{"title":"Randomized Assortment Optimization","authors":"Zhengchao Wang, Heikki Peura, Wolfram Wiesemann","doi":"10.1287/opre.2022.0129","DOIUrl":null,"url":null,"abstract":"<p>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 paper, we introduce the concept of <i>randomization</i> 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.</p><p><b>Funding:</b> Z. Wang acknowledges funding from the Imperial College President’s PhD Scholarship programme. W. Wiesemann acknowledges funding from the Engineering and Physical Sciences Research Council [Grants EP/R045518/1, EP/T024712/1, and EP/W003317/1].</p><p><b>Supplemental Material:</b> The online appendix is available at https://doi.org/10.1287/opre.2022.0129.</p>","PeriodicalId":54680,"journal":{"name":"Operations Research","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research","FirstCategoryId":"91","ListUrlMain":"https://doi.org/10.1287/opre.2022.0129","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MANAGEMENT","Score":null,"Total":0}
引用次数: 0
Abstract
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 paper, 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.
Funding: Z. Wang acknowledges funding from the Imperial College President’s PhD Scholarship programme. W. Wiesemann acknowledges funding from the Engineering and Physical Sciences Research Council [Grants EP/R045518/1, EP/T024712/1, and EP/W003317/1].
Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0129.
期刊介绍:
Operations Research publishes quality operations research and management science works of interest to the OR practitioner and researcher in three substantive categories: methods, data-based operational science, and the practice of OR. The journal seeks papers reporting underlying data-based principles of operational science, observations and modeling of operating systems, contributions to the methods and models of OR, case histories of applications, review articles, and discussions of the administrative environment, history, policy, practice, future, and arenas of application of operations research.