Time: 1:00pm Friday, 4th of December.
Location: SIT 459
Speaker: Gerardo Berbeglia, Uni Melbourne
Title: Revenue optimisation under a general discrete choice model: A tight analysis of revenue ordered assortmentsAbstract:
A central problem in revenue management, known as the assortment problem, consists in deciding which subset of products to offer to consumers in order to maximise revenue. A simple algorithm is to select the best assortment out of all those that are constructed by fixing a threshold revenue r and then choosing all products with revenue at least r. This is known as the revenue-ordered assortments strategy. We provide a precise analysis of how well revenue-ordered assortments approximate the optimum revenue when customers are rational in the following sense: the probability of selecting a specific product from the set being offered cannot increase if the offer set is enlarged. The corresponding discrete choice models form a broad class of models which includes all discrete choice models based on random utility. Our analysis of revenue-ordered assortments match and unify known results for certain models, and improves the best known results for others, suc! h as for the Mixed Multinomial Logit model recently studied by Rusmevichientong et al (2014). An appealing feature of our analysis is that it is simple and relies only on the above-mentioned rationality property, and yet it is best possible even for very specific models within the class. We then show that a large class of problems known as envy-free pricing problems can be seen as assortment problems for a specifically constructed discrete choice model that satisfies the rationality property. In this context, revenue-ordered assortments turn out to be equivalent to the well-studied uniform pricing algorithm.
This is joint work with Gwenaël Joret