Joint replenishment model with substitution

When products are coupled to the same cycle, the joint replenishment model (JRM) is used to determine optimal inventory levels, where the amount to order (for each item) is designed to minimize the joint holding and ordering costs based on a given demand. JRM studies assume that there is no substitution between items. However, this assumption is unrealistic in some settings where substitution cannot be ignored. This paper combines the separate works on substitution and joint replenishment and proposes a solution procedure for solving the joint replenishment model with substitution (JRMS) for two products within the framework of the classical economic order quantity model. We determine the optimal order quantities for each product taking into consideration substitution between them so that demand is partially met and the total cost associated with the delivery, holding, and shortage of the products is minimized. We also provide an extensive scenario analysis and draw insights. In particular, we shed some light on the role of substitution in reducing the fixed cost. We show that JRMS can result in substantial cost savings compared to the ordinary JRM.