OPERATIONS RESEARCH Vol. 63, No. 1, January–February 2015, pp. 134–150 ISSN 0030-364X (print)  ISSN 1526-5463 (online) http://dx.doi.org/10.1287/opre.2014.1326 © 2015 INFORMS Demand Estimation and Ordering Under Censoring: Stock-Out Timing Is (Almost) All You Need Aditya Jain Indian School of Business, Hyderabad 500 032, India, aditya_jain@isb.edu Nils Rudi INSEAD, 138676 Singapore, nils.rudi@insead.edu Tong Wang NUS Business School, National University of Singapore, 119245 Singapore, tong.wang@nus.edu.sg Retailers facing uncertain demand can use observed sales to update demand estimates. However, such learning is limited by the amount of inventory carried; when demand exceeds inventory (i.e., when a stock-out event occurs), a retailer in general cannot observe actual demand. We propose using observations on the timing of sales occurrences in a Bayesian fashion to learn about demand, and we analyze this learning method for a multiperiod newsvendor setting. We find that, as previously shown with the use of only stock-out event observations, the optimal order quantity with timing observations is greater than the optimal order quantity with full demand observations. We prove this result using a novel methodology from the statistics literature on comparison of experiments. Although the optimal over-ordering with timing observations tends to be less than that with only stock-out event observations in most cases, we do observe cases where the opposite is true. Such cases correspond to high demand uncertainty and low margins, where marginal learning from timing observations is significantly higher than using only a stock-out event. In an extensive numerical study we find that, on average and with respect to uncensored demand observations, the use of timing observations eliminates 761% of the loss in expected profit from using only stock-out event observations. We show that, for Poisson and normal demand with unknown mean, the proposed learning method is tractable as well as intuitively appealing: the information contained in the timing of sales occurrences is fully captured by a single number—the timing of stock-out. We also investigate checkpoint models in which the newsvendor can make observations only at predetermined times in a period, and illustrate its convergence to the models with timing and stock-out event observations. Subject classifications : Bayesian inventory; lost sales; censored observations. Area of review : Operations and Supply Chains. History : Received September 2012; revisions received November 2013, May 2014; accepted September 2014. Published online in Articles in Advance December 4, 2014. 1. Introduction and Literature Review With increased product variety, shorter product lifetimes, and longer lead times due to increased levels of global sourcing, managing stock-outs has become a major con- cern for manufacturers and retailers. Not only do stock-outs signify a loss of immediate sales and revenue, they also obscure observations of true demand. Such censoring of demand observations undermines a firm’s ability to improve its demand estimates. Yet, even when a stock-out occurs, additional valuable information is readily available that can be utilized to facilitate better demand estimation. The fol- lowing anecdote, experienced by one of the coauthors, pro- vides an example of such information. The coauthor, accompanied by a senior supply chain man- ager of Yijiaxian (a convenience store chain specializing in fresh food), visited one of the stores in Chengdu, China. During the visit, the manager casually asked a salesper- son to name the store’s best-selling product. The salesper- son pointed toward an empty shelf meant for long beans. Looking surprised, the manager questioned this—according to the daily sales report generated by the firm’s point-of- sale (POS) system, cabbages had consistently outsold long beans. The salesperson clarified that although cabbages also sold well, its sales numbers were larger because of its higher daily stocking levels. In contrast, long beans are stocked in smaller quantities but are sold at a much faster rate; they are usually out of stock within the first few hours of the store opening. This anecdote points out the critical difference between inferences made from observing only aggregate sales (here- after, sales) and observing the occurrence of sales over time. Relying only on sales data, the manager underesti- mated demand for long beans because the demand follow- ing a stock-out is not met and hence not recorded. Yet the salesperson—who observes, in addition, sales over time and the timing of stock-outs—could intuitively use this infor- mation to assess the higher demand levels for long beans. To substantiate this intuition and highlight the value of 134 Downloaded from informs.org by [137.132.123.69] on 21 June 2016, at 20:04 . For personal use only, all rights reserved.