A retail cabinet inventory path decision optimization method and apparatus

Abstract

The application discloses a retail cabinet inventory path decision optimization method and equipment, comprising the following steps: (1) establishing an inventory path optimization model of a retail cabinet, wherein the inventory path optimization model takes the sum of inventory cost, shortage cost and vehicle path cost in a current planning period as a target function, and takes replenishment constraints, maximum inventory level constraints, vehicle capacity constraints, retail cabinet flow balance constraints, vehicle closed loop constraints and elimination sub-loop constraints as constraint conditions; (2) obtaining inventory path related information; (3) according to the inventory path related information, a tabu search method is used to solve the inventory path optimization model, and optimized inventory decisions and path decisions are obtained. The application simultaneously considers replenishment decisions and path planning decisions when making decisions, and is more efficient.

Description

Technical Field

[0001] This invention relates to retail cabinet optimization technology, and more particularly to a method and device for optimizing retail cabinet inventory path decision-making. Background Technology

[0002] Retail kiosks represent a new retail model. Unlike traditional brick-and-mortar stores, retail kiosks are deployed in locations such as office buildings, hospitals, universities, subways, and industrial parks to sell snacks, drinks, and other goods in small quantities, addressing the "last 100 meters" shopping needs of consumers in these enclosed or semi-enclosed spaces. Compared to traditional retail, retail kiosks do not require renting physical stores or investing in human resources; purchases are entirely made by consumers. They offer advantages such as low upfront investment, low operating costs, small footprint, and flexible site selection, making them attractive to many retail giants and investors.

[0003] Retail kiosks are a complex decision-making process. Operators typically plan replenishment on a daily basis. Each day's decisions include the replenishment plan for the following day, a list of kiosks to be replenished, details of the merchandise to be replenished for each kiosk, and the replenishment routes for the drivers. The operator's goal is to maintain a consistently high inventory level in the kiosks to maximize customer satisfaction while minimizing the workload for the drivers, i.e., optimizing their replenishment routes.

[0004] Currently, most retail vending machine operators adopt a process of making replenishment decisions first, followed by route planning decisions. First, based on daily sales volume and remaining inventory, a list of vending machines requiring replenishment the following day is selected, aiming to minimize stockout losses. Second, based on this list, staff plan replenishment routes to minimize delivery costs. Finally, manual screening removes vending machines that are geographically isolated or where drivers cannot replenish them in time. While this approach is clear and easy to execute, it is relatively inefficient and lacks comprehensiveness. Summary of the Invention

[0005] To address the problems existing in the prior art, the purpose of this invention is to provide a highly efficient method and device for optimizing retail cabinet inventory path decision-making.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0007] A method for optimizing inventory path decision-making in retail counters includes the following steps:

[0008] (1) Establish an inventory path optimization model for retail counters. The objective function of the inventory path optimization model is to minimize the sum of inventory cost, stockout cost, and vehicle path cost in the current planning period. The constraints are replenishment constraint, maximum inventory level constraint, vehicle capacity constraint, retail counter flow balance constraint, vehicle closed-loop constraint, and elimination of sub-loop constraint. The objective function of the inventory path optimization model is:

[0009]

[0010]

[0011] In the formula, h i Indicates unit inventory cost, l i Indicates unit stockout loss, These represent inventory levels respectively. The positive and negative parts, that is This represents the remaining inventory level of retail cabinet i at the end of planning period t, and serves as the initial inventory level for planning period t+1. express The main part, c represents the remaining inventory level of retail cabinet i at the end of the planning period t-1. ij This represents the path cost from retail cabinet i to retail cabinet j. This is a 0-1 variable used to indicate whether edge (i,j) is the route of vehicle k in period t. When i, j indicates that edge (i, j) is the route of vehicle k in period t; otherwise, it indicates that it is not. This represents a 0-1 variable used to indicate whether retail cabinet i is replenished in planning period t. If the time is t, it means that retail cabinet i was replenished in the t-th planning period; otherwise, it means that it was not. This represents a 0-1 variable used to indicate whether vehicle k replenishes retail counter i in planning period t. If the vehicle k replenishes retail counter i in the t-th planning period, it means that vehicle k replenishes the retail counter i; otherwise, it means that it does not. This represents a set of points, where vertex 0 represents the supply warehouse, and the other vertices... Represents a collection of retail counter locations. Indicates a collection of vehicles. Represents the set of the planning period. This represents the demand for retail cabinet i in planning period t. This represents the amount of replenishment received by retail counter i in planning period t. This represents the amount of stock that vehicle k replenishes to retail counter i in planning period t;

[0012] (2) Obtain relevant information on inventory path, including warehouse location, location of each retail counter, initial inventory level of each retail counter in the current planning period, maximum inventory level of each retail counter, unit stockout loss of each retail counter, demand of each retail counter in the current planning period, and vehicle capacity.

