On the feasibility of solutions to the split delivery vehicle routing problem represented as edge variables

IF 0.8 4区管理学 Q4 OPERATIONS RESEARCH & MANAGEMENT SCIENCE

Operations Research Letters Pub Date : 2025-01-01 DOI:10.1016/j.orl.2024.107209

Artur Pessoa, Daniel de Araujo, Eduardo Uchoa

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

O (n \log n)

-time recognition algorithm. This challenges assumptions about edge-based formulations and provides new insights into SDVRP solution verification complexity.

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研究了以边缘变量表示的分割配送车辆路径问题解的可行性

分割配送车辆路径问题（SDVRP）的混合整数规划公式通常使用边缘决策变量。认为在多项式时间内无法验证该方法的可行性。我们证明了这个识别问题依赖于公式的约束，并证明了它对于最近的公式是强np困难的。在子游消去约束下，我们提供了一种O（nlog ln n）时间的识别算法。这挑战了关于基于边缘的公式的假设，并提供了对SDVRP解决方案验证复杂性的新见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Operations Research Letters 管理科学-运筹学与管理科学

CiteScore

2.10

自引率

9.10%

发文量

111

审稿时长

83 days

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.