Inventory replenishment and delivery planning in a two-level supply chain with compound Poisson demands

Abstract

This paper presents a model for integrating inventory replenishment and delivery planning in a two-level supply chain consisting of a supplier and a retailer. The supplier is authorized to manage the inventory level of the retailer by using the information on demands from final customers and the inventory level of the retailer. The problem considered here is to determine order-up-to levels of the supplier and the retailer simultaneously for the objective of minimizing the expected long-run average cost, which is composed of replenishment cost at the supplier, delivery cost to the retailer, and inventory holding costs at both members. We develop a renewal theoretic optimization model for a case of compound Poisson demands with distribution-free order quantities and present an approximation method for obtaining a solution of the problem. In addition, a closed-form solution is derived for the problem with a special case of compound Poisson demands, in which demand quantities follow an exponential distribution. A series of simulation tests show that the solutions obtained from the approximated cost functions are reasonably good.