[0013] (3) Based on the relevant information of the inventory path, the tabu search method is used to solve the inventory path optimization model to obtain the optimized inventory decision and path decision.

[0014] Furthermore, the replenishment constraints are specifically as follows:

[0015]

[0016]

[0017] In the formula, C i This indicates the maximum inventory level of retail cabinet i.

[0018] Furthermore, the maximum inventory level constraint specifically refers to:

[0019]

[0020] In the formula, r represents the remaining inventory level at the end of planning periods t and t-1, respectively. t C represents the amount of goods received into the warehouse each period. i This indicates the maximum inventory level of retail cabinet i;

[0021] The vehicle capacity constraint is specifically as follows:

[0022]

[0023] In the formula, Q represents the vehicle's capacity. Let be a 0-1 variable indicating whether the k-th vehicle visited the warehouse in period t. If the vehicle visited the warehouse, then... otherwise

[0024] Furthermore, the retail counter flow balance constraint is specifically as follows:

[0025]

[0026] In the formula, This is a 0-1 variable used to indicate whether edge (j,i) is the route of vehicle k in period t. When the edge (j,i) is the route of vehicle k in period t, it means that the edge is not the route of vehicle k in period t; otherwise, it means that the edge is not the route of vehicle k in period t.

[0027] The specific vehicle closed-loop constraint is as follows:

[0028]

[0029] In the formula, Let (0,j) and (j,0) be 0-1 variables used to indicate whether the edges (0,j) and (j,0) are routes of vehicle k in period t. When the variable is 1, it means that the edge is a route; otherwise, it means that it is not. In (0,j) and (j,0), 0 represents a warehouse. Let be a 0-1 variable indicating whether the k-th vehicle visited the warehouse in period t. If the vehicle visited the warehouse, then... otherwise

[0030] Furthermore, the elimination of sub-loop constraints specifically involves:

[0031]

[0032] In the formula, This represents a subset of the set of retail cabinets. This represents a 0-1 variable used to indicate whether vehicle k replenishes retail counter m in planning period t. If the vehicle k replenishes the retail counter m in the t-th planning period, it means that vehicle k replenishes the retail counter m; otherwise, it means that it does not.

[0033] Furthermore, step (3) specifically includes:

[0034] (3.1) Construct two empty taboo tables and These are used to store the retail counter and replenishment period pairs (i,t) respectively, and to initialize the disturbance length and maximum number of iterations, where i represents the retail counter number and t represents the planned period.

[0035] (3.2) Construct an initial solution and use it as the current solution; the structure of the solution is as follows: This represents the retail counter replenishment decision in solution s. This represents the replenishment quantity decision in solution s. This represents the inventory level decision in solution s. Let represent the path decision in solution s. They represent the solutions in s respectively. The value;

[0036] (3.3) Determine whether the termination condition is met, i.e. whether the number of iterations is greater than the maximum number of iterations. If yes, output the historical optimal solution; otherwise, execute (3.4).

[0037] (3.4) Calculate the neighborhood solutions of the current solution using four different neighborhood operators, and select the best solution from the neighborhood solutions as a candidate solution according to the contempt criterion; wherein, the four different neighborhood operators are specifically Remove operator, Insert operator, Relocate operator and Replace operator;

[0038] (3.5) Determine whether the candidate solution is better than the historical best solution. If not, execute (3.6); if so, execute (3.7).

[0039] (3.6) Randomly perturb the candidate solutions according to the perturbation length, and then execute (3.7);

[0040] (3.7) Improve the candidate solution or the solution after random perturbation of the candidate solution, including improving the replenishment period of each retail counter and improving the route plan, and take the improved solution as the optimal solution and execute (3.8);

[0041] (3.8) Update the tabu list based on the current solution and the optimal solution;

[0042] (3.9) Increment the iteration count by 1 and return to step (3.3).

[0043] Furthermore, step (3.2) specifically includes:

[0044] (3.2.1) Ignoring the impact of path costs, solve the following model to obtain the solution that minimizes inventory costs.

[0045]

[0046] (3.2.2) Using heuristics, based on the obtained Find the solution when the delivery cost is minimized. At this moment As a feasible solution;

[0047] (3.2.3) The feasible solution is improved, and the improved solution is used as the initial solution.

