The robust vehicle routing problem with time windows: Compact formulation and branch-price-and-cut method

Pedro Munari, Alfredo Moreno, Jonathan De La Vega, Douglas Alem, Jacek Gondzio, Reinaldo Morabito

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods.Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods for solving many variants of vehicle routing problems are based on the column generation technique, the RVRPTW has never been addressed by this type of method. In this paper,we introduce a novel robust counterpart model based on the well-known budgeted uncertainty set, which has advantageous features in comparison to other formulations and presents better overall performance when solved by commercial solvers. This model results from incorporating dynamic programming recursive equations into a standard deterministic formulation and does not require the classical dualization scheme typically used in robust optimization. In addition, we propose a branch-price-and-cut method based on a set partitioning formulation of the problem, which relies on a robust resource constrained elementary shortest path problem to generate routes that are robust regarding both vehicle capacity and customer time windows. Computational experiments using Solomons’s instances show that the proposed approach is effective and able to obtain robust solutions within a reasonable running time. The results of an extensive Monte Carlo simulation indicate the relevance of obtaining robust routes for a more reliable decision-making process in real-life settings.
Original languageEnglish
Pages (from-to)917-1212
JournalTransportation Science
Issue number4
Early online date24 Jun 2019
Publication statusPublished - Jul 2019

Keywords / Materials (for Non-textual outputs)

  • vehicle routing
  • time windows
  • robust optimization
  • polyhedral-interval uncertainty
  • compact model
  • branch-price-and-cut


Dive into the research topics of 'The robust vehicle routing problem with time windows: Compact formulation and branch-price-and-cut method'. Together they form a unique fingerprint.

Cite this