Improved formulations and algorithmic components for the electric vehicle routing problem with nonlinear charging functions

Aurélien Froger, Jorge E. Mendoza, Ola Jabali, Gilbert Laporte

Research output: Contribution to journalArticlepeer-review

133 Citations (SciVal)


Electric vehicle routing problems (E-VRPs) are receiving growing attention from the operations research community. Electric vehicles differ substantially from internal combustion engine vehicles, the main difference lying in their limited autonomy, which can be recovered at charging stations. Modeling the charging functions is a focal point of E-VRPs. Most of the research has focused on constant or linear charging functions. The E-VRP with nonlinear charging function (E-VRP-NL) was recently introduced to account for the more realistic nonlinear relationship between the time spent charging and the amount of energy charged. We propose two new formulations for this problem. We first develop an arc-based tracking of the time and the state of charge which, according to our experiments, outperforms the classical node-based tracking of these values. To avoid replicating the charging stations nodes, as done for both node and arc based formulations, we also introduce a path-based model. We develop an algorithm to generate a tractable number of these paths. This path-based model outperforms the classical models in our experiments. We also propose a new model, a heuristic, and an exact labeling algorithm for the problem of finding the optimal charging decisions for a given route. Extensive computational results show that charging decisions considerably impact the quality of the E-VRP-NL solutions. Indeed, we improve 23 out of 120 best known E-VRP-NL solutions by solely revising the charging decisions.

Original languageEnglish
Pages (from-to)256-294
Number of pages39
JournalComputers and Operations Research
Publication statusPublished - Apr 2019


  • Electric vehicle routing problem with nonlinear charging function
  • Labeling algorithm
  • Mixed integer linear programming
  • Vehicle routing problem

ASJC Scopus subject areas

  • General Computer Science
  • Modelling and Simulation
  • Management Science and Operations Research


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