Theoretical analysis and a search procedure for the joint replenishment problem with deteriorating products

We investigate the Joint Replenishment Problem (JRP) with deteriorating products in this paper. Many researchers have been devoting their efforts to solve the JRP for some thirty years. Though, there exists no JRP model that considers deterioration cost incurred from obsolescence, damage, spoilage, evaporation, and decay that often happens in the real world. Our focus in this study is to conduct theoretical analysis on the mathematical model for the JRP with deteriorating products by exploring the optimality structure and deriving several interesting properties on the optimal objective curve. By utilizing our theoretical results, we propose a search procedure that can efficiently solve the optimal solution. Based on our numerical experiments, we show that the proposed algorithm provides significantly better replenishment strategy than the case in which the decision maker ignores the deteriorating factor.