Medicine distribution model under cooperation of multiple distribution centers and double-population genetic simulated annealing algorithm

Abstract

According to the multi-distribution-center collaborative medicine distribution model and the double-population genetic simulated annealing algorithm provided by the invention, aiming at the timeliness, multi-center collaboration and customer satisfaction requirements of medicine distribution, a mathematical model taking the total cost minimization as a target is constructed. The model comprehensively considers the vehicle fixed cost, the transportation cost, the customer satisfaction cost and the goods damage cost, introduces a soft time window function based on cosine distribution to quantify the influence of delivery delay on the cost, optimizes resource allocation through a multi-center order splitting strategy, and solves the problems of low delivery efficiency and high cost of a traditional single-center mode. According to the characteristics of the model, a double-population genetic simulated annealing algorithm (DPGSA) is designed. According to the algorithm, the global search capability is enhanced through a double-population coevolution mechanism, the local optimization efficiency is improved in combination with the Metropolis criterion of the simulated annealing algorithm, the defect of premature convergence of a traditional genetic algorithm is effectively avoided, the drug transportation and distribution path is optimized, and the distribution cost is minimized.

Description

Technical Field

[0001] The present invention relates to the field of logistics distribution, and particularly to a pharmaceutical distribution model with collaborative multi-distribution centers and a double-population genetic simulated annealing algorithm. Background Art

[0002] In the field of pharmaceutical distribution, by means of the collaborative multi-distribution center model, drugs can be delivered to customers safely and efficiently, which can improve the distribution efficiency and service quality. The single-distribution center distribution model has problems such as limited distribution capacity and difficulty in meeting diverse needs. The collaborative distribution of multiple distribution centers can integrate resources and flexibly allocate drugs according to the location and needs of customers. However, the inventory differences among different distribution centers, the vehicle scheduling problems, and the requirements for distribution timeliness pose challenges to collaborative distribution.

[0003] But in actual production, some distribution centers may have insufficient or excessive inventory, and the scheduling of distribution vehicles is complex. If not coordinated properly, it is easy to lead to low distribution efficiency. At the same time, pharmaceutical distribution is extremely sensitive to time. Customers expect drugs to be delivered on time. Exceeding the time limit or arriving too early may affect the customer experience and the quality of drugs. However, most current studies do not fully consider these complex factors. Therefore, the present invention proposes a pharmaceutical distribution model and method under the collaboration of multiple distribution centers. Starting from considering the soft time window limit of pharmaceutical distribution, fully considering factors such as the shelf life of drugs and customers' expectations for distribution time, a mathematical model of collaborative pharmaceutical distribution of multiple distribution centers with the goal of minimizing the total cost is constructed; then, a double-population genetic simulated annealing algorithm is designed to obtain the optimal distribution route plan and realize the overall optimization of the pharmaceutical distribution system under the collaboration of multiple distribution centers. Summary of the Invention

[0004] In view of the above problems, the present invention proposes a pharmaceutical distribution model with collaborative multi-distribution centers and a double-population genetic simulated annealing algorithm. First, consider that a pharmaceutical company has multiple warehouses (distribution centers) in a certain place and is responsible for delivering drugs to pharmacies according to demand. After receiving an order from a pharmacy, the company selects appropriate drugs according to the order and arranges one or more distribution centers to ship. Then, the distribution center dispatches dedicated distribution vehicles to deliver products to customers. After the task is completed, the vehicle needs to return to the original distribution center. After comprehensively considering factors such as the transportation cost generated during vehicle driving, the loss cost of medical supplies, the penalty cost for not arriving on time, and customer satisfaction, by reasonably planning the distribution centers and distribution routes, the total cost is minimized. Specifically, it includes the following:

[0005] The vehicle transportation cost F1 includes the fixed usage cost (rental fee, maintenance fee, start-up cost, etc.) of each refrigerated vehicle and the vehicle unit-time transportation cost;

[0006] The customer satisfaction cost F2. When the delivery time does not meet the expectation, the customer will generate after-sales costs due to dissatisfaction with the delivery service. This cost is determined by the customer satisfaction and the total order quantity.

[0007] The goods damage cost F3. During the drug delivery process, due to the bumps caused by the drug packaging, or partial losses and contaminations caused by untimely delivery, the resulting costs need to be borne by the pharmaceutical company. This cost is determined by the shelf life of the drug, that is, the time starts to be calculated after leaving the distribution center. If this time exceeds the shelf life, the goods damage cost will start to be calculated.

