Estimating Primary Demand for Substitutable Products from Sales Transaction Data

We propose a method for estimating substitute and lost demand when only sales and product availability data are observable, not all products are displayed in all periods (e.g., due to stockouts or availability controls), and the seller knows its aggregate market share. The model combines a multinomi...

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Bibliographic Details
Published in:Operations research 2012-03, Vol.60 (2), p.313-334
Main Authors: Vulcano, Gustavo, van Ryzin, Garrett, Ratliff, Richard
Format: Article
Language:English
Subjects:
Airlines
Analysis
Applied sciences
choice behavior
CONTEXTUAL AREAS
Customers
Demand (Economics)
demand estimation
demand untruncation
Economic forecasting
EM method
Estimating techniques
Estimation bias
Estimation methods
Exact sciences and technology
Market potential
Market share
Marketing
Maximum likelihood estimation
Maximum likelihood method
multinomial logit model
Operational research and scientific management
Operational research. Management science
Parametric models
Poisson distribution
Preliminary estimates
Reliability theory. Replacement problems
Studies
Substitute products
Transaction costs
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Summary:We propose a method for estimating substitute and lost demand when only sales and product availability data are observable, not all products are displayed in all periods (e.g., due to stockouts or availability controls), and the seller knows its aggregate market share. The model combines a multinomial logit (MNL) choice model with a nonhomogeneous Poisson model of arrivals over multiple periods. Our key idea is to view the problem in terms of primary (or first-choice) demand; that is, the demand that would have been observed if all products had been available in all periods. We then apply the expectation-maximization (EM) method to this model, and we treat the observed demand as an incomplete observation of primary demand. This leads to an efficient, iterative procedure for estimating the parameters of the model. All limit points of the procedure are provably stationary points of the incomplete data log-likelihood function. Every iteration of the algorithm consists of simple, closed-form calculations. We illustrate the effectiveness of the procedure on simulated data and two industry data sets.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.1110.1012