Joint economic batch multi-objective optimization method for multi-product multi-stage integrated supply chain

Abstract

The invention provides a joint economic batch multi-objective optimization method and system for a multi-product multi-level integrated supply chain, a storage medium and electronic equipment, and relates to the technical field of task optimization. According to the invention, under the condition of considering the inconsistent capability of each layer of the multi-level integrated supply chain, the joint economic batch problem based on the multi-product multi-level integrated supply chain is optimized, the minimum cost of the supply chain and the minimum replenishment period of the product are comprehensively considered, the problem is solved through a hybrid intelligent algorithm, and an approximate optimal solution is obtained. According to the method, collaborative optimization and design can be powerfully carried out on different levels of product ordering batches of the supply chain, so that resources of the multi-level integrated supply chain are utilized to the maximum extent, the overall cost of the multi-level integrated supply chain is reduced, and the management capability and the operation efficiency of the multi-product multi-level integrated supply chain are improved. According to the hybrid non-dominated sorting genetic algorithm based on neighborhood search, an adaptive selection mechanism is designed, and a plurality of Shaking hybrid neighborhood structures are designed, so that the solution efficiency and the solution quality are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of task optimization, and in particular to a joint economic batch multi-objective optimization method, system, storage medium and electronic equipment for a multi-product multi-level integrated supply chain. Background Art

[0002] The joint economic batch problem plays a key role in the management of multi-product multi-echelon integrated supply chains. By optimizing and integrating the coordination and resource allocation between each level, it ensures the efficient operation and maximum benefits of the supply chain as a whole. From an economic perspective, making effective joint economic batch decisions depends on two key factors: the product order batch size and the product supply batch length agreed by all parties.

[0003] In the related art, when solving the joint economic batch problem of multi-product multi-stage integrated supply chain, it is generally considered that the supply chain consists of a single supplier, a single manufacturer and multiple retailers. The supplier receives raw materials from its suppliers and converts them into semi-finished products at a certain production rate. Then the manufacturer receives these semi-finished products from the supplier in the same batch and converts them into finished products. The number of incoming and outgoing goods of the supplier and the manufacturer in each cycle is a decision variable. After that, the finished products are shipped to the retailers in equal quantities, and the retailers use them to meet the needs of the end customers. During the production process, shipments from specific batches are allowed. Although the retailers receive the goods at the same time during the so-called common replenishment period, the size of these goods may vary depending on the needs of the retailers. Therefore, the problem is to establish an integrated model to specify the ordering, production and delivery batch number strategies to minimize the total cost of the entire chain.

[0004] However, existing research mainly focuses on the joint economic batching problem of multi-product multi-level integrated supply chain under ideal conditions, focusing on the optimal ordering strategy of the three-level supply chain under unconstrained conditions. Existing literature rarely involves the optimization of material replenishment strategies and inventory space constraints in actual operations, especially ignoring the problem of inconsistent supply chain capabilities at various levels. Therefore, these theoretical models have certain limitations when guiding actual supply chain management, resulting in low resource utilization efficiency. Summary of the invention

[0005] 1. Technical issues to be resolved

[0006] In view of the shortcomings of the prior art, the present invention provides a joint economic batch multi-objective optimization method, system, storage medium and electronic device for a multi-product multi-level integrated supply chain, which solves the technical problem that the existing theoretical models are unable to cope with the complexity and variability in reality.

[0007] (II) Technical solution

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

[0009] A joint economic batch multi-objective optimization method for a multi-product multi-echelon integrated supply chain, including:

[0010] Obtaining index information, hierarchical information, cost information, and product information about a multi-level integrated supply chain; wherein the multi-level integrated supply chain is a four-level supply chain consisting of a single supplier, a single manufacturer, a single distributor, and multiple retailers;

[0011] Based on the index information, hierarchical information, cost information and product information, a mathematical model is constructed with minimizing the total cost of the supply chain as a first optimization goal and minimizing the length of the product replenishment cycle as a second optimization goal, and random constraint information is combined;

[0012] A hybrid non-dominated sorting genetic algorithm based on neighborhood search is used to solve the mathematical model, obtain the global optimal solution, and decode the optimal order batch and batch information for the specified category of products at each supply chain level within the complete replenishment cycle.

[0013] Preferably, (1) the index information includes:

[0014] Hierarchical index set A = {s, p, w, r}, where s is the supplier, p is the manufacturer, w is the distributor, and r is the retailer;

[0015] Product category index set i = {1, 2, ..., n}, where n is the total number of product categories;

[0016] (2) The hierarchical information includes:

[0017] Demand rate collection in is the demand rate for product category i at supply chain level A in a single replenishment cycle;

[0018] The productivity set P = {p A}, where p A is the productivity of supply chain level A in a single replenishment cycle;

[0019] Order Bulk Collection in is the order quantity for product category i at supply chain level A in a single replenishment cycle;

[0020] Order batch set m = {m1, m2}, where m1 is the product order batch of the supplier in a single replenishment cycle, and m2 is the product order batch of the manufacturer in a single replenishment cycle;

[0021] (3) The cost information includes:

[0022] Required product preparation cost set in The cost of preparing raw materials for product category i in a single replenishment cycle for supply chain level A;

[0023] Required product ordering cost set in The cost of ordering product category i for supply chain tier A in a single replenishment cycle;

[0024] Required product holding cost set in is the holding cost of product category i at supply chain level a in a single replenishment cycle; represents the finished product holding cost of product category i, represents the raw material holding cost of product category i;

[0025] (4) The product information includes:

[0026] The required product replenishment cycle length set T = {T1,…,T i ,…,T n}, where T i is the replenishment cycle length of the required product category i;

[0027] The required product category inventory size set in The inventory size of product category i is stored for supply chain level A;

[0028] (5) The random constraint information includes:

[0029] The set of random constraint violation probabilities α = {α A}, where α A is the probability of random constraint violation corresponding to supply chain level A;

[0030] Standard normal value critical point set in is the critical point of the standard normal value corresponding to supply chain level A;

[0031] The average value set of resources μ = {μ A}, where μ A It is the average value of resources corresponding to supply chain level A.

