The robust vehicle routing problem with time windows

  • Authors:

  • Agostinho Agra;Marielle Christiansen;Rosa Figueiredo;Lars Magnus Hvattum;Michael Poss;Cristina Requejo

  • Affiliations:

  • CIDMA, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;CIDMA, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal;Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway;CMUC, Department of Mathematics, University of Coimbra, 3001-454 Coimbra, Portugal and UMR CNRS 7253 Heudiasyc, Université de Technologie de Compiègne, Centre de Recherches de Royallieu, ...;CIDMA, Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2013

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Abstract

This paper addresses the robust vehicle routing problem with time windows. We are motivated by a problem that arises in maritime transportation where delays are frequent and should be taken into account. Our model only allows routes that are feasible for all values of the travel times in a predetermined uncertainty polytope, which yields a robust optimization problem. We propose two new formulations for the robust problem, each based on a different robust approach. The first formulation extends the well-known resource inequalities formulation by employing adjustable robust optimization. We propose two techniques, which, using the structure of the problem, allow to reduce significantly the number of extreme points of the uncertainty polytope. The second formulation generalizes a path inequalities formulation to the uncertain context. The uncertainty appears implicitly in this formulation, so that we develop a new cutting plane technique for robust combinatorial optimization problems with complicated constraints. In particular, efficient separation procedures are discussed. We compare the two formulations on a test bed composed of maritime transportation instances. These results show that the solution times are similar for both formulations while being significantly faster than the solutions times of a layered formulation recently proposed for the problem.