[0008] To be general, the following assumptions need to be made for constructing the model of the present invention: (1) The locations of the distribution center, customers, and the demand for each drug are known. After the customer places an order, the delivery can be accepted immediately. (2) All the vehicles used for drug delivery are of the same model. (3) The transportation cost per section of the vehicle's journey is not consistent throughout the whole journey. The average value is used to represent the unit transportation cost. The unit transportation cost and load capacity of the vehicle are known. (4) The vehicle must return to the original distribution center after the delivery is completed. (5) The loss cost of each drug per unit time is known.

[0009] The double-population genetic simulated annealing algorithm utilizes the characteristics of the genetic algorithm with fast solution speed and the characteristics of the simulated annealing algorithm to effectively jump out of the local optimal solution. Through the collaborative optimization of information exchange between the double populations, it avoids the problem of premature convergence of the genetic algorithm and solves the optimal path of the pharmaceutical distribution model under the cooperation of multiple distribution centers with the minimum total cost.

[0010] The vehicle transportation cost F1, the customer satisfaction cost F2, and the goods damage cost F3 are calculated as follows:

[0011]

[0012] Among them, the customer satisfaction s i uses the arrival time of the last vehicle and the customer's expected order delivery time b i for calculation. The calculation formula is:

[0013]

[0014] In the formula, V represents the set of vehicles, N represents the set of all possible points that the vehicle may pass through (including N c and N w ), N c represents the set of customers, N w represents the set of distribution centers, P represents the set of drug types, represents the demand of customer i for product v, C1 represents the vehicle usage cost, C2 represents the unit transportation cost of the vehicle, C3 represents the customer satisfaction coefficient, bi represents the time when customer i expects the order to be delivered, s represents the service time, C v represents the loss cost of goods v per unit time, F v represents the shelf life of drug v, and the loss cost starts to be calculated after this time, t ij represents the time for the vehicle to travel from point i to point j, equals 1 when vehicle k travels from the temporary stop point i to j, otherwise, equals 0, represents whether vehicle k delivers goods l to node i, otherwise, equals 0, is the time when vehicle k arrives at customer i, is the order end time, that is, the time when the last vehicle arrives at customer i;

[0015] To meet the relevant assumptions, there are corresponding constraints on the vehicle routes, specifically as follows:

[0016] (1) Each refrigerated vehicle departs from the warehouse and returns to the same warehouse, and traverses all stop points only once, while ensuring that the flow of the truck route remains balanced. The calculation formula is:

[0017]

[0018] In the formula, N represents the set of vehicle stop points (including the starting warehouse), V represents the set of vehicles, x ij k equals 1 when vehicle k travels from the temporary stop point i to j, otherwise, equals 0.

[0019] (2) The weight of the goods loaded by each refrigerated vehicle needs to be kept within the maximum load limit. Using the truck load balance constraint, the formula for eliminating sub-circuits is:

[0020]

[0021] In the formula, N represents the set of all points, N c represents the set of customers, V represents the set of vehicles, represents the demand of customer i for product v, the load of the truck when vehicle k leaves customer i, M represents a sufficiently large positive integer, x ij k equals 1 when vehicle k travels from the temporary stop point i to j, otherwise, equals 0.

[0022] (3) The time when each refrigerated vehicle arrives at node j is greater than or equal to the time when it arrives at the previous node i plus the service time at node i and the time required to travel from node i to node j. The end time of each customer order is greater than or equal to the time when any vehicle k arrives at customer i. The calculation formula is:

[0023]

[0024] Where N represents the set of all points, N c represents the set of customers, V represents the set of vehicles, represents the demand of customer i for product v, the load of truck k when leaving customer i, is the arrival time of vehicle k at customer i, is the order end time, M represents a sufficiently large positive integer, x ij k equals 1 when vehicle k travels from temporary stop i to j, otherwise, it equals 0.

[0025] The specific operation steps of the double-population genetic simulated annealing algorithm proposed by the present invention are as follows:

[0026] (1) Set the initial parameters, the population size n, the crossover probability p c , the mutation probability p m , the maximum number of iterations i, the initial temperature T, the immigration operator q;

[0027] (2) Randomly generate initial route plans and divide them into two populations, and calculate the total cost of each plan;

[0028] (3) For population 1, use roulette wheel selection, crossover and mutation to generate new pharmaceutical distribution route plans;

[0029] (4) For each individual in population 2, mutate and generate new distribution route plans. If the fitness of the new plan is greater than that of the old plan, accept the new plan. Otherwise, use the Metropolis criterion to calculate the probability of accepting the new plan or discarding the new plan;

[0030] (5) After q iterations, if the optimal solution of population 1 or population 2 has not been updated, randomly exchange the plans in population 1 and population 2 to generate two new populations and continue the iteration.