[0048] Furthermore, step (3.8) specifically includes:

[0049] The optimal solution of the current solution s is adopted from solution s. , This indicates that if retail counter i is restocked during the t-th planning period of solution s, but not during solution s... , If retail counter i is not replenished during the t-th planning period, then the tuple (i,t) is added to the tabu list. In the middle, it means that retail cabinet i is prohibited from being restocked in period t in subsequent iterations;

[0050] If, in the t-th planning period of solution s, the retail counter i is not replenished, but in solution s, If retail counter i is replenished during the t-th planning period, then the tuple (i,t) is added to the tabu list. In the middle, it means that retail cabinet i will remain replenished in period t for several subsequent iterations;

[0051] Among them, the taboo length of both taboo lists is Where L and λ are fixed parameters, n is the number of retail cabinets, and |R(s)| is the number of feasible paths in solution s. It is 0 to Randomly select numbers from between.

[0052] Furthermore, step (3.7) specifically includes:

[0053] (3.7.1) Improve the replenishment period for each retail counter: Add a two-dimensional array DeltaCost to record the impact of changes in replenishment period on total cost. Then the element DeltaCost[i][t] records if Estimate the change in total cost from 0 to 1, when Then DeltaCost[i][t] records if Estimate the change in total cost from 1 to 0; then, extract the element with the smallest negative value from each row of DeltaCost, extract the value of the index (i,t) of that element, and record it as (i0,t0). If the solution before boosting... but Improved value If the solution before the upgrade is in but Improved value Finally, based on the OU strategy... Synchronous promotion yields the promoted value.

[0054] (3.7.2) Based on the improved After replanning the route, improvements were achieved. value After the upgrade As the improved solution of the current solution s.

[0055] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described above.

[0056] Compared with existing technologies, the advantages of this invention are as follows: This invention provides a method and device for optimizing inventory path decision-making in retail counters. By establishing a mathematical model of the inventory path problem and performing joint optimization of replenishment decisions and path planning, this invention can reduce operating costs and improve efficiency. The tabu search algorithm proposed in this invention can significantly improve the solution efficiency. Attached Figure Description

[0057] Figure 1 This is a flowchart illustrating the retail cabinet inventory path decision optimization method provided in an embodiment of the present invention;

[0058] Figure 2 These are schematic diagrams of the four operators provided by this invention;

[0059] Figure 3 This is a flowchart illustrating the tabu algorithm provided by the present invention. Detailed Implementation

[0060] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0061] Example 1

[0062] First, the problem of this invention needs to be analyzed, which requires abstracting the retail cabinet replenishment problem into a mathematical model of the Inventory Routing Problem (IRP). The decision-making elements of the retail cabinet inventory routing problem include warehouses, retail cabinets, and vehicles. Operators need to decide which retail cabinets to replenish stock in a planned future period, as well as the vehicle replenishment routes. Warehouses and retail cabinets can incur inventory costs and stockout losses, and vehicles incur routing costs during the replenishment process. Therefore, the objective of the problem can be defined as minimizing the sum of these costs.

[0063] Based on the above analysis, this embodiment provides a method for optimizing retail cabinet inventory path decision-making, such as... Figure 1 As shown, it includes the following steps:

[0064] (1) Establish an inventory path optimization model for retail counters. The inventory path optimization model takes the minimum sum of inventory cost, stockout cost and vehicle path cost in the current planning period as the objective function, and the replenishment constraint, maximum inventory level constraint, vehicle capacity constraint, retail counter flow balance constraint, vehicle closed loop constraint and elimination of sub-loop constraint as the constraint conditions.

[0065] The objective function of the inventory path optimization model is:

[0066]

[0067] In the formula, h iIndicates unit inventory cost, l i Indicates unit stockout loss, These represent inventory levels respectively. The positive and negative parts, that is This represents the remaining inventory level of retail cabinet i at the end of planning period t, and serves as the initial inventory level for planning period t+1. express The main part, c represents the remaining inventory level of retail cabinet i at the end of the planning period t-1. ij This represents the path cost from retail cabinet i to retail cabinet j. This is a 0-1 variable used to indicate whether edge (i,j) is the route of vehicle k in period t. When i, j indicates that edge (i, j) is the route of vehicle k in period t; otherwise, it indicates that it is not. This represents a 0-1 variable used to indicate whether retail cabinet i is replenished in planning period t. If the time is t, it means that retail cabinet i was replenished in the t-th planning period; otherwise, it means that it was not. This represents a 0-1 variable used to indicate whether vehicle k replenishes retail counter i in planning period t. If the vehicle k replenishes retail counter i in the t-th planning period, it means that vehicle k replenishes the retail counter i; otherwise, it means that it does not. This represents a set of points, where vertex 0 represents the supply warehouse, n represents the number of retail counters, and the other vertices... Represents a collection of retail counter locations. Indicates a collection of vehicles. Represents the set of the planning period. This represents the demand for retail cabinet i in planning period t. This represents the amount of replenishment received by retail counter i in planning period t. This represents the amount of stock that vehicle k replenishes to retail counter i during the t-th planning period.

