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A disjunctive convex programming approach to the pollution-routing problem

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  • Fukasawa, Ricardo
  • He, Qie
  • Song, Yongjia

Abstract

The pollution-routing problem (PRP) aims to determine a set of routes and speed over each leg of the routes simultaneously to minimize the total operational and environmental costs. A common approach to solve the PRP exactly is through speed discretization, i.e., assuming that speed over each arc is chosen from a prescribed set of values. In this paper, we keep speed as a continuous decision variable within an interval and propose new formulations for the PRP. In particular, we build two mixed-integer convex optimization models for the PRP, by employing tools from disjunctive convex programming. These are the first arc-based formulations for the PRP with continuous speed. We also derive several families of valid inequalities to further strengthen both models. We test the proposed formulations on benchmark instances. Some instances are solved to optimality for the first time.

Suggested Citation

  • Fukasawa, Ricardo & He, Qie & Song, Yongjia, 2016. "A disjunctive convex programming approach to the pollution-routing problem," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 61-79.
    • Handle: RePEc:eee:transb:v:94:y:2016:i:c:p:61-79
    DOI: 10.1016/j.trb.2016.09.006
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    2. Ehmke, Jan Fabian & Campbell, Ann M. & Thomas, Barrett W., 2018. "Optimizing for total costs in vehicle routing in urban areas," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 116(C), pages 242-265.
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    8. Mohammad Asghari & Seyed Mohammad Javad Mirzapour Al-E-Hashem, 2021. "Green vehicle routing problem: A state-of-the-art review," Post-Print hal-03182944, HAL.
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    14. Xiao, Yiyong & Zuo, Xiaorong & Huang, Jiaoying & Konak, Abdullah & Xu, Yuchun, 2020. "The continuous pollution routing problem," Applied Mathematics and Computation, Elsevier, vol. 387(C).
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