Robust Inventory Management: A Cycle-Based Approach

37 Pages Posted: 10 Jun 2020 Last revised: 12 Aug 2022

See all articles by Yupeng Chen

Yupeng Chen

Nanyang Business School, Nanyang Technological University

Garud Iyengar

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Chun Wang

Tsinghua University, School of Economics and Management

Date Written: August 10, 2022

Abstract

We study the robust formulation of an inventory model with positive fixed ordering costs, where the unfulfilled demand is either backlogged or lost, the lead time is allowed to be positive, the demand is potentially intertemporally correlated, and the information about the demand distribution is limited. We propose a robust cycle-based policy that manages inventory by dividing the planning horizon into non-overlapping inventory cycles, where an order is placed at the beginning of each cycle. Our policy selects the lengths and order quantities for all inventory cycles to minimize the worst-case total cost incurred over the planning horizon. When the uncertain demand belongs to a general polyhedral uncertainty set, the decisions in our policy can be computed by solving linear programs (LPs) for the backlogging model with any lead time and the lost-sales model with zero lead time; however, the number of LPs that need to be solved grows exponentially in the length of the planning horizon. In the special case where the uncertain demand belongs to a box uncertainty set, the decisions in our policy can be computed using a dynamic programming (DP) recursion whose complexity grows polynomially in the length of the planning horizon. We also propose a one-cycle look-ahead heuristic in order to handle large problem instances with a general polyhedral uncertainty set. This heuristic can be applied for both the backlogging and lost-sales models with any lead time, and it only requires solving LPs whose number grows quadratically in the length of the planning horizon. Results from extensive computational experiments clearly show that both a rolling-cycle implementation of our policy and the one-cycle look-ahead heuristic have very strong empirical performance. Our robust cycle-based policy and the one-cycle look-ahead heuristic are conceptually simple and can accommodate multiple realistic features in inventory management problems. They provide a very effective approach to robust inventory management, especially in the lost-sales setting.

Keywords: inventory management, robust optimization, fixed ordering cost, lost sales

Suggested Citation

Chen, Yupeng and Iyengar, Garud and Wang, Chun, Robust Inventory Management: A Cycle-Based Approach (August 10, 2022). Nanyang Business School Research Paper No. 20-11, Available at SSRN: https://ssrn.com/abstract=3602544 or http://dx.doi.org/10.2139/ssrn.3602544

Yupeng Chen

Nanyang Business School, Nanyang Technological University ( email )

Singapore, 639798
Singapore

Garud Iyengar (Contact Author)

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Chun Wang

Tsinghua University, School of Economics and Management ( email )

Beijing, 100084
China

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