Fight Inventory Shrinkage: Simultaneous Learning of Inventory Level and Shrinkage Rate

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Author Information : Rong Li (Martin J. Whitman School of Management, Syracuse University)
Jing-Sheng Song (The Fuqua School of Business,Duke University)
Shuxiao Sun (Newhuadu Business School, Minjiang University)
Xiaona Zheng (Guanghua School of Management, Peking University)

Year of Publication : (Forthcoming) Production and Operations Management, 2022

Summary of Findings : We developed effective real-time decisions to help retailer flight inventory shrinkage by learning from severely censored demand data.

Research Questions : In 2020, inventory shrinkage eroded $61.7 billion profit in the U.S. retail industry. With growing unobservable inventory shrinkages, how can retailers make the best use of sales data to learn demand and make important decisions on inventory and loss-prevention investment?

What we know : The data-driven heuristics we developed can prevent retailers from stocking too little and falling into a vicious cycle - declining sales data, due to shrinkage, was misinterpreted as declining demand and hence leads to insufficient replenishment. These data-driven heuristics can also quickly learn the actual shrinkage rate and thus help identify early the effectiveness of loss prevention strategies implemented.

Novel Findings : Learning from triple-censored demand data and modeling random shrinkages that are interwoven with sales are the two novel challenges this study took. Despite the challenges, the data-driven heuristics we developed turn out to be surprisingly effective.

Full Citations : Li, R., Song, J-S., Sun, S. & Zheng, X. (2022.) Fight inventory shrinkage: Simultaneous learning of inventory level and shrinkage rate. Forthcoming in Production and Operations Management.

Abstract : In 2020, inventory shrinkage eroded $61.7 billion profit in the U.S. retail industry. Unfortunately, fighting inventory shrinkage to protect retailers’ already slim profits is challenging due to unknown shrinkage rates and invisible inventory levels. While the latter has been studied in the literature, the former has not. To deal with this challenge, we introduced two new features to the Bayesian inventory models: (1) interleaving customer and theft arrival processes that contribute to actual sales and shrinkages, respectively, and (2) learning of both inventory levels and shrinkage rate. We first derive the learning formulae using the triple-censored sales data (invisible lost sales, shrinkages and “lost shrinkages”) and then use them to construct a POMDP (Partially Observable Markov Decision Process) model for making inventory and loss prevention decisions. For different levels of information deficiency, we analyze the model property and design heuristic order policies to capture the benefit of learning. Through a numerical study, we show that our estimated shrinkage rate converges quickly and monotonically to the actual value. For products with high shrinkage rates (5% − 12%), our heuristic policy can help seize 82% − 94% of the ideal profit retailers could earn under full information. We note that feature (1) of our model is crucial. It not only reflects the actual arrival order but also allows us to learn the unknown shrinkage rate, which, in turn, can prevent serious under-ordering and vicious inventory cycles and can increase the profit by 108% in some cases. Our approach thus enables both effective inventory management and early identification of ineffective loss prevention strategies, reducing shrinkage and increasing sales and profit.

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Rong Li
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