A dynamic ordering policy for a stochastic inventory problem with cash constraints. (July 2021)

• Record Type: Journal Article
• Authors: Chen, Zhen; Rossi, Roberto
• Is Part Of: Omega. Volume 102(2021)
• Publication Date: 2021-07
• Subjects: Stochastic inventory -- Non-stationary demand -- Cash-flow constraint -- (s, C(x), S) policy; Management -- Periodicals; 658.4005
• DOI: 10.1016/j.omega.2020.102378
• Languages: English
• ISSNs: 0305-0483

Abstract

Highlights: We investigate a cash-constrained stochastic inventory system with fixed cost. We empirically investigate the optimal policy and prove some structural properties. A heuristic control policy: (s, C(x), S) policy is proposed. We introduce a stochastic dynamic programming approach for computing s, C(x) and S. An efficient algorithm to obtain s, C(x) and S via MILP is also developed. 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.