A vendor–buyer integrated inventory system with variable lead time and uncertain market demand

Abstract

In this paper, we consider a single-vendor single-buyer integrated inventory model in which the replenishment lead time is assumed to be a linear function of batch size, setup time, and transportation time. Both the vendor and the buyer are interested to invest in reducing the ordering cost. Shortages, if occur in buyer’s inventory, are partially backlogged with a certain limit of backorder price discount. The objective of the study is to derive the optimal decisions and the best investment policy by minimizing the expected annual total cost of the integrated system. The existence and uniqueness of the optimal solution are investigated and an efficient algorithm is designed to find the optimal solution of the proposed model numerically. We demonstrate the aids of reducing order-processing cost through numerical examples and show that it has significant effect on lot sizing decisions. It is also observed that transportation delay forces the buyer to stock more in order to defend the stock-out situation.