Inventory Routing Problem With Split Delivery For Small C/S Customers

Under the push delivery model,the supplier determines the customers’ inventory,The supplier needs to decide when to transport what products for which customer,which is a complex decision-making problem.In addition,there are some customers with small inventory capacity and high demand in the distribution network,so the supplier needs to be replenished them frequently and make a proper delivery.Due to the inventory limitation of customers,the replenishment vehicles must be able to serve customers after their accommodation time.If they arrive after their stock-out time,they will have the cost of out-of-stock,so the distribution process receives the constraint of customers’ accommodation time and stock-out time.Furthermore,this time window is closely related to the decision of distribution volume,which further complicates this decision-making problem.This paper proposes the Inventory Routing Problem with Small C/S(IRPSDSC)for optimizing multi-period inventory routes,integrating multiple delivery decisions with vehicle scheduling decisions.We study it in the context of the secondary distribution of refined oil products.The main works are as follows:(1)Inventory Routing Problem with Small C/S(IRPSD-SC)is proposed,and a mathematical model is established.In this paper,based on the analysis of previous research,the IRPSD-SC problem is proposed by combining the theories related to the secondary distribution problem of refined oil products and the inventory routing problem.The problem combines the IRP(Inventory Routing Problem)problem with the SDVRP(Split Delivery Vehicle Routing Problem)problem in the push distribution mode for a supply chain network with multiple customers and one supplier;considering multiple cycles,customers’ storage capacity limits,small capacity-to-sales ratio customers The problem is combined with the SDVRP(Split Delivery Vehicle Routing Problem)problem;considering multiple cycles,customer’s inventory constraints,small c/s ratio customers,allowing multiple deliveries to each customer in one cycle,considering customer’s inventory holding cost and stock-outs.A mixed integer planning model is established to minimize transportation costs,out-of-stock costs,and inventory holding costs.(2)Three hybrid variable neighborhood search algorithms are designed and implemented.For the characteristics of the IRPSD-SC problem,14 kinds of neighborhood structures are designed.On this foundation,the hybrid variableneighborhood search algorithms under the first-improved(VNS-FI)and best-improved(VNS-BI)strategies and the hybrid variable-neighborhood search algorithm incorporating simulated annealing(VNSA)are designed and implemented.In the VNSA algorithm,the idea of accepting worse solutions with a certain probability in the simulated annealing algorithm is introduced into the variable neighborhood search algorithm to improve the global search capability of the algorithm.(3)We have conducted rich experiments and case studies in this paper.The results show that VNS-BI can quickly find better solutions than CPLEX;compared with VNSFI and VNS-BI,VNSA can find better solutions under sufficient running time and thus is suitable for smaller-scale problems.In addition,VNS-FI can find better solutions in a shorter time and is therefore suitable for solving large-scale problems;increasing the number of customers with small c/s will significantly increase the algorithm’s running time and total cost.The results of applying the method in this paper to solve the secondary distribution case of Sinopec’s refined oil products show that compared with the individual decisions of transportation and sales departments,IRPSD-SC integrates the interests of both departments and can significantly reduce the enterprise operation cost.