[0068] The replenishment constraints are specifically as follows:

[0069]

[0070]

[0071] In the formula, C i This indicates the maximum inventory level of retail cabinet i.

[0072] The maximum inventory level constraint is specifically as follows:

[0073]

[0074] In the formula, r represents the remaining inventory level at the end of planning periods t and t-1, respectively. t C represents the amount of goods received into the warehouse each period. i This indicates the maximum inventory level of retail cabinet i;

[0075] The vehicle capacity constraint is specifically as follows:

[0076]

[0077] In the formula, Q represents the vehicle's capacity. Let be a 0-1 variable indicating whether the k-th vehicle visited the warehouse in period t. If the vehicle visited the warehouse, then... otherwise This constraint is used to limit the total replenishment volume of all retail counters on the route to less than the vehicle capacity.

[0078] The specific retail counter flow balance constraint is as follows:

[0079]

[0080] In the formula, This is a 0-1 variable used to indicate whether edge (j,i) is the route of vehicle k in period t. When the edge (j,i) is the route of vehicle k in period t, it indicates that the edge is not the route of vehicle k in period t. The flow balance constraint is used to ensure that the out-degree and in-degree of retail cabinet i are equal, that is, to achieve flow balance.

[0081] The specific vehicle closed-loop constraint is as follows:

[0082]

[0083]

[0084] In the formula, Let (0,j) and (j,0) be 0-1 variables indicating whether edges (0,j) and (j,0) are routes for vehicle k in period t. A value of 1 indicates that the edge is a route, otherwise it is not. The 0 in (0,j) and (j,0) represents a warehouse. This constraint requires that each vehicle starts from warehouse 0 and returns to warehouse 0 in each period.

[0085] The elimination of sub-loop constraints specifically refers to:

[0086]

[0087] In the formula, This represents a subset of the set of retail cabinets. This represents a 0-1 variable used to indicate whether vehicle k replenishes retail counter m in planning period t. If the vehicle k replenishes retail counter m in planning period t, then the vehicle k replenishes the retail counter m; otherwise, the vehicle k does not replenish the retail counter m. This constraint is used to eliminate situations where... Established sub-ring

[0088] (2) Obtain relevant information on inventory paths, including warehouse location, location of each retail counter, initial inventory level of each retail counter in the current planning period, maximum inventory level of each retail counter, unit stockout loss of each retail counter, demand of each retail counter in the current planning period, and vehicle capacity.

[0089] (3) Based on the relevant information of the inventory path, the tabu search method is used to solve the inventory path optimization model to obtain the optimized inventory decision and path decision.

[0090] like Figure 3 As shown, this step specifically includes:

[0091] (3.1) Construct two empty taboo tables and These are used to store the retail counter and replenishment period pairs (i,t) respectively, and to initialize the disturbance length and maximum number of iterations, where i represents the retail counter number and t represents the planned period.

[0092] (3.2) Construct an initial solution and use the initial solution as the current solution.

[0093] The retail counter inventory routing problem requires obtaining: the inventory levels of retail counters and warehouses for each period, the set of retail counter replenishment points for each period, the replenishment quantity for each period, and the replenishment route for each period. Let S denote the solution space of the retail counter inventory routing problem, and s denote a feasible solution in the solution space S. Then s consists of four parts, namely s = {y(s), q(s), i(s), R(s)}. This represents the retail counter replenishment decision in solution s. This represents the replenishment quantity decision in solution s. This represents the inventory level decision in solution s. Let represent the path decision in solution s. They represent the solutions in s respectively. The value of y(s), q(s), I(s), and R(s) can be obtained after obtaining y(s), q(s), I(s), and R(s). Collection of retail cabinet replenishment periods Replenishment quantity and replenishment routes The most critical components of the solution to the retail counter inventory path problem are y(s) and R(s). Under the OU strategy, once y(s) is determined, q(s) and I(s) can be further calculated.

[0094] The initial solution construction methods specifically include:

[0095] (3.2.1) Adopting a greedy approach, construct an initial solution based on minimizing inventory costs. In this step, the impact of path costs is temporarily ignored, and the solution is found that minimizes inventory-related costs. This is a demand-based inventory allocation problem, which can be solved directly using Cplex to solve the following MIP model:

[0096]

[0097] (3.2.2) Using heuristics, based on the obtained Find the solution when the delivery cost is minimized. At this moment As a feasible solution, the purpose of this step is to... Given a fixed path, determine the vehicle route variable. To keep delivery costs as low as possible, which is equivalent to A CVRP (Continuous Path Resolver Problem). Considering that the MIP (Multi-Input Path Injection) model is an NP-hard problem, to ensure efficiency, the exact solution to the CVRP is not calculated during the construction process. Instead, a heuristic approach is used for iteration to quickly obtain high-quality path decision quantities.

