The Traveling Salesman Problem with Draft Limits

  • Authors:

  • Jørgen Glomvik Rakke;Marielle Christiansen;Kjetil Fagerholt;Gilbert Laporte

  • Affiliations:

  • Department of Industrial Economics and Technology Management, The Norwegian University of Science and Technology, Trondheim, Norway;Department of Industrial Economics and Technology Management, The Norwegian University of Science and Technology, Trondheim, Norway;Department of Industrial Economics and Technology Management, The Norwegian University of Science and Technology, Trondheim, Norway;Canada Research Chair in Distribution Management, HEC Montréal, Montréal, Canada H3T 2A7

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2012

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Abstract

In maritime transportation, routing decisions are sometimes affected by draft limits in ports. The draft of a ship is the distance between the waterline and the bottom of the ship and is a function of the load onboard. Draft limits in ports can thus prevent ships to enter these ports fully loaded and may impose a constraint on the sequence of visits made by a ship. This paper introduces the Traveling Salesman Problem with Draft Limits (TSPDL), which is to determine an optimal sequence of port visits under draft limit constraints. We present two mathematical formulations for the TSPDL, and suggest valid inequalities and strengthened bounds. We also introduce a set of instances based on TSPLIB. A branch-and-cut algorithm is applied on both formulations for all these instances. Computational results show that introducing draft limits make the problem much harder to solve. They also indicate that the proposed valid inequalities and strengthened bounds significantly reduce both the number of branch-and-bound nodes and the solution times.