Service Constrained (s, S) Inventory Systems with Priority Demand Classes and Lost Sales

• Published in: Management science Vol. 34; no. 4; pp. 482 - 499
• Main Authors: Cohen, Morris A, Kleindorfer, Paul R, Lee, Hau L
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.04.1988; Institute of Management Sciences; Institute for Operations Research and the Management Sciences
• Series: Management Science
• Subjects: Applied sciences; Approximation; approximations; Business orders; Cost allocation; Cost functions; Exact sciences and technology; Greedy algorithms; Inventories; inventory; Inventory control, production control. Distribution; inventory/production; Lagermanagement; Markov chains; Minimization of cost; Operational research and scientific management; Operational research. Management science; Optimal solutions; ordering; production; Shipments; stochastic models; Theorie; Wahrscheinlichkeitsrechnung; Stockpile control; Supply; Stochastic model; Algorithm; Production control; Heuristic method
• ISSN: 0025-1909; 1526-5501
• DOI: 10.1287/mnsc.34.4.482

This paper presents a model of an ( s , S ) inventory system in which there are two priority classes of customers. The model treats excess demands as lost sales and can accommodate an arbitrary deterministic lead time. After considering the associated Markov-chain model, an approximate, renewal-based model is derived. This approximation is used to develop a greedy heuristic which minimizes expected costs subject to a fill-rate service constraint. The paper concludes with the results of an extensive numerical test of both the accuracy of the approximation and the performance of the heuristic with respect to the true optimal solution. Results indicate good performance which deteriorates as the fill rate requirement and lead time increase.