On a Deterministic Approximation of Inventory Systems with Sequential Service Level Constraints

Operations Research Forthcoming

64 Pages Posted: 12 Feb 2018 Last revised: 31 Aug 2020

See all articles by Lai Wei

Lai Wei

Boston College - Carroll School of Management

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business

Linwei Xin

University of Chicago - Booth School of Business

Date Written: August 30, 2020

Abstract

Service level constraint is often used as a metric to directly control the quality of service (e.g., managing the probability of stock-out) in practice. Many inventory problems with service level constraints are often difficult to solve and are typically approximated by deterministic formulations. This raises an important question regarding the quality of such an approach. To shed light on this question, in this paper, we consider two simplified yet fundamental inventory models (with backorder and lost-sales) with independent demands, positive lead times and sequential probabilistic service level constraints, and study the performance of a natural order-up-to policy whose parameters can be calculated using the optimal solution of a deterministic approximation of the backorder inventory system. We show that it is asymptotically optimal for both the backorder and lost-sales systems in the setting with a high service level requirement, with a stronger performance bound for the backorder system. Our analysis for the lost-sales system involves a construction of an alternative backorder system whose expected total cost can be related to that of the analogous lost-sales system. Overall, our result contributes to the growing body of inventory literature that suggests the near-optimality of simple heuristic policies. Moreover, it also gives credence to the use of deterministic approximation for solving complex inventory problems in practice, at least for applications where the targeted service level is sufficiently high.

Keywords: inventory, service level constraints, lost-sales, deterministic approximation, linear programming, asymptotic optimality

Suggested Citation

Wei, Lai and Jasin, Stefanus and Xin, Linwei, On a Deterministic Approximation of Inventory Systems with Sequential Service Level Constraints (August 30, 2020). Operations Research Forthcoming, Available at SSRN: https://ssrn.com/abstract=3114348 or http://dx.doi.org/10.2139/ssrn.3114348

Lai Wei

Boston College - Carroll School of Management ( email )

140 Commonwealth Avenue
Chestnut Hill, MA 02467
United States

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Linwei Xin (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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