A multi-level supply chain distribution optimization method based on an improved hill climbing method

Abstract

The present invention discloses a multi-level supply chain distribution optimization method based on an improved hill climbing method. The method includes the steps of: (1) establishing a mathematical model for supply chain distribution optimization; (2) solving the optimization mathematical model in step (1) using a greedy algorithm, and optimizing the initial solution using the improved hill climbing method. The present invention uses an improved hill climbing method with an increased memory function to solve the problem that the selection of the starting point of the hill climbing method has a great influence on the search result, so as to effectively solve the multi-level supply chain distribution optimization with large-scale and multi-period demands and the problem of dynamic selection of nodes, and provide certain decision-making references for the optimization of the multi-level supply chain distribution network.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi - level supply chain distribution optimization, and relates to a multi - level supply chain distribution optimization method based on an improved hill - climbing method. Background Art

[0002] After entering the 1980s, the focus of supply chain management has gradually shifted from the management of supply and production links to the demand side, and the entire supply chain has been reflected as a "demand chain" driven by market and customer demands. In a complex manufacturing environment facing customers, the driving force for enterprise development has changed from manufacturing production to creating added value through distribution and services. Constructing a supply chain distribution network in a scientific and reasonable way and strengthening the quality control of the distribution link are important ways to improve customer satisfaction and enhance enterprise competitiveness.

[0003] A distribution network refers to a hierarchical sales network composed of logistics nodes such as supply points, distribution centers, and demand points (customer areas). Commonly used optimization methods are mainly divided into two categories: exact algorithms (branch - and - bound method, integer programming, non - linear programming, etc.) and heuristic algorithms (genetic algorithm, greedy algorithm, hill - climbing method, etc.). Due to its own defects, the exact algorithm is not suitable for solving large - scale problems. The following mainly introduces the application of some heuristic algorithms in the optimization of the supply chain distribution network.

[0004] In the literature "Lang Maoxiang, Hu Siji. Research on solving the optimization problem of logistics distribution path using a hybrid genetic algorithm [J]. Chinese Journal of Management Science, 2002(05):52 - 57", in order to improve the local search ability of the genetic algorithm, the hill - climbing algorithm is combined with the genetic algorithm and used to solve the optimization problem of logistics distribution path; in the literature "Zhang Juanping. Cloud computing optimization of logistics vehicle path planning algorithm [J]. Machinery Design & Manufacture, 2022, 372(02):168 - 170 + 176", the application of the vehicle optimization debugging algorithm based on an improved particle swarm algorithm in the optimal path planning problem of logistics enterprise vehicle distribution under cloud computing conditions is studied; in the literature "Ma Huimin, Ye Chunming, Zhang Shuang, Xu Shengliang. Research on production - distribution collaborative planning problem [J]. Machinery Design & Manufacture, 2009, 221(07):201 - 203", a supply chain network with one factory, multiple products, multiple production cycles, and one distribution center is studied, and the particle swarm algorithm is used to solve the production - distribution collaborative planning problem; in the literature "Hao Juan. Construction and simulation optimization of a multi - level supply chain network considering allowable shortages [D]. Xi'an University of Technology, 2018", the particle swarm algorithm is used to solve the production - distribution collaborative optimization model problem constructed with the core of the lowest overall enterprise operation cost and the best customer evaluation.

[0005] With the rapid development of information technology, the number of distribution tasks to be completed by manufacturing enterprises is gradually increasing in a massive manner. However, existing research methods rarely consider the optimization problem of supply chain distribution networks with large-scale and multi-period demands, making it difficult to meet the needs of complex development trends. How to quickly solve the distribution problem of supply chain networks with large-scale and multi-period demands and improve the response speed of supply chain distribution networks has become one of the important issues that need to be concerned in the optimization of supply chain distribution networks. The literature "Ramiz (2022). Applying Greedy Algorithm and Local Search in a Supply Chain distribution problem, MATLAB Central File Exchange. Retrieved April 7, 2022" constructed a two-level supply chain network distribution model considering production restrictions in factories and sales losses at sales points, and solved the model using a heuristic algorithm. However, due to the lack of consideration of the multi-level characteristics of the supply chain network and the significant influence of the starting point on the algorithm search results, the guiding significance for actual decision-making is greatly reduced. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a multi-level supply chain distribution optimization method based on an improved hill-climbing method, which applies the greedy algorithm and the improved hill-climbing method with a memory function to the optimization problem of multi-level supply chain distribution networks, and effectively solves the problems of multi-level supply chain distribution optimization with large-scale and multi-period demands and dynamic selection of nodes.

