Tractable Consideration Set Structures for Assortment Optimization and Network Revenue Management

Production and Operations Management · 2017 · Volume 26 · Issue 7

Abstract

Discrete-choice models are widely used to model consumer purchase behavior in assortment optimization and revenue management. In many applications, each customer segment is associated with a consideration set that represents the set of products that customers in this segment consider for purchase. The firm has to make a decision on what assortment to offer at each point in time without the ability to identify the customer's segment. A linear program called the Choice-based Deterministic Linear Program (CDLP) has been proposed to determine these offer sets. Unfortunately, its size grows exponentially in the number of products and it is NP-hard to solve when the consideration sets of the segments overlap. The Segment-based Deterministic Concave Program with some additional consistency equalities (SDCP+) is an approximation ofCDLPthat provides an upper bound onCDLP's optimal objective value.SDCP+ can be solved in a fraction of the time required to solveCDLPand often achieves the same optimal objective value. This raises the question under what conditions can one guarantee equivalence ofCDLPandSDCP+. In this study, we obtain a structural result to this end, namely that if the segment consideration sets overlap with a certain tree structure or if they are fully nested,CDLPcan be equivalently replaced withSDCP+. We give a number of examples from the literature where this tree structure arises naturally in modeling customer behavior.

Keywords

discrete choice models, assortment optimization, network revenue management, consideration sets

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