{"title":"Corrigendum to “Bilevel time minimizing transportation problem” [Discrete Optim.] 5 (4) (2008) 714–723","authors":"Sonia , Ankit Khandelwal","doi":"10.1016/j.disopt.2024.100863","DOIUrl":null,"url":null,"abstract":"<div><div>This is a corrigendum to our research paper titled “Bilevel time minimizing transportation problem” published in 2008. We deeply regret a minor error in the formulation of an intermediate problem solved as part of the algorithm. The intermediate problem, <span><math><msubsup><mrow><mrow><mo>(</mo><mi>T</mi><mi>P</mi><mo>)</mo></mrow></mrow><mrow><mi>t</mi></mrow><mrow><mi>T</mi></mrow></msubsup></math></span>, used to iteratively generate the prospective solution pairs, was initially modeled as a linear programming problem. But the correct formulation of its objective function now involves a binary function, thus making it an NP-hard problem. The algorithm is no longer polynomially bound as it involves solving a finite number of mixed 0-1 programming problems. The manuscript’s original contribution stands correct and there is no change to the structure or the accuracy of the algorithm. The changes required to the original paper, due to this error, are presented in this corrigendum.</div></div>","PeriodicalId":50571,"journal":{"name":"Discrete Optimization","volume":"54 ","pages":"Article 100863"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Optimization","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572528624000422","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This is a corrigendum to our research paper titled “Bilevel time minimizing transportation problem” published in 2008. We deeply regret a minor error in the formulation of an intermediate problem solved as part of the algorithm. The intermediate problem, , used to iteratively generate the prospective solution pairs, was initially modeled as a linear programming problem. But the correct formulation of its objective function now involves a binary function, thus making it an NP-hard problem. The algorithm is no longer polynomially bound as it involves solving a finite number of mixed 0-1 programming problems. The manuscript’s original contribution stands correct and there is no change to the structure or the accuracy of the algorithm. The changes required to the original paper, due to this error, are presented in this corrigendum.
期刊介绍：
Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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