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

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Author Info

  • Ravi Anupindi

    (J.L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

  • Maqbool Dada

    (Krannert Graduate School of Management, Purdue University, West Lafayette, Indiana 47907)

  • Sachin Gupta

    (J.L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60208)

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    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. We show an application of the model to daily sales and stocking data pooled across multiple beverage vending machines in a midwestern U.S. city. The vending machines in the application carry identical assortments of six brands. Since the number of parameters to be estimated is too large given the available data, we discuss possible restrictions of the consumer choice model to accomplish the estimation. Our results indicate that demand rates estimated naively by using observed sales rates are biased, even for items that have very few occurrences of stock-outs. We also find significant differences among the substitution rates of the six brands. The methods proposed in our paper can be modified to apply to many nonvending retail settings in which consumer choices are observed, not their preferences, and choices are constrained because of unavailability of items in the choice set. One such context is in-store grocery retailing, where similar issues of information availability arise. In this context an important issue that would need to be dealt with is changes in the retail environment caused by retail promotions.

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    File URL: http://dx.doi.org/10.1287/mksc.17.4.406
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    Bibliographic Info

    Article provided by INFORMS in its journal Marketing Science.

    Volume (Year): 17 (1998)
    Issue (Month): 4 ()
    Pages: 406-423

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    Handle: RePEc:inm:ormksc:v:17:y:1998:i:4:p:406-423

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    Related research

    Keywords: Demand Estimation; Maximum Likelihood; Vending; Poisson; Stock-outs; Substitution; EM Algorithm; Inventory Management;

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    Citations

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    Cited by:
    1. Ioannis Ioannou & Julie Holland Mortimer & Richard Mortimer, 2008. "The Effects of Capacity on Sales Under Alternative Vertical Contracts," NBER Working Papers 14611, National Bureau of Economic Research, Inc.
    2. Vaagen, Hajnalka & Wallace, Stein W. & Kaut, Michal, 2011. "Modelling consumer-directed substitution," International Journal of Production Economics, Elsevier, vol. 134(2), pages 388-397, December.
    3. Christopher T. Conlon & Julie Holland Mortimer, 2010. "Demand Estimation Under Incomplete Product Availability," Boston College Working Papers in Economics 799, Boston College Department of Economics, revised 07 Aug 2012.
    4. Bayle-Tourtoulou, Anne-Sophie & Laurent, Gilles & Macé, Sandrine, 2006. "Assesing the frequency and clauses of out-of-stock events through store scanner data," Les Cahiers de Recherche 830, HEC Paris.
    5. Rajaram, Kumar & Tang, Christopher S., 2001. "The impact of product substitution on retail merchandising," European Journal of Operational Research, Elsevier, vol. 135(3), pages 582-601, December.
    6. Yang, Hongsuk & Schrage, Linus, 2009. "Conditions that cause risk pooling to increase inventory," European Journal of Operational Research, Elsevier, vol. 192(3), pages 837-851, February.

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