Replenishment decisions under quantity discounts and expiry dates

Abstract

In this study, we model a single buyer-single seller system under a quantity discount schedule with expiry dates. The buyer faces constant demand and shortages are not allowed. The seller o§ers a quantity discount which is e§ective on the buyerís next purchase to be exercised by a certain expiry date given that the current purchase exceeds a minimum quantity. We derive the optimal replenishment policy structure for the buyer which minimizes his/her total cost rate. We obtain the expressions for the operating characteristics of the buyer and investigate the structural properties of the objective function. Under a speciÖc inventory holding cost structure, we also investigate the impact of the buyerís decisions on the entire buyer-seller inventory system. We conduct an extensive numerical study. Our Öndings show that quantity discount schedules with expiry dates may be beneÖcial for both the buyer and the seller in a variety of operating cost settings.