[0031] (6) Judge the termination condition. When the i - th iteration number is satisfied or the calculation time exceeds the set value, the algorithm terminates and outputs the optimal solution. Brief Description of the Drawings

[0032] Figure 1 is a schematic diagram of the model process of the present invention;

[0033] Figure 2 is a framework diagram of the genetic simulated annealing algorithm of the present invention;

[0034] Figure 3 is a coding diagram of the genetic simulated annealing algorithm of the present invention;

[0035] Figure 4 It is a schematic diagram of the crossover and mutation of the genetic simulated annealing algorithm of the present invention;

[0036] Figure 5 It is a comparison of the present invention with other methods under three data sets P04 / 05 / 06, Pr02 / 03 / 04. Specific implementation manner

[0037] For the purpose, technical solution and advantages of the present invention to be more clearly understood, the following combines the accompanying drawings to elaborate on the pharmaceutical distribution model and method for the collaboration of multiple distribution centers proposed by the present invention. It should be understood that the specific implementation methods described herein are only used to explain the present invention and are not used to limit the present invention. Any changes, modifications, additions, or substitutions made by those of ordinary skill in the art within the scope of the present invention should be covered by the scope of the claims of the present invention.

[0038] Figure 1 It is a specific schematic diagram of a truck - drone collaborative distribution model based on contactless distribution of the present invention. From Figure 1 It can be seen that a pharmaceutical company has multiple warehouses (distribution centers) in a certain place and is responsible for delivering drugs to pharmacies according to demand. After receiving an order from a pharmacy, the company selects appropriate drugs according to the order and arranges one or more distribution centers to ship the goods. Then, the distribution center dispatches special distribution vehicles to deliver products to customers. After the task is completed, the vehicle needs to return to the original distribution center. Among them, each customer can be served by one or more vehicles. Compared with traditional truck distribution, multi - center collaborative distribution expands the service radius and improves the overall distribution efficiency and flexibility.

[0039] Figure 2 It is a framework diagram of a two - population genetic simulated annealing algorithm of the present invention. From Figure 2 It can be seen that a two - stage algorithm for truck - drone collaborative distribution based on contactless distribution proposed by the present invention includes an improved K - means clustering and a variable - neighborhood simulated annealing algorithm for optimizing the paths of trucks and drones according to the designed model. The specific implementation steps are as follows:

[0040] (1) Set initial parameters, the population size n, the crossover probability p c , the mutation probability p m , the maximum number of iterations i, the initial temperature T, and the immigration operator q;

[0041] (2) Randomly generate initial route plans and divide them into two populations, and calculate the total cost of each plan;

[0042] (3) For population 1, use roulette wheel selection, crossover and mutation to generate new pharmaceutical distribution path plans;

[0043] (4) For each individual in population 2, mutate and generate a new distribution route plan. If the fitness of the new plan is greater than that of the old plan, accept the new plan; otherwise, accept the new plan or discard it with the probability calculated by the Metropolis criterion.

[0044] (5) After q iterations, if the optimal solution of population 1 or population 2 has not been updated, randomly exchange the plans in population 1 and population 2 to generate two new populations and continue the iteration.

[0045] (6) Judge the termination condition. When the number of iterations reaches i or the calculation time exceeds the set value, the algorithm terminates and outputs the optimal solution.

[0046] Figure 3 is the coding diagram of a dual-population genetic simulated annealing algorithm of the present invention. The feasible solution includes the truck route, which will affect the arrival time at the customer and thus generate penalty costs. Co-optimizing the truck route requires first encoding its route: use the double-matrix real number encoding method for chromosome encoding. First, determine the number of distribution centers, the points responsible for each distribution center, and the selection of distribution vehicles for each type of medicine in each order. Assume that there are 3 distribution centers and 4 vehicles in total. The distribution center numbers are 0 - 2, the vehicle numbers are 0 - 3, the numbers of 10 demand points are set as 3 - 12, and the numbers of 4 types of medicines are 0 - 3; the double-matrix real number encoding uses one matrix to represent the visiting order of each vehicle to each point, and another matrix to represent the distribution vehicle of each type of medicine at each point. Each row of the path matrix represents the distribution order of one vehicle; each row of the medicine allocation matrix represents one commodity, each column represents one customer, and the value in the matrix is the vehicle number, indicating that the medicine j of customer i is delivered by vehicle k. Taking vehicle 0 as an example, the first row of the path matrix is 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, representing the visiting order of this vehicle. At the same time, it can be seen from the medicine allocation matrix that the medicines assigned to vehicle 0 are medicine 2 of customer 3, medicine 0 and medicine 2 of customer 8, and medicine 1 of customer 12. After removing the customers that do not need to be delivered, the actual distribution route of vehicle 0 is 3, 8, 12. And so on, the distribution route of vehicle 1 is 3, 7, 11, 12, the distribution route of vehicle 2 is 5, 9, 10, 12, and the distribution route of vehicle 3 is 4, 6.