[0007] The technical solution adopted by the present invention is: a multi-level supply chain distribution optimization method based on an improved hill-climbing method, which includes the following steps:

[0008] (1) Establish a mathematical model for supply chain distribution optimization:

[0009]

[0010] The constraint conditions are:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017] In the formula, L, σ, N, y ∈ [0, 1], F number of factories, S number of primary sales points, M number of secondary sales points, t time unit, i factory, j primary sales point, n secondary sales point, ij transportation from factory i to primary sales point j, jn transportation from primary sales point j to secondary sales point n, σ inventory quantity, N number of vehicles, quantity of sales loss, y determines whether the factory starts production, C factory capacity, d demand of sales point, T time range, h inventory cost, L sales loss cost, vehicle capacity, k transportation cost, production start-up cost of factory, Cap capacity of product, q transportation quantity;

[0018] Where:

[0019] Equation (1): The sum of the factory inventory cost, production start-up cost, and the inventory costs and sales loss costs of the primary / secondary sales points, as well as the transportation costs from the factory to the primary sales point and between the primary and secondary sales points within the entire time range T;

[0020] Equations (2), (3): The relationships between inventory, transportation quantity, lost sales, and demand at times t and t - 1;

[0021] Equations (4), (5): The relationships between production activation and inventory surplus between times t and t - 1. It is important to emphasize that when the factory is activated, its production will reach the maximum;

[0022] Equations (6), (7): Used to calculate the number of vehicles N for each route from i to j and from j to n ij / N jn ;

[0023] (2) Use the greedy algorithm to solve the optimization mathematical model in step (1), and use the improved hill climbing method to optimize the initial solution.

[0024] The process of solving the optimization mathematical model includes the following steps:

[0025] S1: Start, input the initial data, t = 1;

[0026] S2: Select the secondary sales point according to Equation (8);

[0027]

[0028] In the formula, Inventory quantity of secondary sales point n at time t; L n : Sales loss cost of secondary sales point n;

[0029] S3: Select the primary sales points according to Equation (9); obtain the distribution plan from the primary sales points to the secondary sales points at time t; record the selected secondary sales points and the corresponding primary sales points in sequence for each t value into matrix M1;

[0030]

[0031] S4: Select the primary sales points according to Equation (10);

[0032]

[0033] where, The inventory quantity of primary sales point j at time t; L j : The sales loss cost of primary sales point j;

[0034] S5: Select the corresponding factories according to Equation (11); obtain the distribution plan from the factories to the primary sales points at time t; record the selected primary sales points and the corresponding factories in sequence for each t value into matrix M2;

[0035]

[0036] S6: Determine whether t is greater than the threshold T (let T = 12). If so, output the initial distribution plan matrix; if not, return to S2 until t meets the condition;

[0037] S7: Improve the initial TM in a certain order using M1 and M2, changing the value of one cell of the initial TM each time;

[0038] S8: Recalculate the cost of the modified distribution plan, only retaining the modifications that reduce the cost;

[0039] S9: Determine whether t is greater than the threshold T (T = 12). If so, output the changed optimal TM, cost, and time; if not, return to S7 until t meets the condition.

[0040] Advantages of the present invention: Compared with the prior art, the present invention uses an improved hill-climbing method with an increased memory function to solve the problem that the selection of the starting point of the hill-climbing method has a greater impact on the search results, thereby effectively solving the optimization of multi-level supply chain distribution with large-scale and multi-period demands and the problem of dynamic selection of nodes, providing a certain decision-making reference for the optimization of the multi-level supply chain distribution network. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a three-level distribution network diagram; in the figure, F: factory; PPOS: primary sales point; SPOS: secondary sales point;

[0042] Figure 2 is the flowchart of IHCM;

[0043] Figure 3 It is a cost comparison chart. Specific implementation manners

[0044] The present invention will be further introduced below in conjunction with specific embodiments.