[0098] (3.2.3) The feasible solution is improved, and the improved solution is used as the initial solution. The above feasible solution is essentially a greedy solution. In (3.2.1), to ensure the minimum inventory cost, the replenishment frequency of the retail counters is very high, resulting in extremely high path costs in (3.2.2). During the improvement phase, each retail counter in the replenishment plan is evaluated to estimate the impact on the total cost if they are removed; at the same time, each retail counter not in the replenishment plan is evaluated to estimate the impact on the total cost if they are added to the replenishment plan. For example, removing retail counter i from the replenishment in period t would reduce the total cost, so in the improved solution... Then the paths are reassigned. The specific steps for solution lifting are described in detail in step (3.7) below.

[0099] (3.3) Determine whether the termination condition is met, i.e. whether the number of iterations is greater than the maximum number of iterations. If yes, output the historical optimal solution; otherwise, execute (3.4).

[0100] (3.4) Calculate the neighborhood solutions of the current solution s using four different neighborhood operators, and select the best solution from the neighborhood solutions as a candidate solution according to the contempt criterion. The contempt criterion means that if the quality of the neighborhood solution is better than the historical best solution, and the operator operation happens to be taboo by the tabu list, then the effect of the tabu list is "contemptuous", and the current solution is updated to the neighborhood solution.

[0101] The four different neighborhood operators are the Remove operator, Insert operator, Relocate operator, and Replace operator; the four operators are as follows: Remove operator: selects retail cabinet i and planning period t∈T i (s), let Then according to renew And R(s). Insert operator: Select retail counter i and planning period make Then according to renew And R(s). Relocate operator: select retail counter i and planning period t1∈T i (s), planning period make Then according to renew And R(s). Replace operator: Select retail counters i and j, with a planning period t1∈T i (s) and make Then according to renew And R(s). Schematic diagrams of the four operators are shown below. Figure 2 As shown.

[0102] After using the neighborhood operator, the calculation of the change in total cost includes two parts: the change in inventory-related costs and the change in path costs.

[0103] Changes in inventory-related costs are due to changes in the replenishment period of retail counter i. A change in the replenishment status of retail counter i in period t directly affects the inventory levels of both retail counter i and the warehouse in each subsequent period, thus impacting inventory-related costs. In calculating cost changes, this is achieved through... Recalculate the changes in inventory levels at retail counter i and in the warehouse, and then calculate the changes in inventory-related costs.

[0104] The path change is caused by two factors: firstly, the deletion (insertion) of retail counter i in planning period t shortens (lengthens) the path in planning period t; secondly, the deletion (insertion) of retail counter i in planning period t changes the replenishment quantity after period t, potentially rendering the previously feasible path infeasible. Therefore, accurately calculating the path cost change after the deletion (insertion) of retail counter i is equivalent to solving every CVRP after period t, which is very time-consuming. In actual calculations, an approximate cost approach is adopted. If retail counter i needs to be deleted from planning period t, its predecessor and successor nodes in the path are connected. If retail counter i needs to be inserted into planning period t, the CheapestInsert strategy for retail counter i is executed on the path in planning period t, i.e., traversing every position in the path in planning period t to minimize the increase in path cost after the insertion of retail counter i.

[0105] In addition to calculating the total cost change of the current solution *s* after the neighborhood operator operation, it is also necessary to determine the feasibility of the neighborhood operator. When executing the operator operation, the main considerations are whether the warehouse inventory level is negative and whether inserting retail counter *i* into a certain path exceeds the vehicle capacity limit. However, the vehicle capacity limit after the planning period *t* is not considered temporarily. This is because during the iteration process, there will be solution improvement and shake mechanisms, both of which will cause all paths to be replanned.

[0106] The Remove operator is described by a quintuple opt1, which includes retail counter i, the planning period t, the path number, the location within the path, and the approximate cost change after removal. The Insert operator is described by a quintuple opt2, which includes retail counter i, the insertion planning period t, the insertion path number, the location within the path, and the approximate cost change after insertion. The Relocate operator is described by an octple opt3, which includes retail counter i, the planning period t1, the path number, the location within the path, the insertion planning period t2, the insertion path number, the location within the path, and the approximate cost change after relocation. The Replace operator is described by a hexatuple opt4, which includes retail counter i, the planning period t1, the path number, the location within the path, the retail counter j that replaces retail counter i, and the approximate cost change after replacement.

[0107] (3.5) Determine whether the candidate solution is better than the historical best solution. If not, execute (3.6) and if yes, execute (3.7).