[0047] Figure 4 is the schematic diagram of crossover and mutation of a dual-population genetic simulated annealing algorithm of the present invention. According to the continuous iteration of the algorithm, the vehicle route determines the crossover and mutation methods according to the randomly generated probability: two-point crossover, segment crossover, and two-point mutation

[0048] , flipping mutation, random mutation. Taking two-point crossover as an example, assume the vehicle sub-paths are r1(3 - 4 - 5 - 6 - 7 - 8 - 9 - 10 - 11 - 12) and r2(7 - 8 - 3 - 9 - 4 - 12 - 5 - 11 - 6 - 10). Select two points corresponding to (6, 10) in r1 and (9, 5) in r2. Then the transformed truck sub-paths are (3 - 4 - 6 - 9 - 7 - 8 - 10 - 5 - 11 - 12) and (7 - 8 - 3 - 6 - 9 - 4 - 12 - 10 - 11 - 5); if reverse exchange is selected, the transformed truck sub-path is (0 - f - h - g - d - e - a - c - b - 0);

[0049] Further, the following situation is taken as an example for illustration:

[0050] Taking P04 / 05 / 06 and Pr02 / 03 / 04 as examples, 20, 40, and 80 customer points are respectively selected to generate different examples, which include information such as the position coordinates, demand, service time, and time window of each point.

[0051] (1) According to a truck - drone collaborative distribution model based on contactless distribution of the present invention, the fitness function is to minimize the total distribution cost, and the calculation formula is as follows:

[0052] minZ = F1 + F2 + F3

[0053]

[0054] In the formula, F1 is the vehicle transportation cost, F2 is the customer satisfaction cost, and F3 is the cargo damage cost.

[0055] (2) Set the unit fixed cost of the truck to be 30 yuan respectively, the mileage costs to be 1.25 yuan / km and 0.15 yuan / km, and the speeds to be 40 km / h and 60 km / h; the unit waiting cost and the unit delay cost are 0.2 yuan and 0.5 yuan respectively. The initial temperature t0 of the double - population genetic simulated annealing is 5000, The maximum number of iterations is 5000. Calculate the fitness of the generated paths according to the position coordinates, demand, service time, and time window of each point in the example, and perform iterations to continuously obtain feasible solutions.

Claims

1. A pharmaceutical distribution model under the coordination of multiple distribution centers and a double-population genetic simulated annealing algorithm are used to improve the distribution quality and reduce the distribution cost in the pharmaceutical logistics distribution link, including the following: The vehicle transportation cost F1 includes the fixed usage cost (rental fee, maintenance fee, start-up cost, etc.) of each refrigerated vehicle and the vehicle unit-time transportation cost; The customer satisfaction cost F2. When the distribution time does not meet the expectation, the customer generates after-sales costs due to dissatisfaction with the distribution service, and this cost is determined by the customer satisfaction and the total order quantity; The goods damage cost F3. During the pharmaceutical distribution process, due to the bumps caused by the pharmaceutical packaging, or some losses, contaminations, etc. caused by untimely distribution, the costs generated need to be borne by the pharmaceutical company. This cost is determined by the shelf life of the medicine, that is, the time is calculated starting from when it leaves the distribution center. If this time exceeds the shelf life, the goods damage cost starts to be calculated. To be general, the following assumptions need to be made first to construct the model of the present invention: (1) The positions of the distribution centers, customer positions, and the demand for each type of medicine are known, and the customers can accept the distribution after placing an order. (2) The vehicles used for distributing medicines are of the same model. (3) The transportation cost of each section of the vehicle's journey is not the same throughout the whole journey, and the average value is used to represent the unit transportation cost. The vehicle unit transportation cost and load capacity are known. (4) The vehicle must return to the original distribution center after the distribution is completed. (5) The loss cost of each type of medicine per unit time is known. The double-population genetic simulated annealing algorithm makes use of the characteristics of the fast solution speed of the genetic algorithm and the characteristics of the simulated annealing algorithm to effectively jump out of the local optimal solution. Through the collaborative optimization of the information exchange between the two populations, it avoids the problem of premature convergence of the genetic algorithm and solves the optimal path of the pharmaceutical distribution model under the coordination of multiple distribution centers with the minimum total cost.