[0032] Preferably, the mathematical model includes:

[0033]

[0034]

[0035]

[0036] Wherein, formula (1) indicates that minimizing the total cost TC of the supply chain is the first optimization objective; Min is the minimization function; TC s is the total cost of the supplier; TC p is the total cost of the manufacturer; TC w is the total cost of the distributor; TC r is the total cost to the retailer;

[0037] j is the retailer index, m is the total number of retailers; The cost of ordering product category i for retailer j in a single replenishment cycle; is the holding cost of product category i for retailer j in a single replenishment cycle; is the demand rate of product category i by retailer j in a single replenishment cycle;

[0038] Formula (6) indicates that minimizing the product replenishment cycle length T is the second optimization goal; W, Y, ε1, ε2, δ1, and δ2 are all intermediate variables and have no practical meaning;

[0039] Formula (15) represents the order quantity constraint;

[0040] Formula (16) represents the inventory space constraint.

[0041] Preferably, the coding rules of the hybrid non-dominated sorting genetic algorithm based on neighborhood search are as follows:

[0042] Solution X consists of solution X1 for the order batch size of different categories of products at each supply chain level and solution X2 for the order batch size of different categories of products; assuming there are l replenishment cycles:

[0043] Solution X1 is represented by a three-dimensional integer array, which includes a list of supply chain levels SC, product categories PL, and product order batch sizes OP. The length of the sequence or list is n*(m1+m2)*l. The numbers in SC represent the number of the supply chain level, the numbers in PL represent the number of the product category, and OP represents the order batch size of the product category PL at the level SC. The list SC-PL represents the product categories required at each supply chain level, and the list SC-PL-OP represents the order batch size of the specified category of products at a certain level of the supply chain.

[0044] Solution X2 is represented by a two-dimensional integer array, which includes the product category code PL and the product supply batch size TM. The length of the sequence or list is n*(m1+m2)*l. Each column in the array represents the order batch size for the specified category of products at the corresponding level.

[0045] Preferably, the decoding rule of the hybrid non-dominated sorting genetic algorithm based on neighborhood search is as follows:

[0046] Step 100, extract the supply chain hierarchy table SC from the code of X1, and represent the number of each supply chain hierarchy according to the code SC; when decoding, identify the position of each supply chain hierarchy in the code;

[0047] Step 200, parse the product categories and extract the number of each product category in PL to associate each product category with different supply chain levels;

[0048] Step 300, decoding the order batch size OP, extracting the order batch size of each product category at different supply chain levels from OP, and matching the corresponding demand according to the supply chain level and product category; wherein the decoding result of the order batch is a multidimensional array, and each dimension corresponds to a specific supply chain level and product category;

[0049] Step 400, converting SC-PL-OP into ordering decisions at each supply chain level; through the combination of SC-PL-OP, allocating the order batch of each level to the corresponding product category and supply chain level to determine the order batch and order quantity information of each supply chain level;

[0050] Step 500, according to the code of X2, obtain the product category number from PL during decoding, and extract the order batch information from TM;

[0051] Step 600, determine the batches of each product category in different cycles from the combination of TM in PL;

[0052] Step 700: After decoding, the order quantity and batch information of each product category are allocated to each supply chain level to form an ordering plan within the complete cycle.

[0053] Preferably, the adopting of a hybrid non-dominated sorting genetic algorithm based on neighborhood search to solve the mathematical model and obtain a global optimal solution includes:

[0054] S31. Set input parameters, including: p A , m1, m2, T i , α A , μ A ;

[0055] S32, set execution parameters, including: maximum number of iterations Gen1; algorithm population size N; maximum number of iterations Gen2 for local search; initial cycle selection probability PTi =1 / T; neighborhood set Each Shaking mixed neighborhood structure NS k The initial selection probability P k =1 / k max ;

[0056] S33, based on the encoding rule, generate an initial population, perform non-dominated sorting and crowding calculation, and record the current global optimal solution μ best ;

[0057] S34, performing a crossover operation based on the current population;

[0058] S35, performing non-dominated sorting and crowding calculation on the current population;

[0059] S36, select individuals according to the minimum dominance and maximum crowding strategy;

[0060] S37, Roulette-based selection of Shaking hybrid neighborhood structure NS k , according to the Shaking hybrid neighborhood structure NS k Generate a neighborhood solution μ′ of the optimal individual μ of the population, and compare the neighborhood solution μ′ and the objective function value of the optimal individual μ of the population to compare the two; if the neighborhood solution μ′ is better, update the optimal individual μ of the population, and if the local search falls into the local optimal solution, perform the shaking operation;

[0061] S38, determine whether gen2≤Gen2 is true, if so, set gen2=gen2+1, and go to S37; otherwise, go to S39;

[0062] S39, output the optimal solution μ″ of the neighborhood search, update the population and the current global optimal solution μ best ;

[0063] S310, determine whether gen1≤Gen1 is true, if so, set gen1=gen1+1 and go to S34; otherwise, go to S311;

[0064] S311, output global optimal solution μ best .

[0065] Preferably, the non-dominated sorting and congestion calculation comprises:

[0066] Step 10, define the non-dominated sorting rule: for individual x s and individual x t , for any s=1,2,...,N, f1(x s )≤f1(x t ), and there exists at least one f1(x s) <f1(x t ) holds true, then the individual x s Dominant individual x t , and set s=1;

[0067] Step 20: Perform non-dominated sorting on the individuals in the current population and assign them to different non-dominated layers: for all t = 1, 2, ..., N and t ≠ s, compare the individuals x according to the definition. s and individual x t The non-dominance relationship between them; if there is no individual x t Better than individual x s , then label the individual x s is a non-dominated individual and is added to the set Y1;

[0068] Step 30, let s = s + 1, go to Step 20, until all non-dominated individuals are found, go to Step 40;

[0069] Step 40, calculate the difference between population X and set Y1 and use it as the new set X′, go to Step 20, repeat the non-dominated selection for the individuals in set X′, until all individuals in the population are classified according to the non-dominated relationship, go to Step 50;

[0070] Step 50: Calculate the crowding distance value C for individuals in the same non-dominated level. r Calculation of

[0071]

[0072] Wherein, subscript m is the index of the objective function, m = 1 or 2;

[0073] C r [s] m is the individual x in the mth objective function s The crowding distance value of

[0074] f m is the mth objective function;

[0075] f m (x s+1 ), f m (x s-1 ) are the individual x s The objective function values ​​of the next and previous individuals after sorting;

[0076] f m (x max ), f m (x min ) are the maximum and minimum values ​​of the individual objective function values, respectively.

