A disjunctive convex programming approach to the pollution-routing problem

Ricardo Fukasawa, Qie He, Yongjia Song

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)61-79
Number of pages19
JournalTransportation Research Part B: Methodological
StatePublished - Dec 1 2016

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Ltd


  • Green transportation
  • Mixed-integer convex programming
  • Pollution-routing problem
  • Speed optimization


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