Logic-Based Decomposition Methods for the Travelling Purchaser Problem

  • Kyle E. C. Booth
  • Tony T. Tran
  • J. Christopher Beck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9676)

Abstract

We present novel branch-and-check and logic-based Benders decomposition techniques for the Travelling Purchaser Problem, an important optimization problem with applications in vehicle routing, logistics, and warehouse management. Our master problem determines a set of markets and directed travel arcs that satisfy product purchase constraints with relaxed travel costs. Our subproblem identifies subtours within this master assignment and produces a set of generalized subtour elimination cuts. We show that the proposed technique demonstrates strong performance on the asymmetric problem variants, finding optimal solutions to previously unsolved instances, while performing competitively on a number of symmetric problem classes. Furthermore, our model is implemented unchanged for the four problem variants whereas other state-of-the-art approaches are variant-specific.

Keywords

Travelling Salesman Problem Master Problem Valid Inequality Uncapacitated Facility Location Problem Subtour Elimination Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Kyle E. C. Booth
    • 1
  • Tony T. Tran
    • 1
  • J. Christopher Beck
    • 1
  1. 1.Department of Mechanical and Industrial EngineeringUniversity of TorontoTorontoCanada

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