Multivariate Customer Demand: Modeling and Estimation from Censored Sales

33 Pages Posted: 29 Jan 2009

See all articles by Catalina Stefanescu

Catalina Stefanescu

ESMT European School of Management and Technology

Date Written: January 28, 2009


Demand modeling and forecasting is important for inventory management, retail assortment and revenue management applications. Current practice focuses on univariate demand forecasting, where models are built separately for each product. However, in many industries there is empirical evidence of correlated product demand. In addition, demand is usually observed in several periods during a selling horizon, and it may be truncated due to inventory constraints so that in practice only censored sales data are recorded. Ignoring the inter-product demand correlation or the serial correlation of demand from one selling period to the next leads to biased and inefficient estimates of the true demand distributions. In this paper we propose a class of models for multi-product multiperiod aggregate demand forecasting. We develop an approach for estimating the parameters of the demand models from censored sales data in a maximum likelihood framework using the Expectation-Maximization (EM) algorithm. Through a simulation study, we show that the algorithm is computationally attractive and leads to maximum likelihood estimates with good properties, under different demand and censoring scenarios. We exemplify the methodology with the analysis of two booking data sets from the entertainment and the airline industries, and show that the use of these models in a revenue management setting for airlines increases the revenue by up to 11% relative to the use of alternative demand forecasting methods.

Keywords: Demand estimation, multivariate models, maximum likelihood, EM algorithm, revenue management

Suggested Citation

Stefanescu, Catalina, Multivariate Customer Demand: Modeling and Estimation from Censored Sales (January 28, 2009). Available at SSRN: or

Catalina Stefanescu (Contact Author)

ESMT European School of Management and Technology ( email )

Schlossplatz 1
10117 Berlin

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