[0077] Preferably, the following Shaking hybrid neighborhood structures are designed:

[0078] Shaking hybrid neighborhood structure 1: Define variables a and b, and randomly generate two integers within the interval and assign them to a and b, where a < b. Reverse the encoding between positions a and b in the sequence PL-OP; Shaking: Randomly select two relatively distant points for swapping, or randomly select a sequence for shuffling;

[0079] Shaking hybrid neighborhood structure 2: Define variables a and b, and randomly generate two integers within the interval and assign them to a and b, where a < b. Swap the encoding to the left of position a and to the right of position b in the sequence PL-OP; Shaking: Randomly shuffle the positions of several non-adjacent points;

[0080] Shaking hybrid neighborhood structure 3: Define variables a and b, and randomly generate two integers within the interval and assign them to a and b, where a < b. Swap the encoding at positions a and b in the sequence PL-OP; shaking: Randomly select multiple positions in the sequence, randomly shuffle the encoding at these positions, and re-execute local search on the new arrangement;

[0081] Shaking hybrid neighborhood structure 4: Define variables a and b, arbitrarily select two product categories from PL, assign the product category positions to variables a and b such that a < b, and swap the encoding at positions a and b in the sequence OP; shaking: Randomly select multiple product categories in the sequence, perform a large-scale swap of the encoding of these categories, and re-execute local search on the new arrangement;

[0082] Shaking hybrid neighborhood structure 5: Define variables a and b, arbitrarily select two product categories from PL, assign the product category positions to variables a and b such that a < b, and reverse the encoding at positions a and b in the sequence OP; shaking: Randomly select multiple different product categories in the sequence, or randomly select a sequence and perform a large-scale reverse or other random perturbation on it, and re-execute local search on the new arrangement;

[0083] Shaking Hybrid Neighborhood Structure 6: Define variables a and b, randomly select two product categories from PL, assign the positions of the product categories to variables a and b such that a < b, and swap the codes on the left side of position a and the right side of position b in the sequence OP; shaking: randomly select the codes of product categories or disrupt a relatively long coding sequence on the left side to greatly perturb the structure of the solution, and re - execute local search based on the new arrangement.

[0084] A joint economic lot - sizing multi - objective optimization system for a multi - product multi - level integrated supply chain, comprising:

[0085] An information acquisition module for acquiring index information, hierarchical information, cost information, and product information regarding the multi - level integrated supply chain; wherein, the multi - level integrated supply chain is a four - level supply chain composed of a single supplier, a single manufacturer, a single distributor, and multiple retailers;

[0086] A model construction module for constructing a mathematical model based on the index information, hierarchical information, cost information, and product information, with minimizing the total cost of the supply chain as the first optimization objective, minimizing the product replenishment cycle length as the second optimization objective, and combining random constraint information;

[0087] A solution solving module for solving the mathematical model by using a hybrid non - dominated sorting genetic algorithm based on neighborhood search to obtain the global optimal solution, and decoding to obtain the order batch and batch information of each supply chain level for the specified category of products within the complete replenishment cycle.

[0088] A storage medium storing a computer program for joint economic lot - sizing multi - objective optimization of a multi - product multi - level integrated supply chain, wherein the computer program causes a computer to execute the joint economic lot - sizing multi - objective optimization method as described above.

[0089] An electronic device, comprising:

[0090] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs include those for executing the joint economic lot - sizing multi - objective optimization method as described above.

[0091] (III) Advantageous Effects

[0092] The present invention provides a joint economic lot - sizing multi - objective optimization method, system, storage medium, and electronic device for a multi - product multi - level integrated supply chain. Compared with the prior art, the following beneficial effects are achieved:

[0093] The present invention recognizes the inventory and joint economic batch constraints of the multi-level integrated supply chain, that is, taking into account the inconsistencies in inventory and ordering capabilities of suppliers, manufacturers, distributors, and retailers, the joint economic batch problem of the multi-product multi-level integrated supply chain is optimized, and the capacity indicators of different levels are comprehensively considered. The problem is solved and an approximate optimal solution is obtained by using a hybrid non-dominated sorting genetic algorithm based on neighborhood search. This can effectively coordinate and optimize and design the order batches of multiple products at multiple levels, thereby maximizing the use of supplier resources and reducing the overall cost of the emergency supply chain, thereby improving the management capability and operational efficiency of the multi-product multi-level integrated supply chain. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] 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.

[0095] Figure 1 A block diagram of a joint economic batch multi-objective optimization method for a multi-product multi-stage integrated supply chain provided by an embodiment of the present invention;

[0096] FIG. 2( a ) is a diagram showing an example of encoding of a solution X1 for order batch sizes of different categories of products at each supply chain level provided by an embodiment of the present invention;

[0097] FIG. 2( b ) is a diagram showing an example of coding of a solution X2 for order batch sizes of different categories of products provided by an embodiment of the present invention;

[0098] Figure 3 A decoding example diagram provided by an embodiment of the present invention;

[0099] Figure 4 A flowchart of a hybrid non-dominated sorting genetic algorithm based on neighborhood search is provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0100] 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.

[0101] The embodiments of the present application solve the technical problem that existing theoretical models are unable to cope with the complexity and variability in reality by providing a joint economic batch multi-objective optimization method, system, storage medium and electronic device for a multi-product multi-level integrated supply chain, and pay more attention to the actual needs and constraints in the multi-product multi-level integrated supply chain, thereby optimizing resource utilization and improving the overall efficiency of the supply chain.

[0102] The technical solution in the embodiment of the present application is to solve the above technical problems, and the overall idea is as follows:

[0103] The existing joint economic batch problems focus more on the joint economic batch problems of multi-level supply chains under ideal conditions, with the emphasis on the optimal strategies for ordering, production and transportation batches of secondary and tertiary supply chains. The existing multi-level supply chain joint economic batch problems rarely consider various optimal strategies based on the actual needs of supply chain material replenishment. In addition, existing research usually ignores the inventory space constraints of supply chains at different levels, and also pays less attention to the problem of inconsistent capabilities of multi-level supply chains in reality.

