A dynamic ordering policy for a stochastic inventory problem with cash constraints

Abstract

This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product and sells it to customers while facing non-stationary demand. In each period, the retailer’s available cash restricts the maximum quantity that can be ordered. There is a fixed ordering cost incurred when an order is issued by the retailer. We introduce a heuristic (s,C(x),S) policy inspired by numerical findings and by a structural analysis. The policy operates as follows: when the initial inventory x is less than s and the initial cash is greater than the state-dependent value C(x), the retailer should order a quantity that brings inventory as close to S as possible; otherwise, the retailer should not order. We first determine the values of the controlling parameters s,C(x) and S via the results of stochastic dynamic programming and test their performance in an extensive computational study. The results show that the (s,C(x),S) policy performs well, with a maximum optimality gap of less than 1%, and an average gap of approximately 0.03%. We then develop a simple and time-efficient heuristic method for computing policy (s,C(x),S) by solving a mixed-integer linear programming problem: the average gap for this heuristic is less than 1% on our test bed.