2. The pharmaceutical distribution model and double-population genetic simulated annealing algorithm under the coordination of multiple distribution centers according to claim 1, characterized in that The vehicle transportation cost F1, the customer satisfaction cost F2, and the goods damage cost F3 are calculated as follows: Among them, the customer satisfaction s i Use the arrival time of the last vehicle And the customer's expected order delivery time b i Calculate, and the calculation formula is: Where \(V\) represents the set of vehicles, \(N\) represents the set of all possible points that the vehicles may pass through (including \(N\) c and \(N\) w ), \(N\) c represents the set of customers, \(N\) w represents the set of distribution centers, \(P\) represents the set of drug types, represents the demand of customer \(i\) for product \(v\), \(C1\) represents the vehicle usage cost, \(C2\) represents the unit transportation cost of the vehicle, \(C3\) represents the customer satisfaction coefficient, \(b\) i represents the time when customer \(i\) expects the order to be delivered, \(s\) represents the service time, \(C\) v represents the loss cost of goods \(v\) per unit time, \(F\) v represents the shelf life of drug \(v\), and the loss cost starts to be calculated after this time, \(t\) ij represents the time for the vehicle to travel from point \(i\) to point \(j\), is 1 when vehicle \(k\) travels from the temporary stop point \(i\) to \(j\), otherwise, it is 0, represents whether vehicle \(k\) delivers goods \(l\) to node \(i\), otherwise, it is 0, is the time when vehicle \(k\) arrives at customer \(i\), is the order end time, that is, the time when the last vehicle arrives at customer \(i\); To meet the relevant assumptions, there are corresponding constraint limitations for the vehicle routes, specifically as follows: (1) Each refrigerated vehicle starts from the warehouse and returns to the same warehouse, and traverses all stops only once, while ensuring that the flow of the truck route remains balanced. The calculation formula is: where \(N\) represents the set of vehicle stops (including the starting warehouse), \(V\) represents the set of vehicles, and \(x\) ij k equals 1 when vehicle \(k\) travels from the temporary stop \(i\) to \(j\), otherwise, it equals 0. (2) The weight of the goods loaded on each refrigerated vehicle needs to be kept within the maximum load limit. Using the truck load balance constraint, the sub-circuit elimination calculation formula is: where \(N\) represents the set of all points, \(N\) c represents the set of customers, \(V\) represents the set of vehicles, represents the demand of customer \(i\) for product \(v\), the load of truck \(k\) when leaving customer \(i\), \(M\) represents a sufficiently large positive integer, \(x\) ij k equals 1 when vehicle \(k\) travels from temporary stop \(i\) to \(j\), otherwise, it equals 0. (3) The time when each refrigerated vehicle arrives at node j is greater than or equal to the time when it arrives at the previous node i plus the service time at node i and the time required to travel from node i to node j. The end time of each customer order is greater than or equal to the time when any vehicle k arrives at customer i. The calculation formula is: where N represents the set of all points, N c represents the set of customers, V represents the set of vehicles, represents the demand of customer i for product v, the load of truck k when leaving customer i, is the arrival time of vehicle k at customer i, is the order end time, M represents a sufficiently large positive integer, x ij k equals 1 when vehicle k travels from temporary stop point i to j, otherwise, it equals 0.

3. A pharmaceutical distribution model and a double-population genetic simulated annealing algorithm under the collaboration of multiple distribution centers according to claim 1, characterized in that The double-population genetic simulated annealing algorithm. The specific operation steps of the double-population genetic simulated annealing algorithm are as follows: (1) Set initial parameters, the population size n, the crossover probability p c , the mutation probability p m , the maximum number of iterations i, the initial temperature T, the immigration operator q; (2) Randomly generate an initial route plan, divide it into two populations, and calculate the total cost of each plan; (3) For population 1, use roulette wheel selection, crossover and mutation to generate a new pharmaceutical distribution route plan; (4) For each individual in population 2, mutate and generate a new delivery route plan. If the fitness of the new plan is greater than that of the old plan, accept the new plan; otherwise, accept the new plan or discard it with the probability calculated by the Metropolis criterion. (5) After q iterations, if the optimal solutions of population 1 or population 2 have not been updated, randomly exchange the plans in population 1 and population 2 to generate two new populations and continue the iteration. (6) Judge the termination condition. When the number of iterations reaches i or the calculation time exceeds the set value, the algorithm terminates and outputs the optimal solution.

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