phase A , the number of workpieces of product B n B , the number of workpieces n of product C of agent 2 C ; Total number of workpieces N = n A +n B +n C ; Maximum number of production lines L in the production phase; Production line startup cost sc; Product X workpiece processing time The set of artifacts for product X is 3. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening according to claim 2 is characterized in that: S3 specifically includes the following steps: S3.

1. Based on the restricted conditions in the high-end equipment production stage, give priority to processing the workpiece C of Agent 2; on this basis, randomly generate the encoding of the production stage, and add all the initial solutions x to the initial solution set X; S3.

2. Judge whether the number of initial solutions in the initial solution set X is greater than the number N0 of initial solutions in the initial solution set. If not, return to S3.1 to continue generating initial solutions, otherwise output the initial solution set X; S3.

3. Calculate the fitness value of each solution in the initial solution set X, and select the solution with the smallest fitness value as the initial solution x0.

4. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening as claimed in claim 3 is characterized in that: The fitness value calculation formula in S3.3 is expressed as follows: in, Among them, F min It means that the total cost is minimized; D A represents the deadline time of product A in agent 1; D B Indicates the deadline time of product B in agent 1; α and β are the delay penalty cost coefficients of product A and product B respectively; sc represents the setup cost of starting a production line; represents the maximum completion time of job X, X∈{A, B, C}; Q c represents the latest completion time of agent 2; represents the production time of the process of high-end equipment product X at the i-th position on production line l, X∈{A, B, C}; It represents the production time of the process of high-end equipment product X at the last process position j on production line l, X∈{A, B, C}.

5. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening according to claim 1 is characterized in that: S4 specifically includes the following steps: S4.

1. Define variables i, j, g = 1, obtain the input x0, and the current iteration number is k; S4.

2. Randomly generate two integers within the range of [1, N], and assign them to the variables i and j; S4.

3. Select the i-th and j-th elements in x0, and exchange these two elements to obtain a new solution x1; S4.

4. Let g = g + 1, and judge whether g ≤ k holds. If it holds, return to S4.2; Otherwise, execute step S4.5; S4.

5. Calculate the fitness value, and judge whether the solution x1 is better than x0. If so, output x1; otherwise, let x1 = x0.

6. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening according to claim 1 is characterized in that: S5 specifically includes the following steps: S5.

1. When setting the algorithm parameters initially, due to the unknown structural validity of the local search neighborhood, the default setting of the initial neighborhood structure weights is equal; the local search neighborhood structure set of the variable neighborhood search algorithm is N s , s=1,2,3,...s max , where the initial weights corresponding to each neighborhood structure are S5.

2. Calculate the probability of each neighborhood structure by combining the probability formula of roulette S5.

3. Calculate the cumulative probability of each neighborhood structure That is, the sum of the selection probabilities of all neighborhood structures before each neighborhood structure; S5.

4. Define a variable r, randomly generate a number between (0, 1), and assign it to the variable r. If Q s-1 <r<Q s , then select the neighborhood structure N s Perform a local search.

7. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening according to claim 1 is characterized in that: The neighborhood structure includes: Neighborhood structure 1: Define variables x1, x2, y1, y2. For the production line sequence encoding, randomly select two integers within the range of [1, L], and assign them to x1 and x2 and x1 < x2, and take the average of the numbers at the x1-th position and the x2-th position in the encoding of the current solution; for the workpiece sequence encoding, randomly select two integers within the range of [1, N], and assign them to y1 and y2 and y1 < y2, and swap the numbers before the y1-th position and after the y2-th position in the encoding of the current solution; Neighborhood Structure 2: Define variables x1, x2, y1, y2. For the production line sequence coding, randomly select two integers in the interval [1, L], assign them to x1 and x2 and x1 < x2, and take the average of the numbers at the x1-th position and the x2-th position in the coding of the current solution; for the workpiece sequence coding, randomly select two integers in the interval [1, N], assign them to y1 and y2 and y1 < y2, and reverse the production line position numbers corresponding to the y1-th position and the y2-th position in the coding of the current solution. Neighborhood Structure 3: Define variables x1, x2, x3, y1, y2. For the production line sequence coding, randomly select three integers in the interval [1, L], assign them to x1, x2, and x3 and x1 < x2 < x3, and take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the coding of the current solution; for the workpiece sequence coding, randomly select two integers in the interval [1, N], assign them to y1 and y2 and y1 < y2, exchange the production line position numbers corresponding to the y1-th position and the y2-th position in the coding of the current solution, and exchange the production line position numbers before the y1-th position and between the y1-th position and the y2-th position. Neighborhood Structure 4: Define variables x1, x2, y1, y2, y3. For the production line sequence coding, randomly select two integers in the interval [1, L], assign them to x1 and x2 and x1 < x2, and take the average of the numbers at the x1-th position and the x2-th position in the coding of the current solution; for the workpiece sequence coding, randomly select three integers in the interval [1, N], assign them to y1, y2, and y3 and y1 < y2 < y3, and exchange the production line position numbers between the y1-th position and the y2-th position and between the y2-th position and the y3-th position in the coding of the current solution. Neighborhood Structure 5: Define variables x1, x2, y1, y2, y3. For the production line sequence coding, randomly select two integers in the interval [1, L], assign them to x1 and x2 and x1 < x2, and take the average of the numbers at the x1-th position and the x2-th position in the coding of the current solution; for the workpiece sequence coding, randomly select three integers in the interval [1, N], assign them to y1, y2, and y3 and y1 < y2 < y3, exchange the left side of the y1-th position and the production line position numbers between the y1-th position and the y2-th position in the coding of the current solution, and then exchange the production line position numbers corresponding to the y2-th position and the y3-th position. Neighborhood Structure 6: Define variables x1, x2, y1, y2, y3, z. For the production line sequence coding, randomly select two integers in the interval [1, L], and assign them to x1 and x2 with x1 < x2, and take the average of the numbers at the x1-th position and the x2-th position in the coding of the current solution; for the workpiece sequence coding, randomly select three integers in the interval [1, N], and assign them to y1, y2, and y3 with y1 < y2 < y3, swap the production line position numbers on the left side of the y1-th position and on the right side of the y3-th position in the coding of the current solution, assign the production line position number at the y1-th position to z, then assign the production line position number at the y3-th position to the y1-th position, assign the production line position number at the y2-th position to the y3-th position, and assign z to the y2-th position; Neighborhood Structure 7: Define variables x1, x2, x3, y1, y2, z. For the production line sequence coding, randomly select three integers in the interval [1, L], and assign them to x1, x2, and x3 with x1 < x2 < x3, and take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the coding of the current solution; for the workpiece sequence coding, randomly select two integers in the interval [1, N], and assign them to y1 and y2, assign the coding of the current solution to form 2 solutions, swap the two sides of the y1-th position in the coding of one solution, and then swap the two sides of the y2-th position in the coding of the other solution, randomly select an integer in the interval [1, N], and assign it to z, take the production line position coding on the left side of the z-th position and including the z-th position in the coding of the first solution and the production line position coding on the right side of the z-th position in the coding of the second solution to form a new solution; Neighborhood Structure 8: Define variables x1, x2, x3, y1, y2, y3, y4. For the production line sequence coding, randomly select three integers in the interval [1, L], and assign them to x1, x2, and x3 with x1 < x2 < x3, and take the average of the numbers at the x1-th position, the x2-th position, and the x3-th position in the coding of the current solution; for the workpiece sequence coding, randomly select four integers in the interval [1, N], and assign them to y1, y2, y3, and y4 with y1 < y2 < y3 < y4, swap the y1-th position and the y2-th position in the coding of the current solution, swap the y3-th position and the y4-th position in the coding of the current solution, and then swap the production line position numbers between the y1-th position and the y2-th position and the production line position numbers between the y3-th position and the y4-th position.

8. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening according to claim 1 is characterized in that: The specific steps of S9 are as follows: S9.1, by solving x best Generate a set of workpieces PN assigned to production line l l ; S9.2, h l The number of the set of workpieces processed on the lth production line is S9.3, for the workpiece number on the first production line Sort by S9.4, according to the formula Calculate the manufacturing span CmaxX,X∈{A,B} of product A and product B; S9.5, according to the formula Output F min .

9. The dual-agent collaborative scheduling method for high-end equipment supply chain based on flexible production line opening as claimed in claim 8 is characterized in that: The heuristic rules set in S9.3 are as follows: S9.3.1, if the workpiece number y i >n A +n B When the workpiece number {n A +n B +1,...,N}, and number this part of the workpiece {n A +n B +1, ..., N} are sorted in non-increasing order by processing time; S9.3.

2. Find the critical point Q of the processing time of product C on production line l, and set the workpiece number {n A +n B +1,…,N} is placed before the critical point Q; S9.3.3, number the remaining workpieces {1, 2, ..., n A +n B }Sort in non-increasing order by processing time.

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