[0104] The embodiment of the present invention optimizes the joint economic batch problem based on a multi-product multi-level integrated supply chain while taking into account the inconsistent capabilities of each layer of the multi-level integrated supply chain. It comprehensively considers the minimum cost of the supply chain and the minimum replenishment cycle of the product, solves the problem through a hybrid intelligent algorithm and obtains an approximate optimal solution. It can effectively coordinate and optimize and design the order batches of products at different levels of the supply chain, thereby maximizing the use of resources of the multi-level integrated supply chain and reducing the overall cost of the multi-level supply chain, thereby improving the management capability and operational efficiency of the multi-product multi-level integrated supply chain.

[0105] 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.

[0106] Embodiment 1:

[0107] like Figure 1 As shown, an embodiment of the present invention provides a joint economic batch multi-objective optimization method for a multi-product multi-stage integrated supply chain, including:

[0108] S1. Obtaining index information, hierarchical information, cost information, and product information about a multi-level integrated supply chain; wherein the multi-level integrated supply chain is a four-level supply chain consisting of a single supplier, a single manufacturer, a single distributor, and multiple retailers;

[0109] S2. Based on the index information, hierarchical information, cost information and product information, a mathematical model is constructed with minimizing the total cost of the supply chain as the first optimization goal and minimizing the length of the product replenishment cycle as the second optimization goal, and random constraint information is combined;

[0110] S3. A hybrid non-dominated sorting genetic algorithm based on neighborhood search is used to solve the mathematical model, obtain the global optimal solution, and decode the optimal order batch and batch information for the specified category of products at each supply chain level within the complete replenishment cycle.

[0111] The embodiments of the present invention pay more attention to the actual requirements and constraints in the multi-product multi-level integrated supply chain, thereby optimizing resource utilization and improving the overall efficiency of the supply chain.

[0112] Next, we will introduce the steps of the above scheme in detail:

[0113] First, it should be noted that the mathematical modeling in the embodiment of the present invention requires the use of the known information shown in Table 1. For details, see the description of the corresponding steps:

[0114] Table 1

[0115]

[0116]

[0117] In step S1, index information, hierarchical information, cost information and product information about a multi-level integrated supply chain is obtained; wherein the multi-level integrated supply chain is a four-level supply chain consisting of a single supplier, a single manufacturer, a single distributor and multiple retailers.

[0118] The embodiment of the present invention studies the joint economic batching problem of a four-stage supply chain consisting of a single supplier, a single manufacturer, a single distributor, and multiple retailers.

[0119] Accordingly, this step obtains the necessary information for modeling the problem, and the symbol set definition is shown in Table 2:

[0120] Table 2

[0121]

[0122] In step S2, based on the index information, hierarchical information, cost information and product information, a mathematical model is constructed with minimizing the total cost of the supply chain as the first optimization goal and minimizing the length of the product replenishment cycle as the second optimization goal, and combined with random constraint information.

[0123] For mathematical modeling, the embodiment of the present invention also introduces random constraint information as shown in Table 3:

[0124] Table 3

[0125]

[0126]

[0127] On this basis, the mathematical model constructed in this step includes:

[0128]

[0129]

[0130] Wherein, formula (1) indicates that minimizing the total cost TC of the supply chain is the first optimization objective; Min is the minimization function; TC s is the total cost of the supplier; TC p is the total cost of the manufacturer; TC w is the total cost of the distributor; TC r is the total cost to the retailer;

[0131] j is the retailer index, m is the total number of retailers; The cost of ordering product category i for retailer j in a single replenishment cycle; is the holding cost of product category i for retailer j in a single replenishment cycle; is the demand rate of product category i by retailer j in a single replenishment cycle;

[0132] Formula (6) indicates that minimizing the product replenishment cycle length T is the second optimization goal; W, Y, ε1, ε2, δ1, and δ2 are all intermediate variables and have no practical meaning;

[0133] Formula (15) represents the order quantity constraint; that is, the order quantity at each supply chain level must not exceed the maximum order quantity limit;

[0134] Formula (16) represents the inventory space constraint; that is, the size of products stored in the inventory space at each supply chain level must not exceed the maximum inventory space limit.

[0135] In step S3, a hybrid non-dominated sorting genetic algorithm based on neighborhood search is used to solve the mathematical model, obtain the global optimal solution, and decode the optimal order batch and batch information for the specified category of products at each supply chain level within the complete replenishment cycle.

[0136] The embodiment of the present invention designs a hybrid non-dominated sorting genetic algorithm based on neighborhood search, which combines the global optimization ability of the non-dominated sorting genetic algorithm with the local search ability of the variable neighborhood search algorithm. A corresponding adaptive selection mechanism is designed in the non-dominated sorting genetic algorithm and the variable neighborhood search algorithm, and a special crossover operator and a local search neighborhood structure are designed, which effectively improves the algorithm's solution efficiency and the quality of the solution.

[0137] Among them, Figure 2(a) to 2(b)As shown, the coding rules of the hybrid non-dominated sorting genetic algorithm based on neighborhood search are as follows:

[0138] Solution X consists of solution X1 for the order batch size of different categories of products at each supply chain level and solution X2 for the order batch size of different categories of products; assuming there are l replenishment cycles:

[0139] Solution X1 is represented by a three-dimensional integer array, which includes a list of supply chain levels SC, product categories PL, and product order batch sizes OP. The length of the sequence or list is n*(m1+m2)*l. The numbers in SC represent the number of the supply chain level, the numbers in PL represent the number of the product category, and OP represents the order batch size of the product category PL at the level SC. The list SC-PL represents the product categories required at each supply chain level, and the list SC-PL-OP represents the order batch size of the specified category of products at a certain level of the supply chain.

[0140] Solution X2 is represented by a two-dimensional integer array, which includes the product category code PL and the product supply batch size TM. The length of the sequence or list is n*(m1+m2)*l. Each column in the array represents the order batch size for the specified category of products at the corresponding level.

