A robust location-arc routing problem under uncertainty: mathematical model with lower and upper bounds
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A robust location-arc routing problem under uncertainty: mathematical model with lower and upper bounds Alireza Amini1 · Reza Tavakkoli-Moghaddam2
· Sadoullah Ebrahimnejad3
Received: 18 May 2020 / Revised: 25 September 2020 / Accepted: 1 October 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract This paper deals with a robust location-arc routing problem with uncertainty on demand and traversing cost parameters. In this regard, a deterministic mathematical model is presented inspired by those available in the related literature and then, a robust optimization approach is used to deal with uncertainty. Due to the complexity of the deterministic and uncertain mathematical models, this paper finds the lower and upper bounds of the solutions to estimate a suitable range in which the optimum values exist. The lower and upper bounds are obtained by modifying the developed mathematical models and developing a two-phase heuristic algorithm, respectively. Furthermore, three single-solution-based meta-heuristics, called hill climbing, late acceptance hill climbing, and Tabu search are employed to enhance the upper bounds. According to the robust optimization approach, the paper on hand proposes a manual sorting method to approximate the value of uncertain parameters to be used in the heuristics and meta-heuristics. Finally, the paper evaluates the models, manually sorting method, heuristic, and meta-heuristic algorithms using some numerical examples and finds that all of them works appropriately. Keywords Location-arc routing · Mathematical model · Lower and upper bounds · Robust optimization · Heuristic Mathematics Subject Classification 90-08 · 90B80 · 90C11 · 90C17 · 90C59
1 Introduction So far, many studies have been conducted by lots of researchers to study the problem of supplying customer demands and many approaches have been proposed to route demand
Communicated by Gabriel Haeser.
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Reza Tavakkoli-Moghaddam [email protected]
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School of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran
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School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran
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Department of Industrial Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran 0123456789().: V,-vol
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nodes for this purpose. Enhanced transportation and routing systems can lead to reduced unnecessary distances and improved paths. Also, these can help to optimize the traveled routes within each supply chain. One of the important problems in this field is a vehicle routing problem (VRP) so that a huge cost reduction can be obtained by assigning customers to the routes optimally. In this regard, many VRP models have been employed to reduce supply costs. Generally, a VRP model consists of a warehouse, the vehicles being used in the warehouse, and customers. The studies conducted in this area have had different objectives; some addressed one objective and some multiple ones. The researchers developed more comp
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