[0108] (3.6) Randomly perturb the candidate solutions according to the perturbation length, and then execute (3.7).

[0109] De-perturbation is a common method in heuristic algorithms to increase the breadth of the search and escape local optima. If, during many iterations, no improvement over the historical best solution has been found, it's likely that the current solution is trapped in a local optimum. Besides increasing the tabu length, one can directly perturb (shake) the current solution, causing it to "jump" significantly. The perturbation method in this chapter requires the perturbation length as a parameter; the perturbation step begins when the number of iterations before the current solution is updated equals a multiple of the perturbation length. Generally, the perturbation direction is random in metaheuristic algorithms, but the de-perturbation in this chapter's tabu search algorithm shifts the retail counter from the current replenishment time to a time when replenishment is not typically required.

[0110] Disruption can be achieved using a tabu list. and It actually stores information about historical operator operations. If the tabu list... Each element is initialized to 0. When the i-th retail counter changes from not restocking to restocking in period t during the k-th iteration, then the tabu list is... The (i, t) element is assigned the value k. Thus, when de-perturbation is needed, only the tabu list needs to be... By taking the minimum value from each row, we can obtain the time when the retail counter is least frequently accessed.

[0111] (3.7) Improve the candidate solution or the solution after random perturbation of the candidate solution, including improving the replenishment period of each retail counter and improving the route plan, and take the improved solution as the optimal solution and execute (3.8).

[0112] Solution boosting is applied to three stages: initial solution generation, neighborhood-optimal solution boosting (when the neighborhood solution is better than the historical best solution), and solution perturbation. At these three stages, the current solution can be considered to have entered a "new region," where solution boosting yields better results. The purpose of solution boosting is to improve the performance of a feasible solution by analyzing its neighborhood and estimating directions for improvement. In effect, solution boosting is more like a combination of multiple neighborhood search operators, representing a "leap" improvement in the current solution. Based on computational examples, the design of the solution boosting program can significantly accelerate the convergence of the tabu search algorithm to the optimal solution.

[0113] The improvement solution includes two parts: improving the replenishment period of each retail counter and improving the route planning.

[0114] Improve the replenishment period for each retail counter: Add a two-dimensional array DeltaCost to record the impact of changes in replenishment period on total cost. Then the element DeltaCost[i][j] records if Estimation of changes in total cost, when Then DeltaCost[i][j] records if Estimate the change in total cost; then, extract the element with the smallest negative value from each row of DeltaCost, extract the value of the index (i,t) of that element, and record it as (i0,t0). If the solution before boosting... but Improved value If the solution before the upgrade is in but Improved value Finally, based on the OU strategy... Synchronous promotion yields the promoted value. The OU strategy refers to replenishing retail cabinet i's inventory to the maximum inventory level C every time it is restocked. i ;

[0115] (3.7.2) Based on the improved After replanning the route, improvements were achieved. value After the upgrade This is the improved solution from the current solution s. Because solution improvement may simultaneously change the replenishment period of multiple retail counters, the path cost estimation method using the previous operator is no longer accurate. Therefore, in solution improvement, it is necessary to replan the path R(s) for the new y(s). Another function of replanning the path is to re-estimate the path cost of the current solution. This is because the approximate path cost estimate used when performing operator operations may lead to a large deviation in path cost after multiple iterations. Replanning the path solves this problem.

[0116] (3.8) Update the tabu list based on the current solution and the optimal solution.

[0117] The specific steps for updating are: The optimal solution for solution s is adopted from solution s. , This indicates that if retail counter i is restocked during the t-th planning period of solution s, but not during solution s... , If retail counter i is not replenished during the t-th planning period, then the tuple (i,t) is added to the tabu list. In the solution s, retail cabinet i is prohibited from being replenished in period t in subsequent iterations; if retail cabinet i is not replenished in planning period t in solution s, but is not replenished in solution s... , If retail counter i is replenished during the t-th planning period, then the tuple (i,t) is added to the tabu list. In the middle, it means that retail cabinet i will remain replenished in period t for several subsequent iterations; where the taboo length of both taboo tables is 1. Where L and λ are fixed parameters, n is the number of retail cabinets, and |R(s)| is the number of feasible paths in solution s. It is 0 to Randomly select numbers from between.

[0118] (3.9) Increment the iteration count by 1 and return to step (3.3).

[0119] This invention provides a method for optimizing inventory routing decisions in retail stores. By establishing a mathematical model of the inventory routing problem and performing joint optimization of replenishment decisions and routing planning, operating costs can be reduced. The tabu search algorithm proposed in this invention can significantly improve solution efficiency. Furthermore, the results of this invention can be extended to other practical IRP scenarios, promoting enterprise supply chain optimization and further reducing enterprise operating costs.