[0141] Correspondingly, the decoding process is to calculate the order batch size that minimizes the total supply chain cost among all product supply batches according to the actual scenario. Figure 3 As shown, the decoding rules of the hybrid non-dominated sorting genetic algorithm based on neighborhood search are as follows:

[0142] Step 100, extract the supply chain hierarchy table SC from the code of X1, and represent the number of each supply chain hierarchy according to the code SC; during decoding, identify the position of each supply chain hierarchy in the code.

[0143] Step 200: Parse product categories and extract the number of each product category in PL to associate each product category with different supply chain levels.

[0144] Step 300, decode the order batch size OP, extract the order batch size of each product category at different supply chain levels from OP, and match the corresponding demand according to the supply chain level and product category; the decoding result of the order batch is a multidimensional array, and each dimension corresponds to a specific supply chain level and product category.

[0145] Step 400, convert SC-PL-OP into ordering decisions for each supply chain level; through the combination of SC-PL-OP, allocate the order batch of each level to the corresponding product category and supply chain level to determine the order batch and order quantity information of each supply chain level.

[0146] Step 500: According to the encoding of X2, the product category number is obtained from PL during decoding, and the order batch information is extracted from TM.

[0147] Step 600, determine the batches of each product category in different cycles from the combination of TM in PL; for example, for a specific product category, the order batch size generated in each cycle should correspond to the order batch of TM.

[0148] Step 700: After decoding, the order quantity and batch information of each product category are allocated to each supply chain level to form an ordering plan within the complete cycle.

[0149] On this basis, if Figure 4 As shown, in this step, a hybrid non-dominated sorting genetic algorithm based on neighborhood search is used to solve the mathematical model to obtain a global optimal solution, including:

[0150] S31. Set input parameters, including: m1, m2, T i , α A , μ A .

[0151] S32, set execution parameters, including: maximum number of iterations Gen1; algorithm population size N; maximum number of iterations Gen2 for local search; initial cycle selection probability PT i =1 / T; neighborhood set Each Shaking mixed neighborhood structure NS k The initial selection probability P k =1 / k max .

[0152] S33, based on the encoding rule, generate an initial population, perform non-dominated sorting and crowding calculation, and record the current global optimal solution μ best .

[0153] This step and the subsequent step S35 perform non-dominated sorting and congestion calculation; including:

[0154] Step 10, define the non-dominated sorting rule: for individual x s and individual x t , for any s=1,2,...,N, f1(x s )≤f1(x t ), and there exists at least one f1(x s ) <f1(x t ) holds true, then the individual xs Dominant individual x t , and set s=1;

[0155] Step 20. Perform non-dominated sorting on the individuals in the current population and assign them to different non-dominated layers: for all t = 1, 2, ..., N and t ≠ s, compare the individuals x according to the definition. s and individual x t The non-dominance relationship between them; if there is no individual x t Better than individual x s , then label the individual x s is a non-dominated individual and is added to the set Y1;

[0156] Step 30, let s = s + 1, go to Step 20, until all non-dominated individuals are found, go to Step 40;

[0157] Step 40, calculate the difference between population X and set Y1 and use it as the new set X′, go to Step 20, repeat the non-dominated selection for the individuals in set X′ until all individuals in the population are classified according to the non-dominated relationship, and go to Step 50;

[0158] Step 50: Calculate the crowding distance value C for individuals in the same non-dominated level. r Calculation of

[0159]

[0160] Wherein, subscript m is the index of the objective function, m = 1 or 2;

[0161] C r [s] m is the individual x in the mth objective function s The crowding distance value of

[0162] f m is the mth objective function;

[0163] f m (x s+1 ), f m (x s-1 ) are the individual x s The objective function values ​​of the next and previous individuals after sorting;

[0164] f m (x max ), f m (x min ) are the maximum and minimum values ​​of the individual objective function values, respectively.

[0165] S34. Perform a crossover operation based on the current population.

[0166] Exemplarily, this step adopts a two-point intersection method, which is as follows:

[0167] Step 1a, randomly select two parent chromosomes p1 and p2, and use the roulette method to randomly determine a cycle in the (1, T) interval, perform a crossover operation in the selected cycle, and record the number of times the cycle is selected CT i .

[0168] Step 2a, in the parent chromosome interval Randomly generate two integers Cut1 and Cut2 as the intersection points, where

[0169] Step 3a, New Individual X s 'Copy individual X t The SC-PL-OP is located between Cut1 and Cut2, and the remaining codes are copied from the parent X in sequence. s The code that is not copied in the new individual X t 'Copy individual X s The SC-PL-OP is located between Cut1 and Cut2, and the remaining codes are copied from the parent X in sequence. t The encoding that was not copied in .

[0170] Step 4a: To maintain the population size, determine whether the number of crossovers k is greater than popsize / 2. If so, terminate the crossover operation and update the cycle selection probability. Otherwise, execute step S2 to reselect two parent individuals.

[0171] S35. Perform non-dominated sorting and crowding calculation on the current population.

[0172] S36. Select individuals according to the minimum dominance and maximum crowding strategies.

[0173] In this step, based on the non-dominated sorting and crowding values ​​of each individual in the updated new population, the selection operation is performed using the minimum dominance and maximum crowding strategies. The levels are selected in order from low to high non-dominated levels. In the same level, individuals are selected in order from large to small crowding levels as individuals of the next generation population, guiding the selection of N population individuals to obtain a new population with the same population size.

[0174] S37, Roulette-based selection of Shaking hybrid neighborhood structure NS k , according to the Shaking hybrid neighborhood structure NS kGenerate the neighborhood solution μ′ of the optimal individual μ in the population, and compare the objective function values of the neighborhood solution μ′ and the optimal individual μ in the population to compare their advantages and disadvantages; if the neighborhood solution μ′ is better, update the optimal individual μ in the population, and if the local search falls into a local optimal solution, perform the Shaking operation.