[0045] Embodiment 1: A multi-level supply chain distribution optimization method based on an improved hill climbing method, the method comprising the following steps:

[0046] (1) Establish a mathematical model for supply chain distribution optimization:

[0047] 1.1. Problem description and assumptions

[0048] The research object is a three-level supply chain distribution network composed of F factories (Factory, F), S primary points of sale (Primary Point Of Sale, PPOS), and M secondary points of sale (Secondary Point Of Sale, SROS), as Figure 1 shown. For each factory i ∈ F, it has a fixed capacity C i , and the secondary point of sale n ∈ M transmits a demand d n to the primary point of sale j ∈ S. After the primary point of sale j meets the demand of the secondary point of sale n, it sends a demand d j to the factory. In order to truly simulate the distribution network from an overall perspective, a suitable distribution plan is considered within the time range T. Given data such as the demand of the secondary point of sale and the production capacity of the factory in advance (as shown in Tables 2 to 6), an appropriate master distribution plan can be formulated over the time range T (for example, a year), where T consists of multiple t (for example, months). Thus, our goal is to minimize the total distribution cost within the time range T.

[0049] Use σ t to represent the inventory of each factory i, primary point of sale j, and secondary point of sale n at time t. Considering practical factors such as production and transportation delays, it is allowed for the point of sale to hold a certain amount of inventory, and the inventory cost is represented by h. Regarding the factory, under the start-up production cost , according to the relationship between the factory inventory and the demand of the point of sale, it decides whether to produce within the time unit t; regarding the point of sale, the inventory σ between two time periods can be used to meet the demand of the next time period. In a traditional distribution network, the connection between the factory and the distribution point is fixed. Here, it is allowed for the path connection between the factory and the point of sale to change, enabling dynamic selection of each cycle node. Given a general time unit t, the demand data is known at the start of the time unit t, all decisions are made after the start of the time unit t, and only the evaluation of the inventory σ is at the end of the time unit t.

[0050] In the supply chain, transportation activities are usually carried out by trucks or other transportation means, and the total transportation cost will depend on the number of vehicles N used for transportation activities. N ij / N jn is the number of vehicles used to transport a certain quantity of products q ij / q jn from factory i / j to the sales point j / n. Given that the vehicle capacity is the transportation cost is k ij / k jn . In addition, it is assumed that only one type of vehicle can be used, i.e., the vehicle capacity is fixed. If the demand d j / d n at the sales point cannot be met, a loss quantity is generated and a cost L j / L n needs to be paid.

[0051] 1.2 Mathematical Model

[0052] Based on the above description and assumptions, the objective function of the total distribution cost of the three-level supply chain distribution network model within the time range T is established as follows in Equation (1), where the symbols and meanings of the relevant parameters of the three-level supply chain distribution network model are shown in Table 1.

[0053]

[0054] The constraints are:

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] In the formula, L, σ, N, y ∈ [0, 1], F is the number of factories, S is the number of primary sales points, M is the number of secondary sales points, t is the time unit, i is the factory, j is the primary sales point, n is the secondary sales point, ij is from factory i to primary sales point j, jn is from primary sales point j to secondary sales point n, σ is the inventory quantity, N is the number of vehicles, The quantity of sales loss, y determines whether the factory starts production, C is the factory capacity, d is the demand at the sales point, T is the time range, h is the inventory cost, L is the sales loss cost, The vehicle capacity, k is the transportation cost, The production start-up cost of the factory, Cap is the capacity of the product, q is the transportation quantity;

[0062] Table 1 Model parameter symbols and their meanings

[0063]

[0064] Where:

[0065] Equation (1): The sum of the factory inventory cost, production start-up cost, and the inventory cost and sales loss cost at the first / second-level sales points, as well as the transportation cost from the factory to the first-level sales point and the transportation cost between the first-level and second-level sales points within the entire time range T;

[0066] Equations (2), (3): The relationships between inventory, transportation quantity, lost sales, and demand at times t and t - 1;

[0067] Equations (4), (5): The relationships between production activation and inventory surplus between times t and t - 1. It is important to emphasize that when the factory is activated, its production will reach the maximum;

[0068] Equations (6), (7): Used to calculate the number of vehicles N for each route from i to j and j to n ij / N jn ;

[0069] (2) The greedy algorithm is used to solve the optimization mathematical model in step (1). To improve the solution obtained by the greedy algorithm, the improved hill-climbing method is used to optimize the initial solution.

