Inventory management for stockout-based substitutable products under centralised and competitive settings

AbstractInventory planning in fashion markets is highly challenging, owing to uncertain demand; yet, in making inventory decisions, retailers may be able to capitalise on high substitutability between products. This research develops single-period inventory-management models describing a market with two substitutable products, under stockout-based substitution; i.e. when a customer's preferred product is out-of-stock, s/he may choose to purchase the substitute. Two settings are considered: centralised (a single retailer who sells both products) and competitive (two retailers, each selling one product). For each setting, we derive closed-form analytical solutions for the inventory levels that maximise expected profit. The model is further enriched with sales data from an online apparel retailer offering substitutable products (a sneaker in different colours), and we analyse the sensitivity of the optimal inventory levels and profits to parameter values. Key findings include the following: (i) Under competitive conditions, both retailers always order positive inventory so as not to lose customers. However, in a single-retailer setting, there are situations in which the retailer orders inventory for only one product. (ii) The optimal inventory levels and corresponding profits are highly sensitive to consumers' willingness to substitute between products. These findings provide concrete insights that can guide fashion brands' inventory-management decisions.KEYWORDS: Inventory managementstockout-based substitutionfashion industrygame theorysupply chain management AcknowledgementsThe authors would like to thank Isaac Meilijson for his help in estimating the joint demand and the three anonymous reviewers for their constructive comments and suggestions which have significantly improved the paper.Disclosure statementNo potential conflict of interest was reported by the author(s).Data availability statementData available on request from the authors.Additional informationFundingThis research was partially supported by the Israel Science Foundation (grant number 1898/21).Notes on contributorsMichal KorenMichal Koren holds a Ph.D. and an M.A. in Industrial Management, both from the Department of Management, Bar-Ilan University in Israel, and a B.Sc. in Industrial Engineering and Management from Shenkar- Engineering. Design. Art. Currently, she is a faculty member and deputy dean at the School of Industrial Engineering and Management at Shenkar- Engineering. Design. Art. Her research interests include Operations Research, Supply Chain, Machine Learning and Artificial Intelligence.Yael PerlmanYael Perlman is an Associate Professor of Operations Management in the Department of Management at Bar-Ilan University, Israel. She holds a BSc in Mathematics (TAU) an MBA in Operations Research (TAU) and a PhD in Industrial Engineering (BGU). Yael Perlman develops game theory-based models and queuing theory-based models to investigate strategic decisions of the supply chain members and the effect of intra-supply chain competition on the overall supply chain performance. Her papers have been published in some of the leading journals of Supply Chain Management and Operations Management.Matan ShnaidermanMatan Shnaiderman received M.S. and Ph.D. degrees in the Department of Mathematics, Bar-Ilan University in Israel. He is currently Senior Lecturer at the Department of Management, Bar-Ilan University. His research interests include supply-chain and inventory management, information sharing, public transit, frequency setting, energy production and stochastic dynamic programming.