[0120] Example 2

[0121] This invention provides a computer device that provides services for implementing the method described in Embodiment 1. The device may include: a memory storing a computer-executable program; a processor coupled to the memory; and the processor calling the computer-executable program stored in the memory to execute the steps of the method described in Embodiment 1.

[0122] The memory may include computer system readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The device may further include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, the memory may be used to read and write non-removable, non-volatile magnetic media (commonly referred to as a "hard disk drive"). A program / utility having a set (at least one) of program modules may be stored in, for example, memory. Such program modules include, but are not limited to, an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. The computer-executable program of the program modules typically performs the functions and / or methods described in the embodiments of the present invention.

[0123] The processor executes various functional applications and data processing by running programs stored in memory, such as the method provided in Embodiment 1 of the present invention.

[0124] The code of a computer executable program can be written in one or more programming languages ​​or a combination thereof. Programming languages ​​include object-oriented programming languages ​​such as Java, Smalltalk, and C++, as well as conventional procedural programming languages ​​such as the "C" language or similar programming languages.

[0125] It should be understood that the embodiments and descriptions above are only the principles, main features and advantages of the present invention. Various changes and modifications can be made to the present invention without departing from the spirit and scope of the invention, and all such changes and modifications fall within the protection scope of the present invention.

Claims

1. A method for optimizing inventory path decision-making in retail counters, characterized in that, Includes the following steps: (1) Establish an inventory path optimization model for retail counters. The inventory path optimization model takes the minimum sum of inventory cost, stockout cost, and vehicle path cost for the current planning period as its objective function, and uses replenishment constraints, maximum inventory level constraints, vehicle capacity constraints, retail counter flow balance constraints, vehicle closed-loop constraints, and sub-loop elimination constraints as constraints. The objective function of the inventory path optimization model is: ， In the formula, Indicates unit inventory cost. Indicates unit stockout loss. , These represent inventory levels respectively. The positive and negative parts, that is , , Indicates retail counter In the The remaining inventory level at the end of the planning period, and as the first +1 Initial inventory level for the planning period, express The main part, Indicates retail counter In the -1 represents the remaining inventory level at the end of the planning period. Representing an edge Path cost, Indicates the edge used for indicating Is it the first Vehicles The 0-1 variables of the route, when When =1, it represents an edge. For the first Vehicles If it is the correct route, then it is not; Indicates the use of retail counters Is it in the first The 0-1 variable that is replenished during the planning period, when At that time, it indicates a retail counter In the If the planned stock is replenished, then it means there is no stock available. Indicates the vehicle k In the Does the planning period include retail counters? The 0-1 variable of replenishment, when When, it indicates the vehicle k In the Planned supply to retail counters Restock; otherwise, it means there is no stock. This represents a set of locations, where vertex 0 represents a warehouse and n represents the number of retail counters. Represents a collection of retail counter locations. Indicates a collection of vehicles. Represents the set of the planning period. Indicates retail counter In the Demand during the planning period Indicates retail counter In the The amount of replenishment received during the planned period. Indicates that vehicle k is in the first position. Planned supply to retail counters The amount of replenishment; (2) Obtain relevant information on inventory paths, including warehouse location, location of each retail counter, initial inventory level of each retail counter in the current planning period, maximum inventory level of each retail counter, unit stockout loss of each retail counter, demand of each retail counter in the current planning period, and vehicle capacity; (3) Based on the relevant information of the inventory path, the tabu search method is used to solve the inventory path optimization model to obtain the optimized inventory decision and path decision; Step (3) specifically includes: (3.1) Construct two empty taboo tables and These are used for storing retail counters and replenishment period pairs, respectively. The perturbation length and maximum number of iterations are initialized, where, Indicates the retail counter serial number. Indicates the planned period; (3.2) Construct an initial solution and use it as the current solution, where the structure of the solution is as follows: , This represents the retail counter replenishment decision in solution s. This represents the replenishment quantity decision in solution s. This represents the inventory level decision in solution s. Let represent the path decision in solution s. , , , They represent the solutions in s respectively. , , , The value; (3.3) Determine whether the termination condition is met, i.e. whether the number of iterations is greater than the maximum number of iterations. If yes, output the historical optimal solution; otherwise, execute (3.4). (3.4) Calculate the neighborhood solutions of the current solution using four different neighborhood operators, and select the best solution from the neighborhood solutions as a candidate solution according to the contempt criterion; wherein, the four different neighborhood operators are specifically Remove operator, Insert operator, Relocate operator and Replace operator; (3.5) Determine whether the candidate solution is better than the historical best solution. If not, execute (3.6); if so, execute (3.7). (3.6) Randomly perturb the candidate solutions according to the perturbation length, and then execute (3.7). (3.7) Improve the candidate solution or the solution after random perturbation of the candidate solution, including improving the replenishment period of each retail counter and improving the route plan, and take the improved solution as the optimal solution and execute (3.8). (3.8) Update the tabu list based on the current solution and the optimal solution; (3.9) Increment the iteration count by 1 and return to step (3.3); Step (3.2) specifically includes: (3.2.1) Ignoring the impact of path costs, we solve the simplified model to obtain the solution that minimizes inventory costs. , The simplified model takes the minimum sum of inventory cost and stockout cost in the current planning period as the objective function, and replenishment constraints and maximum inventory level constraints as constraints. (3.2.2) Using heuristics, based on the obtained , Find the solution when the delivery cost is minimized. , at this time As a feasible solution; (3.2.3) The feasible solution is improved and the improved solution is used as the initial solution.