[0070] The greedy algorithm (Greedy Algorithm, GR) is a common, simple, and rapid method for solving optimization problems. It has the characteristics of fast solution speed and obtaining a relatively good approximate solution in solving large-scale multi-period demand distribution problems. However, since it does not consider the problem as a whole and always chooses the best change at present, it is difficult to obtain the global optimal solution.

[0071] The Hill Climbing Method (HCM) is a classic local search algorithm that moves only when it finds a better position, i.e., if the objective function improves, then we adopt the provided solution; otherwise, we return to the previous step. If there is no adjacent move with a better objective function value, the algorithm stops; however, whether the hill climbing method can find the global optimal solution is highly related to the choice of the starting point. A poor choice of the starting point may lead to unsatisfactory search results. Therefore, we use an improved hill climbing method with an added memory function to solve the problem that the choice of the starting point of the hill climbing method has a significant impact on the search results; in this problem, a solution (obtained by the greedy algorithm) tells us the quantity sent from factory i to primary sales point j and from primary sales point j to secondary sales point n within time period t. q ij / q jn is an integer value that requires a certain number of vehicles for transportation. There is often some unused space in the vehicles, so the improved hill climbing method rounds the transportation quantity q jn in a certain order and applies it to the greedy algorithm, and then tries to see the objective function value obtained through such modification.

[0072] First, according to the choice of the greedy strategy in the greedy algorithm, an added memory function is used to record the order of the sales points and the corresponding factories selected by the greedy algorithm at each time into matrices M1 and M2; second, M1 and M2 are applied to the choice of the starting point of the hill climbing method; finally, local search of the hill climbing method is performed with the goal of minimizing the total distribution cost within the entire time range. The flowchart of the improved hill climbing method (IHCM) is as Figure 2 shown.

[0073] t represents a time unit; TM represents the distribution plan matrix; matrix M1 is used to record the order of selecting secondary sales points and the corresponding primary sales points within the entire time range (T = 12); matrix M2 is used to record the order of selecting primary sales points and the corresponding factories within the entire time range (T = 12).

[0074] The specific process of solving the optimization mathematical model includes the following steps:

[0075] S1: Start, input the initial data, t = 1;

[0076] S2: The core of the greedy algorithm lies in the choice of the greedy strategy. First, use the greedy algorithm to determine the sales point with the potential maximum loss of sales cost, aiming to improve the objective equation by reducing this cost. Within the given time t, select the secondary sales point according to Equation (8);

[0077]

[0078] In the formula, the inventory quantity of secondary sales point n at time t; Ln : The sales loss cost of the secondary sales point n;

[0079] After selecting a secondary sales point using formula (8), the next step is to select a primary sales point to meet the demand generated at time t. The selection of the primary sales point is based on inventory cost transportation cost the lowest combined cost; where each cost is unitized according to the mathematical formula in formula (9), and the primary sales point initially has a capacity of Cap j ;

[0080] S3: Select the primary sales point according to formula (9); obtain the distribution plan from the primary sales point to the secondary sales point at time t; record the selected secondary sales point and the corresponding primary sales point sequence at each t value into matrix M1;

[0081]

[0082] With each step of the calculation, the remaining inventory of each primary sales point is updated. If there are enough products in a given primary sales point to meet the demand of a secondary sales point, then these products will be used first;

[0083] After completing the distribution plan between the primary sales point and the secondary sales point, the primary sales point sends a demand d to the factory j , select the primary sales point according to formula (10), and select the factory according to formula (11). It should be noted that the y in this algorithm i depends on two factors: if the factory does not produce during this time t, then the value of y i is zero; if production is selected to be activated, its value will be 1; the factory initially has a capacity of Cap j ;

[0084] S4: Select the primary sales point according to formula (10);

[0085]

[0086] In the formula, the inventory quantity of the primary sales point j at time t; L j : The sales loss cost of the primary sales point j;

[0087] S5: Select the corresponding factory according to formula (11); obtain the distribution plan from the factory to the primary sales point at time t; record the selected primary sales point and the corresponding factory sequence at each t value into matrix M2;

[0088]

[0089] S6: Determine whether t is greater than 12 (let T = 12). If so, output the initial distribution plan matrix; if not, return to S2 until t meets the condition.