[0175] Exemplarily, the embodiments of the present invention design the following Shaking hybrid neighborhood structures:

[0176] Shaking hybrid neighborhood structure 1: Define variables a and b, and randomly generate two integers in the interval and assign them to a and b, where a < b, and reverse the encoding of the positions between position a and position b in the sequence PL-OP; Shaking: Randomly select two relatively far points for exchange, or randomly select a segment of the sequence for scrambling;

[0177] Shaking hybrid neighborhood structure 2: Define variables a and b, and randomly generate two integers in the interval and assign them to a and b, where a < b, and swap the encodings of the positions to the left of position a and to the right of position b in the sequence PL-OP; Shaking: Randomly scramble the positions of several non-adjacent points;

[0178] Shaking hybrid neighborhood structure 3: Define variables a and b, and randomly generate two integers in the interval and assign them to a and b, where a < b, and swap the encodings of the positions at a and b in the sequence PL-OP; shaking: Randomly select multiple positions (not limited to a and b) in the sequence, randomly scramble the encodings of these positions, and re-perform local search on the basis of the new arrangement;

[0179] Shaking hybrid neighborhood structure 4: Define variables a and b, arbitrarily select two product types from PL, assign the product type positions to variables a and b so that a < b, and swap the encodings at positions a and b in the sequence OP; shaking: Randomly select multiple product types in the sequence (not limited to a and b), greatly exchange the encodings of these types, and re-perform local search on the basis of the new arrangement;

[0180] Shaking hybrid neighborhood structure 5: Define variables a and b, arbitrarily select two product types from PL, assign the product type positions to variables a and b so that a < b, and reverse the encoding of the positions at a and b in the sequence OP; shaking: Randomly select multiple different product types in the sequence, or randomly select a segment of the sequence, perform a large-scale reverse order or other random perturbations on it, and re-perform local search on the basis of the new arrangement;

[0181] Shaking Hybrid Neighborhood Structure 6: Define variables a and b, arbitrarily select two product categories from PL, assign the positions of the product categories to variables a and b such that a < b, and swap the codes to the left of position a and to the right of position b in sequence OP; shaking: randomly select the codes of product categories (not limited to a and b), or disrupt a relatively long code sequence on the left to greatly perturb the structure of the solution, and re - execute local search based on the new arrangement.

[0182] S38. Determine whether gen2 ≤ Gen2 holds. If so, set gen2 = gen2 + 1 and transfer to S37; otherwise, transfer to S39.

[0183] Furthermore, the embodiments of the present invention can also record the successful times of each neighborhood structure and dynamically adjust the selection probability of the neighborhood structure to more effectively explore the solution space.

[0184] S39. Output the optimal solution μ″ of the neighborhood search, update the population and the current global optimal solution μ best 。

[0185] S310. Determine whether gen1 ≤ Gen1 holds. If so, set genn1 = gen1 + 1 and transfer to S34; otherwise, transfer to S311.

[0186] S311. Output the global optimal solution μ best 。

[0187] Finally, based on the output global optimal solution μ best , the order batches and batch quantities of each supply chain level for the specified category of products within the complete replenishment cycle are decoded according to the above - mentioned decoding rules.

[0188] Thus far, the embodiments of the present invention have completed all the processes of the joint economic lot - sizing multi - objective optimization method for a multi - product multi - level integrated supply chain.

[0189] Embodiment 2:

[0190] The embodiments of the present invention provide a joint economic lot - sizing multi - objective optimization system for a multi - product multi - level integrated supply chain, including:

[0191] An information acquisition module, configured to acquire index information, level information, cost information, and product information about the multi - level integrated supply chain; wherein, the multi - level integrated supply chain is a four - level supply chain composed of a single supplier, a single manufacturer, a single distributor, and multiple retailers;

[0192] A model building module, for building a mathematical model based on the index information, hierarchical information, cost information and product information, with minimizing the total cost of the supply chain as a first optimization goal, minimizing the length of the product replenishment cycle as a second optimization goal, and combining random constraint information;

[0193] The solution solving module is used to solve the mathematical model by using a hybrid non-dominated sorting genetic algorithm based on neighborhood search, obtain the global optimal solution, and decode the optimal order batch and batch information for the specified category of products at each supply chain level within the complete replenishment cycle.

[0194] Embodiment 3:

[0195] An embodiment of the present invention provides a storage medium storing a computer program for joint economic batch multi-objective optimization of a multi-product multi-level integrated supply chain, wherein the computer program enables a computer to execute the joint economic batch multi-objective optimization method as described in Example 1.

[0196] Embodiment 4:

[0197] An embodiment of the present invention provides an electronic device, including:

[0198] One or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, the programs including methods for executing the joint economic batch multi-objective optimization method as described in Example 1.

[0199] It can be understood that the joint economic batch multi-objective optimization system, storage medium and electronic device for the multi-product multi-level integrated supply chain provided in the embodiments of the present invention correspond to the joint economic batch multi-objective optimization method for the multi-product multi-level integrated supply chain provided in the embodiments of the present invention, and the explanations, examples and beneficial effects of the relevant contents can refer to the corresponding parts in the joint economic batch multi-objective optimization method, which will not be repeated here.

[0200] In summary, compared with the prior art, the present invention has the following beneficial effects:

[0201] 1. The embodiment of the present invention optimizes the joint economic batch problem based on a multi-product multi-level integrated supply chain while taking into account the inconsistent capabilities of each layer of the multi-level integrated supply chain. It comprehensively considers the minimum cost of the supply chain and the minimum replenishment cycle of the product, solves the problem through a hybrid intelligent algorithm and obtains an approximate optimal solution. It can effectively coordinate and optimize and design the order batches of products at different levels of the supply chain, thereby maximizing the use of resources of the multi-level integrated supply chain and reducing the overall cost of the multi-level supply chain, thereby improving the management capability and operation efficiency of the multi-product multi-level integrated supply chain.

[0202] 2. The embodiment of the present invention designs a hybrid non-dominated sorting genetic algorithm based on neighborhood search, which combines the global optimization ability of the non-dominated sorting genetic algorithm with the local search ability of the variable neighborhood search algorithm. A corresponding adaptive selection mechanism is designed in the non-dominated sorting genetic algorithm and the variable neighborhood search algorithm, and a special crossover operator and local search neighborhood structure are designed, which effectively improves the algorithm's solution efficiency and the quality of the solution.

[0203] 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.

