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Exact and Compact Formulation of the Fixed-Destination Travelling Salesman Problem by Cycle Imposement Through Node Currents

In: Operations Research Proceedings 2013

Author

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  • Mernout Burger

    (Delft University of Technology)

Abstract

The Travelling Salesman Problem (TSP) has been studied extensively for over half a century, but due to its property of being at the basis of many scheduling and routing problems it still attracts the attention of many research. One variation of the standard TSP is the multi-depot travelling salesman problem (MTSP) where the salesmen can start from and return to several distinct locations. This article focusses on the MTSP with the extra restriction that each salesman should return to his home depot, known as the fixed-destination MTSP. This problem (and its variations such as the multi-depot vehicle routing problem) is usually formulated using three-index binary variables, making the problem computationally expensive to solve. Here an alternative formulation is presented using two-index binary variables through the introduction of a limited amount of continuous variables to ensure the return of the salesmen to their home depots.

Suggested Citation

  • Mernout Burger, 2014. "Exact and Compact Formulation of the Fixed-Destination Travelling Salesman Problem by Cycle Imposement Through Node Currents," Operations Research Proceedings, in: Dennis Huisman & Ilse Louwerse & Albert P.M. Wagelmans (ed.), Operations Research Proceedings 2013, edition 127, pages 83-88, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-07001-8_12
    DOI: 10.1007/978-3-319-07001-8_12
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    Cited by:

    1. Burger, M. & Su, Z. & De Schutter, B., 2018. "A node current-based 2-index formulation for the fixed-destination multi-depot travelling salesman problem," European Journal of Operational Research, Elsevier, vol. 265(2), pages 463-477.

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