{"title":"The inverse optimal value problem for linear fractional programming","authors":"Sina Nadi , Taewoo Lee , Oleg A. Prokopyev","doi":"10.1016/j.orl.2025.107251","DOIUrl":null,"url":null,"abstract":"<div><div>We study the inverse optimal value problem for linear fractional programming, where the goal is to find the coefficients of the fractional objective function such that the resulting optimal objective function value is as close as possible to some given target value. We show that this problem is <em>NP</em>-hard. Then, we provide some structural results, which are exploited to derive several reformulations and two solution algorithms. The proposed approaches are based on the Charnes-Cooper and parametric transformations.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"59 ","pages":"Article 107251"},"PeriodicalIF":0.9000,"publicationDate":"2025-03-01","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/S0167637725000124","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/1/31 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
We study the inverse optimal value problem for linear fractional programming, where the goal is to find the coefficients of the fractional objective function such that the resulting optimal objective function value is as close as possible to some given target value. We show that this problem is NP-hard. Then, we provide some structural results, which are exploited to derive several reformulations and two solution algorithms. The proposed approaches are based on the Charnes-Cooper and parametric transformations.
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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