[0204] 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 joint economic batch multi-objective optimization method for a multi-product multi-stage integrated supply chain, characterized in that: include: Obtaining index information, hierarchical information, cost information, and product information about a multi-level integrated supply chain; wherein the multi-level integrated supply chain is a four-level supply chain consisting of a single supplier, a single manufacturer, a single distributor, and multiple retailers; Based on the index information, hierarchical information, cost information and product information, a mathematical model is constructed with minimizing the total cost of the supply chain as a first optimization goal and minimizing the length of the product replenishment cycle as a second optimization goal, and random constraint information is combined; A hybrid non-dominated sorting genetic algorithm based on neighborhood search is used to solve the mathematical model, obtain the global optimal solution, and decode the optimal order batch and batch information for the specified category of products at each supply chain level within the complete replenishment cycle.

2. The joint economic batch multi-objective optimization method according to claim 1, characterized in that: (1) The index information includes: Hierarchical index set A = {s, p, w, r}, where s is the supplier, p is the manufacturer, w is the distributor, and r is the retailer; Product category index set i = {1, 2, ..., n}, where n is the total number of product categories; (2) The hierarchical information includes: Demand rate collection in is the demand rate for product category i at supply chain level A in a single replenishment cycle; The productivity set P = {p A }, where p A is the productivity of supply chain level A in a single replenishment cycle; Order Bulk Collection in is the order quantity for product category i at supply chain level A in a single replenishment cycle; Order batch set m = {m1, m2}, where m1 is the product order batch of the supplier in a single replenishment cycle, and m2 is the product order batch of the manufacturer in a single replenishment cycle; (3) The cost information includes: Required product preparation cost set in The cost of preparing raw materials for product category i in a single replenishment cycle for supply chain level A; Required product ordering cost set in The cost of ordering product category i for supply chain tier A in a single replenishment cycle; Required product holding cost set in HP is the holding cost of product category i at supply chain level A in a single replenishment cycle; i A HP represents the finished product holding cost of product category i. i A represents the raw material holding cost of product category i; (4) The product information includes: The required product replenishment cycle length set T = {T1,…,T i ,…,T n }, where T i is the replenishment cycle length of the required product category i; The required product category inventory size set in The inventory size of product category i is stored for supply chain level A; (5) The random constraint information includes: The set of random constraint violation probabilities α = {α A }, where α A is the probability of random constraint violation corresponding to supply chain level A; The set of critical points of standard normal value Z={Z αA }, where Z αA is the critical point of the standard normal value corresponding to supply chain level A; The average value set of resources μ = {μ A }, where μ A It is the average value of resources corresponding to supply chain level A.

3. The joint economic batch multi-objective optimization method according to claim 2, characterized in that: The mathematical model includes: Wherein, formula (1) indicates that minimizing the total cost TC of the supply chain is the first optimization objective; Min is the minimization function; TC s is the total cost of the supplier; TC p is the total cost of the manufacturer; TC w is the total cost of the distributor; TC r is the total cost to the retailer; j is the retailer index, m is the total number of retailers; The cost of ordering product category i for retailer j in a single replenishment cycle; is the holding cost of product category i for retailer j in a single replenishment cycle; is the demand rate of product category i by retailer j in a single replenishment cycle; Formula (6) indicates that minimizing the product replenishment cycle length T is the second optimization goal; W, Y, ε1, ε2, δ1, and δ2 are all intermediate variables and have no practical meaning; Formula (15) represents the order quantity constraint; Formula (16) represents the inventory space constraint.

4. The joint economic batch multi-objective optimization method according to claim 3, characterized in that: The coding rules of the hybrid non-dominated sorting genetic algorithm based on neighborhood search are as follows: Solution X consists of solution X1 for the order batch size of different categories of products at each supply chain level and solution X2 for the order batch size of different categories of products; assuming there are l replenishment cycles: Solution X1 is represented by a three-dimensional integer array, which includes a list of supply chain levels SC, product categories PL, and product order batch sizes OP. The length of the sequence or list is n*(m1+m2)*l. The numbers in SC represent the number of the supply chain level, the numbers in PL represent the number of the product category, and OP represents the order batch size of the product category PL at the level SC. The list SC-PL represents the product categories required at each supply chain level, and the list SC-PL-OP represents the order batch size of the specified category of products at a certain level of the supply chain. Solution X2 is represented by a two-dimensional integer array, which includes the product category code PL and the product supply batch size TM. The length of the sequence or list is n*(m1+m2)*l. Each column in the array represents the order batch size for the specified category of products at the corresponding level. And the decoding rules of the hybrid non-dominated sorting genetic algorithm based on neighborhood search are as follows: Step 100, extract the supply chain hierarchy table SC from the code of X1, and represent the number of each supply chain hierarchy according to the code SC; when decoding, identify the position of each supply chain hierarchy in the code; Step200. Analyze the product categories, extract the numbers of each product category from the PL to associate each product category with different supply chain levels; Step300. Decode the order quantity OP, extract the order quantity of each product category at different supply chain levels from the OP, and match the corresponding demand according to the supply chain level and product category respectively; where the decoding result of the order quantity is a multi-dimensional array, and each dimension corresponds to a specific supply chain level and product category; Step400. Convert SC-PL-OP into order decisions for each supply chain level; through the combination of SC-PL-OP, allocate the order quantity of each level to the corresponding product category and supply chain level to determine the order batch and order quantity information of each supply chain level; Step500. According to the encoding of X2, obtain the product category number from the PL during decoding, and extract the order batch information from the TM; Step600. Determine the batches of each product category in different periods from the combination of PL and TM; Step700. After decoding, allocate the order quantity and batch information of each product category to each supply chain level to form an order plan within a complete cycle.