[0090] S7: Improve the initial TM using M1 and M2 in a certain order, changing the value of one cell of the initial TM each time.

[0091] S8: Recalculate the cost of the modified distribution plan and only retain the modifications that result in cost reduction.

[0092] S9: Determine whether t is greater than 12 (T = 12). If so, output the changed optimal TM, cost, and time; if not, return to S7 until t meets the condition.

[0093] To illustrate the effect of the present invention, the following simulation is carried out:

[0094] 1 Basic data

[0095] To verify the effectiveness of the constructed model and algorithm, a three - level supply chain distribution network example is considered. The relevant data is given in the reference "Ramiz(2022).Applying Greedy Algorithm and Local Search in a Supply Chain distribution problem, MATLAB Central File Exchange.Retrieved April 7, 2022" and simulation tests are carried out. Suppose there is a three - level supply chain network consisting of 4 factories (F), 5 primary sales points (PPOS), and 6 secondary sales points (SPOS). The goal is to minimize the total cost of distributing products within 12 time periods (assuming T = 12) given the demands of the secondary sales points (SPOS) and the production capacities of the factories (F). In addition, assume the vehicle capacity is 70 units. The basic data of SPOS is shown in Table 2, the basic data of F is shown in Table 3, the basic data of PPOS is shown in Table 4, the transportation costs from F to PPOS are shown in Table 5, and the transportation costs from PPOS to SPOS are shown in Table 6

[0096] Table 2 Basic data of SPOS

[0097] SPOS1 SPOS2 SPOS3 SPOS4 SPOS5 SPOS6 <![CDATA[d t-1 > 35 35 60 80 100 100 <![CDATA[d t-2 > 25 100 125 55 20 20 <![CDATA[d t-3 > 150 120 100 60 110 110 <![CDATA[d t-4 > 50 70 40 140 40 40 <![CDATA[d t-5 > 90 110 90 50 30 30 <![CDATA[d t-6 > 0 110 90 40 50 50 <![CDATA[d t-7 > 60 70 0 110 10 10 <![CDATA[d t-8 > 140 70 90 100 30 30 <![CDATA[d t-9 > 10 130 130 40 140 140 <![CDATA[d t-10 > 30 90 70 40 0 0 <![CDATA[d t-11 > 70 100 100 50 90 90 <![CDATA[d t-12 > 110 50 50 110 100 100 / unit 30 35 25 40 55 55 / unit 24 28 30 40 16 12

[0098] Table 3 Basic data of F

[0099] F1 F2 F3 F4 Cap 400 500 300 300 p 4500 2000 2500 3000 / unit 5 2 4 3

[0100] Table 4 Basic data of PPOS

[0101] PPOS1 PPOS2 PPOS3 PPOS4 PPOS5 Cap 300 500 250 150 150 / unit 30 35 25 40 55 / unit 12 14 23 50 8

[0102] Table 5 Transportation costs from F to PPOS

[0103]

[0104] Table 6 Transportation costs from PPOS to SPOS

[0105]

[0106] Note: d t-i : Demand at t = i (i = 1:12); Cap: Product capacity; L: Sales loss cost; h: Inventory cost; Factory startup production cost.

[0107] Result comparison and analysis:

[0108] All simulation tests were performed on a computer running Windows 10 × 64, which has an Intel Core i7 CPU and 8GB of RAM. The evaluation parameters considered in the comparison are the algorithm calculation time and the minimum distribution cost value over the entire time range T. The time range was selected as T = 12, and the time and cost comparison results are shown in Table 7, Figure 3 as shown.

[0109] Table 7 Time and cost comparison

[0110]

[0111] Note: GR: Greedy algorithm; IHCM: Improved hill climbing method; The optimal values in Table 7 are shown in bold.

[0112] From Table 7 and Figure 3 it can be seen that within the time range T = 12, the distribution cost for each t of the IHCM algorithm is less than that of GR. Taking T = 12 as an example, its total cost is saved by 138,755 yuan compared to GR, which is approximately 8.2% of the total cost of GR for 12 cycles (T = 12), which is 1,685,980 yuan. It can be seen that under the same initial conditions, the IHCM algorithm with a memory function, due to improving the selection of the starting point on the basis of local search, only accepts a new transportation plan when a better position is found. The execution times of both algorithms are very small and are not considered here.

