A cash constrained single item stochastic lot-sizing problem

Abstract

We investigate a dynamic inventory management problem where a cash-constrained small retailer periodically purchases an item from a supplier and sells it to the customers with non-stationary demands. At each period, the retailer’s available cash restricts the maximum inventory level that it can replenish. There exists a fixed ordering cost for the retailer when ordering and this results in a stochastic lot-sizing problem. We build a stochastic dynamic programming model for this problem and find some characteristics of the optimal ordering pattern.