5. The joint economic batch multi-objective optimization method according to claim 4, characterized in that: The use of a hybrid non-dominated sorting genetic algorithm based on neighborhood search to solve the mathematical model and obtain the global optimal solution includes: S31. Set input parameters, including: pA, m1, m2, T i , α A , μ A ; S32, set execution parameters, including: maximum number of iterations Gen1; algorithm population size N; maximum number of iterations Gen2 for local search; initial cycle selection probability PT i =1 / T; neighborhood set Each Shaking mixed neighborhood structure NS k The initial selection probability P k =1 / k max ; Let gen1 = gen2 = 1; S33, based on the encoding rule, generate an initial population, perform non-dominated sorting and crowding calculation, and record the current global optimal solution μ best ; S34. Perform crossover operations based on the current population; S35. Perform non-dominated sorting and crowding degree calculation on the current population; S36. Select individuals according to the minimum domination degree and maximum crowding strategy; S37, Roulette-based selection of Shaking hybrid neighborhood structure NS k , according to the Shaking hybrid neighborhood structure NS k Generate a neighborhood solution μ′ of the optimal individual μ of the population, and compare the neighborhood solution μ′ and the objective function value of the optimal individual μ of the population to compare the advantages and disadvantages of the two; if the neighborhood solution μ′ is better, update the optimal individual μ of the population; if the local search falls into the local optimal solution, execute operate; S38. Determine whether gen2 ≤ Gen2 holds. If so, set gen2 = gen2 + 1 and transfer to S37; otherwise, transfer to S39; S39, output the optimal solution μ″ of the neighborhood search, update the population and the current global optimal solution μ best ; S310. Determine whether gen1 ≤ Gen1 holds. If so, set gen1 = gen1 + 1 and transfer to S34; otherwise, transfer to S311; S311, output global optimal solution μ best .

6. The joint economic batch multi-objective optimization method according to claim 5, characterized in that: The non-dominated sorting and crowding degree calculation includes: Step 10, define the non-dominated sorting rule: for individual x s and individual x t , for any s=1,2,...,N, f1(x s )≤f1(x t ), and there exists at least one f1(x s ) <f1(x t ) holds true, then the individual x s Dominant individual x t , and set s=1; Step 20. Perform non-dominated sorting on the individuals in the current population and assign them to different non-dominated layers: for all t = 1, 2, ..., N and t ≠ s, compare the individuals x according to the definition. s and individual x t The non-dominance relationship between them; if there is no individual x t Better than individual x s , then label the individual x s is a non-dominated individual and is added to the set Y1; Step30. Let s = s + 1, and transfer to Step20 until all non-dominated individuals are found, then transfer to Step40; Step40. Calculate the difference between the population X and the set Y1 and use it as the new set X′, transfer to Step20, and repeat non-dominated selection for the individuals in the set X′ until all individuals in the population are classified according to the non-dominated relationship, then transfer to Step50; Step 50: Calculate the crowding distance value C for individuals in the same non-dominated level. r Calculation of Among them, the subscript m is the index of the objective function, m = 1 or 2; C r [s] m is the individual x in the mth objective function s The crowding distance value of f m is the mth objective function; f m (x s+1 ), f m (x s-1 ) are the individual x s The objective function values ​​of the next and previous individuals after sorting; f m (x max ), f m (x min ) are the maximum and minimum values ​​of the individual objective function values, respectively.

7. The joint economic batch multi-objective optimization method according to claim 5, characterized in that: Design the following Shaking hybrid neighborhood structure: Shaking Hybrid Neighborhood Structure 1: Define variables a and b, and randomly generate two integers within the interval and assign them to a and b, where a < b. Reverse the encoding of the sequence PL-OP between positions a and b; Shaking: Randomly select two relatively distant points for swapping, or randomly select a sequence segment for scrambling; Shaking Hybrid Neighborhood Structure 2: Define variables a and b, and randomly generate two integers within the interval and assign them to a and b, where a < b. Swap the encodings at positions to the left of a and to the right of b in the sequence PL-OP; Shaking: Randomly shuffle the positions of several non-adjacent points; Shaking Hybrid Neighborhood Structure 3: Define variables a and b, and randomly generate two integers within the interval and assign them to a and b, where a < b. Swap the encodings at positions a and b in the sequence PL-OP; shaking: Randomly select multiple positions in the sequence, randomly shuffle the encodings at these positions, and re-execute local search based on the new arrangement; Shaking hybrid neighborhood structure 4: Define variables a and b, arbitrarily select two product types from the PL, assign the positions of the product types to variables a and b so that a < b, and swap the encodings at positions a and b in the sequence OP; shaking: randomly select multiple product types in the sequence, perform a large-scale exchange of the encodings of these types, and re-execute local search based on the new arrangement; Shaking Hybrid Neighborhood Structure 5: Define variables a and b, arbitrarily select two product categories from PL, assign the positions of the product categories to variables a and b such that a < b, and reverse the codes at positions a and b in sequence OP; shaking: randomly select multiple different product categories in the sequence, or randomly select a section of the sequence, reverse it or perform other random perturbations on a large scale, and re - execute local search based on the new arrangement; Shaking Hybrid Neighborhood Structure 6: Define variables a and b, arbitrarily select two product categories from PL, assign the positions of the product categories to variables a and b such that a < b, and swap the codes to the left of position a and to the right of position b in sequence OP; shaking: randomly select the codes of product categories, or disrupt a relatively long coding sequence on the left to greatly perturb the structure of the solution, and re - execute local search based on the new arrangement.

8. A joint economic batch multi-objective optimization system for a multi-product multi-stage integrated supply chain, characterized in that: Including: An information acquisition module for acquiring index information, hierarchical information, cost information, and product information regarding a multi - level integrated supply chain; wherein, the multi - level integrated supply chain is a four - level supply chain composed of a single supplier, a single manufacturer, a single distributor, and multiple retailers; A model construction module for constructing a mathematical model based on the index information, hierarchical information, cost information, and product information, with minimizing the total cost of the supply chain as the first optimization objective, minimizing the product replenishment cycle length as the second optimization objective, and combining random constraint information; A solution solving module for solving the mathematical model using a hybrid non - dominated sorting genetic algorithm based on neighborhood search, obtaining the global optimal solution, and decoding to obtain the order batch and batch information of each supply chain level for the specified category of products within the complete replenishment cycle.

9. A storage medium, characterized in that: It stores a computer program for the joint economic lot - sizing multi - objective optimization of a multi - product multi - level integrated supply chain, wherein the computer program causes a computer to execute the joint economic lot - sizing multi - objective optimization method according to any one of claims 1 to 7.

10. An electronic device, characterized in that: Including: One or more processors; A memory; And one or more programs, wherein the one or more programs are stored in the memory and are configured to be executed by the one or more processors, and the programs include those for executing the joint economic lot - sizing multi - objective optimization method according to any one of claims 1 to 7.

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