Control of lead time for retailer-supplier contract with stochastic demand and order cancellation

Abstract

We consider a retailer-supplier inventory system exposed to probabilistic demands and retums or cancellations of demands. Retailer maintains extra inventories to share the burden of inventory cost and an order is placed when the amount of extra inventories falls below a predetermined level. We compute the probability distribution of the length of lead-time in both continuous review and periodic review cases. This is utilized to derive the allowable replenishment length and penalty cost for delivery delay, with which a proper way of contract between both parties is proposed. Numerical example is provided to illustrate the method.