Forecasting Models for Correlated Demand

Demand forecasting is a crucial component of revenue management, as forecasts are almost always inputs into optimization routines for pricing decisions. The performance of many revenue management systems often depends critically on the quality of demand forecasts. Indeed, industry estimates suggest that a 20% reduction of forecast error may lead to 1% incremental increase in revenue (Talluri and van Ryzin, 2004). Most of current research and many practical revenue management systems rely on univariate stochastic models for demand. These usually consist of popular statistical distributions, such as the normal and gamma distributions (McGill and van Ryzin 1999; Lee 1990). However, in practice the available capacity is allocated dynamically between different products and thus is makes sense to take into account the potential correlations among product demand. At the same time, demand for any single product is recorded over the entire booking horizon at fixed time points (snapshots). In this framework it is natural to investigate whether there is correlation among realizations of demand for any individual product in different booking periods. Inter–product and inter–temporal correlations of demand have been documented empirically (McGill 1995). For efficiency reasons, it is therefore important to take them into account in a demand forecasting model. Correlation between demands for different products may arise in several different ways. For instance, in the travel industry some discount fare passengers may have a tendency to upgrade to the full fare if the discount fare is not available, thus giving rise to correlation between discount and full fare