Randomized Assortment Optimization
– Free seminar
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Tel: +352 46 66 44 6283
When a firm selects an assortment of products to offer to customers, it uses a choice model to anticipate their probability of purchasing each product. In practice, the estimation of these models is subject to statistical errors, which may lead to significantly suboptimal assortment decisions. Recent work has addressed this issue using robust optimization, where the true parameter values are assumed unknown and the firm chooses an assortment that maximizes its worst-case expected revenues over an uncertainty set of likely parameter values, thus mitigating estimation errors. In this talk, we introduce the concept of randomization into the robust assortment optimization literature. We show that the standard approach of deterministically selecting a single assortment to offer is not always optimal in the robust assortment optimization problem. Instead, the firm can improve its worst-case expected revenues by selecting an assortment randomly according to a prudently designed probability distribution. We demonstrate this potential benefit of randomization both theoretically in an abstract problem formulation as well as empirically across three popular choice models: the multinomial logit model, the Markov chain model, and the preference ranking model. We show how an optimal randomization strategy can be determined exactly and heuristically. Besides the superior in-sample performance of randomized assortments, we demonstrate improved out-of-sample performance in a data- driven setting that combines estimation with optimization. Our results suggest that more general versions of the assortment optimization problem—incorporating business constraints, more flexible choice models and/or more general uncertainty sets—tend to be more receptive to the benefits of randomization.
About Wolfram Wiesemann:
Wolfram Wiesemann is Professor of Analytics & Operations as well as the head of the Analytics, Marketing & Operations department at Imperial College Business School. His research interests evolve around decision-making under uncertainty, with applications to supply chain management, healthcare and energy. Wolfram is an elected member of the boards of the Mathematical Optimization Society and the Stochastic Programming Society, and he serves as an area editor for Operations Research Letters as well as an associate editor for Mathematical Programming, Operations Research, Manufacturing & Service Operations Management and SIAM Journal on Optimization.
Supported by the Luxembourg National Research Fund (FNR) 17931929