Estimation of Consumer Demand with Stock-Out Based Substitution: An Application to Vending Machine Products

Anupindi, Ravi; Dada, Maqbool; Gupta, Sachin
December 1998
Marketing Science;1998, Vol. 17 Issue 4, p406
Academic Journal
Abstract The occurrence of temporary stock-outs at retail is common in frequently purchased product categories. Available empirical evidence suggests that when faced with stock-outs, consumers are often willing to buy substitute items. An important implication of this consumer behavior is that observed sales of an item no longer provide a good measure of its core demand rate. Sales of items that stock-out are right-censored, while sales of other items are inflated because of substitutions. Knowledge of the true demand rates and substitution rates is important for the retailer for a variety of category management decisions such as the ideal assortment to carry, how much to stock of each item, and how often to replenish the stock. The estimated substitution rates can also be used to infer patterns of competition between items in the category. In this paper we propose methods to estimate demand rates and substitution rates in such contexts.We develop a model of customer arrivals and choice between goods that explicitly allows for possible product substitution and lost sales when a customer faces a stock-out. The model is developed in the context of retail vending, an industry that accounts for a sizable part of the retail sales of many consumer products. We consider the information set available from two kinds of inventory tracking systems. In the best case scenario of a perpetual inventory system in which times of stock-out occurrence and cumulative sales of all goods up to these times are observed, we derive Maximum Likelihood Estimates (MLEs) of the demand parameters and show that they are especially simple and intuitive.However, state-of-the-art inventory systems in retail vending provide only periodic data, i.e., data in which times of stock-out occurrence are unobserved or "missing." For these data we show how the Expectation-Maximization (EM) algorithm can be employed to obtain the MLEs of the demand parameters by treating the stock-out times as missing data....


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