2. The retail counter inventory path decision optimization method according to claim 1, characterized in that, The replenishment constraints are specifically as follows: ， In the formula, This indicates the maximum inventory level of the retail counter.

3. The retail counter inventory path decision optimization method according to claim 1, characterized in that, The maximum inventory level constraint is specifically as follows: ， In the formula, , These represent the warehouses in the [number]th [year]. The remaining inventory level at the end of the t-1 planning period. This indicates the amount of goods received into the warehouse each period. Indicates retail counter Maximum inventory level; The vehicle capacity constraint is specifically as follows: ， In the formula, Indicates the vehicle's capacity. Let be a 0-1 variable indicating whether the k-th vehicle visited the warehouse in period t. If the vehicle visited the warehouse, then... ,otherwise .

4. The retail counter inventory path decision optimization method according to claim 1, characterized in that, The specific retail counter flow balance constraint is as follows: ， In the formula, Indicates the edge used for indicating Is it the first Vehicles The 0-1 variables of the route, when When =1, it represents an edge. For the first Vehicles If it is the correct route, then it is not; The specific vehicle closed-loop constraint is as follows: ， ， In the formula, , These represent the edges used for indicating the edges. , Is it the first Vehicles The path is represented by a 0-1 variable. A value of 1 indicates that the edge is part of the path, and a value of 1 indicates that it is not. , The 0 in the text represents a warehouse. Let be a 0-1 variable indicating whether the k-th vehicle visited the warehouse in period t. If the vehicle visited the warehouse, then... ,otherwise .

5. The retail counter inventory path decision optimization method according to claim 1, characterized in that, The elimination of sub-loop constraints specifically refers to: ， In the formula, This represents a subset of the set of retail cabinets. Indicates the vehicle k A 0-1 variable indicating whether to replenish retail counter m in planning period t, when... When, it indicates the vehicle k Replenish retail counter m with stock during the t-th planning period; otherwise, it indicates that there is no stock.

6. The retail counter inventory path decision optimization method according to claim 1, characterized in that, The simplified model is specifically as follows: ， 。 7. The retail counter inventory path decision optimization method according to claim 1, characterized in that, Step (3.7) specifically includes: (3.7.1) Improve the replenishment period for each retail counter: Add a two-dimensional array DeltaCost to record the impact of changes in replenishment period on total cost. Then DeltaCost's element DeltaCost[ ][ Record if Estimate the change in total cost from 0 to 1, when Then DeltaCost[ ][ Record if Estimate the change in total cost from 1 to 0; then, extract the element with the smallest negative number from each row of DeltaCost and extract its index. The value is recorded as ( If the solution before the upgrade is in , The solution s is used to indicate the retail counter. Is it in the first For 0-1 variables that are replenished during the planning period, then Improved value If the solution before the upgrade is in ,but Improved value Finally, based on the OU strategy... Synchronous promotion yields the promoted value. ; (3.7.2) Based on the improved , After replanning the route, improvements were achieved. value The upgraded As the solution after the improvement of solution s.

8. The retail counter inventory path decision optimization method according to claim 1, characterized in that, Step (3.8) specifically includes: Solution The optimal solution is obtained by using the solution This indicates that if in the solution The Middle Planned supply to retail counters Restocking but in progress The Middle No retail counters during the planning period Replenishment will then involve the binary pair. Add to taboo list In the middle, it represents the retail cabinet in subsequent iterations. Banned in Replenishment; If in the solution The Middle No retail counters during the planning period Restocking but in progress The Middle Planned supply to retail counters Replenishment will involve the binary pair. Add to taboo list In the middle, it represents the retail cabinet in subsequent iterations. Will remain in the first Replenishment; Among them, the taboo length of both taboo lists is ,in and All are fixed parameters. Solution The number of feasible paths in the middle, It is 0 to Randomly select numbers from between.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: The processor executes the computer program to implement the method as described in any one of claims 1-8.

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