Using an Efficient New Gene for Genetic Algorithm to Solve the Multi-buyer Joint Replenishment Problem

Abstract

The multi-buyer joint replenishment problem (MJRP) is the multi-item inventory problem which deals with the replenishment of a group of product items that are jointly delivered to multi-buyer. The objective of MJRP is to develop policy to minimize the total cost which consists of the holding cost and the transport cost. In this paper, we propose a modified genetic algorithm (called GAT) which adopts a New Gene, basic cycle time, to solve the multi-buyer joint replenishment problem (MJRP). The genetic algorithm (GA) has been widely applied to solve MJRP. However, most of the literature which used the genes for chromosomes were the ratio of each product delivery cycle time to the basic cycle time. This searching method is called GAK here. The disadvantage of GAK is that the number of genes is determined by the number of product items and buyers, and the length of chromosomes will be expanded when the number of product items or buyers is increased. The length of chromosomes will impact the CPU running time in the genetic algorithm. The proposed GAT can improve the disadvantage of GAK. Simulation experiments demonstrate that the GAT is very efficient and outperforms GAK. The running time of GAK is improved over 96% by GAT. Keywords: Joint Replenishment Problem, Multi-item Multi-buyer, Genetic Algorithm