{"title":"Unary NP-hardness of transportation and batching scheduling to minimize the total weighted completion time","authors":"Hongjun Wei, Yuan Gao, Jinjiang Yuan","doi":"10.1016/j.dam.2025.02.023","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we study the coordination of transportation and batching scheduling with one single vehicle to minimize the total weighted completion time. When the batch capacity is 2, the computational complexity of this problem has been reported open in the literature. We show in this paper that the problem is unary NP-hard.</div></div>","PeriodicalId":50573,"journal":{"name":"Discrete Applied Mathematics","volume":"369 ","pages":"Pages 45-52"},"PeriodicalIF":1.0000,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166218X2500099X","RegionNum":3,"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
In this paper, we study the coordination of transportation and batching scheduling with one single vehicle to minimize the total weighted completion time. When the batch capacity is 2, the computational complexity of this problem has been reported open in the literature. We show in this paper that the problem is unary NP-hard.
期刊介绍：
The aim of Discrete Applied Mathematics is to bring together research papers in different areas of algorithmic and applicable discrete mathematics as well as applications of combinatorial mathematics to informatics and various areas of science and technology. Contributions presented to the journal can be research papers, short notes, surveys, and possibly research problems. The "Communications" section will be devoted to the fastest possible publication of recent research results that are checked and recommended for publication by a member of the Editorial Board. The journal will also publish a limited number of book announcements as well as proceedings of conferences. These proceedings will be fully refereed and adhere to the normal standards of the journal.
Potential authors are advised to view the journal and the open calls-for-papers of special issues before submitting their manuscripts. Only high-quality, original work that is within the scope of the journal or the targeted special issue will be considered.
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