{"title":"Assortment optimization under the multinomial logit choice model with product-specific capacities","authors":"Woonghee Tim Huh , Siyue Liu","doi":"10.1016/j.orl.2024.107238","DOIUrl":null,"url":null,"abstract":"<div><div>We consider assortment optimization with product-specific capacities under the multinomial logit (MNL) choice model, wherein each product has a finite capacity, i.e., a limited number of units for sale. The number of customers served by each product is the smaller of its demand and capacity. We assume the demand of each product is deterministic as a function of the assortment offered. We show that this assortment optimization problem is NP-hard. We devise a 1/2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) by exploiting its connection to a series of knapsack problems.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107238"},"PeriodicalIF":0.8000,"publicationDate":"2025-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research Letters","FirstCategoryId":"91","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167637724001743","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We consider assortment optimization with product-specific capacities under the multinomial logit (MNL) choice model, wherein each product has a finite capacity, i.e., a limited number of units for sale. The number of customers served by each product is the smaller of its demand and capacity. We assume the demand of each product is deterministic as a function of the assortment offered. We show that this assortment optimization problem is NP-hard. We devise a 1/2-approximation algorithm and a fully polynomial-time approximation scheme (FPTAS) by exploiting its connection to a series of knapsack problems.
期刊介绍：
Operations Research Letters is committed to the rapid review and fast publication of short articles on all aspects of operations research and analytics. Apart from a limitation to eight journal pages, quality, originality, relevance and clarity are the only criteria for selecting the papers to be published. ORL covers the broad field of optimization, stochastic models and game theory. Specific areas of interest include networks, routing, location, queueing, scheduling, inventory, reliability, and financial engineering. We wish to explore interfaces with other fields such as life sciences and health care, artificial intelligence and machine learning, energy distribution, and computational social sciences and humanities. Our traditional strength is in methodology, including theory, modelling, algorithms and computational studies. We also welcome novel applications and concise literature reviews.
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