Joint replenishment with substitution and lost sales -

Abstract

The joint replenishment problem has received considerable attention in inventory control; it is the problem of coordinating the order of a group of products from a single supplier. 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 product) is designed to minimize the joint holding and ordering costs based on a given demand. JRM studies assume that there is no substitution between products. However, this assumption is unrealistic in some settings where substitution cannot be ignored. This thesis 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(EOQ) model and with a common ordering cycle. I determine the optimal order quantities for each product taking into consideration substitution between so that demand is partially met and the total cost associated with the delivery, holding, and shortage of the products is minimized. I also provide an extensive scenario analysis and draw insights. In particular, I shed some light on the role of substitution in reducing the fixed cost. I show that JRMS can result in substantial cost savings compared to the ordinary JRM. The joint replenishment model with substitution motivated us to study the joint replenishment with lost sales since when the shortage cost is low, substitution becomes no longer profitable and it is better to have lost sales in this case. For this reason, I extend the traditional joint replenishment model by allowing for lost sales to better reflect the reality. Lost sales represent the case where a demand occurring when the system is out of stock is lost forever. Although it is well known that if the inventory system should be operated at all, then it is never optimal to incur any stockouts in EOQ- type settings, e.g., Hadley and Whitin,1963, I show tha