{"title":"On the feasibility of solutions to the split delivery vehicle routing problem represented as edge variables","authors":"Artur Pessoa, Daniel de Araujo, Eduardo Uchoa","doi":"10.1016/j.orl.2024.107209","DOIUrl":null,"url":null,"abstract":"<div><div>Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an <span><math><mi>O</mi><mo>(</mo><mi>n</mi><mi>log</mi><mo></mo><mi>n</mi><mo>)</mo></math></span>-time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.</div></div>","PeriodicalId":54682,"journal":{"name":"Operations Research Letters","volume":"58 ","pages":"Article 107209"},"PeriodicalIF":0.9000,"publicationDate":"2025-01-01","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/S0167637724001457","RegionNum":4,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/11/19 0:00:00","PubModel":"Epub","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Mixed integer programming formulations for the Split Delivery Vehicle Routing Problem (SDVRP) typically use edge decision variables. It was believed that feasibility couldn't be verified in polynomial time. We show that this recognition problem depends on the formulation's constraints and prove that it's strongly NP-hard for a recent formulation. With subtour elimination constraints, we provide an -time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.
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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