[0113] Summary: For the multi-level supply chain distribution optimization of large-scale and multi-period demands and the problem of dynamic node selection, first, a multi-level supply chain distribution network model including sales loss, inventory cost, and multi-period demands is established; second, the greedy algorithm and the improved hill climbing method with a memory function are applied to the multi-level supply chain distribution network optimization problem; finally, simulation tests are carried out.

[0114] The results show that the improved hill-climbing method with memory function can always obtain a better solution than the greedy algorithm because it only moves when a better position is found; it can effectively solve the proposed problem and provide certain decision-making references for the optimization of multi-level supply chain distribution networks. Moreover, imagine that when it is large enough, the IHCM algorithm can save more enterprise distribution costs, and has the advantages of simplicity, high speed, and reduced distribution waiting time in solving large-scale problems, which can improve customer satisfaction and enterprise competitiveness to a certain extent.

[0115] However, the considered supply chain distribution system only includes one vehicle capacity, and different vehicle capacities may face a more complex environment. How to effectively solve the optimization problem of multi-level supply chain distribution networks under different vehicle capacities is the direction of future research.

[0116] As described above, the above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claimed rights.

Claims

1. A multi - level supply chain distribution optimization method based on an improved hill - climbing method, characterized in that: The method includes the following steps: (1) Establish an optimization mathematical model for supply chain distribution: The constraints are: In the formula, L, σ, N y ∈ [0, 1], F is the number of factories, S is the number of primary sales points, M is the number of secondary sales points, t is the time unit, i is the factory, j is the primary sales point, n is the secondary sales point, ij is the transportation from factory i to primary sales point j, jn is the transportation from primary sales point j to secondary sales point n, σ is the inventory quantity, N is the number of vehicles, ζ is the quantity of sales losses, y determines whether the factory starts production, C is the factory capacity, d is the demand of the sales point, T is the time range, h is the inventory cost, L is the sales loss cost, Vehicle capacity, k is the transportation cost, Factory start-up production cost, Cap is the capacity of the product, q is the transportation quantity; Where: Equation (1): The sum of the factory inventory cost, start-up production cost, and the inventory costs of the first / second-level sales points, the sales loss costs of the first / second-level sales points, and the transportation costs from the factory to the first-level sales points and between the first-level and second-level sales points within the entire time range T; Equations (2) and (3): The relationships between inventory, transportation quantity, lost sales, and demand at times t and t-1; Equations (4) and (5): The relationships between production activation and inventory surplus between times t and t-1. It is important to emphasize that when the factory is activated, its production will reach the maximum; Equations (6) and (7): used to calculate the number of vehicles N for each route from i to j and from j to n ij / N jn ; (2) Use the greedy algorithm to solve the optimization mathematical model in step (1), and use the improved hill-climbing method to optimize the initial solution; The process of solving the optimization mathematical model includes the following steps: S1: Start, input the initial data, t = 1; S2: Select the second-level sales points according to Equation (8); In the formula, Inventory quantity of secondary sales point n at time t; L n : Sales loss cost of secondary sales point n; S3: Select the first-level sales points according to Equation (9); obtain the distribution plan from the first-level sales points to the second-level sales points at time t; record the selected second-level sales points and the corresponding first-level sales points in order for each t value into matrix M1; S4: Select the first-level sales points according to Equation (10); In the formula, Inventory quantity of the first-level sales point j at time t; L j : Sales loss cost of the first-level sales point j; S5: Select the corresponding factory according to Equation (11); obtain the distribution plan from the factory to the first-level sales points at time t; record the selected first-level sales points and the corresponding factories in order for each t value into matrix M2; S6: Judge whether t is greater than the threshold T. If so, output the initial distribution plan matrix; if not, return to S2 until t meets the condition; S7: Use M1 and M2 to improve the initial distribution plan matrix TM in a certain order, changing the value of one cell of the initial distribution plan matrix TM each time; S8: Recalculate the cost of the modified distribution plan, and only retain the modifications that reduce the cost; S9: Judge whether t is greater than T. If so, output the changed optimal distribution plan matrix TM, cost, and time; if not, return to S7 until t meets the condition.

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