Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection

Abstract

We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.

Keywords:

• tour planning
• Travelling Salesman Problem
• Travelling Salesman Problem with Multiple Time Windows
• Travelling Salesman Problem with Hotel Selection

Acknowledgements

This work and the corresponding software originated in a cooperation project ‘Design of Efficient Algorithms for Region and Tour Planning in Traffic Networks’ with the company FLS (http://www.fls-service.de/Eng/) located in Germany. We would like to thank our cooperation partner FLS for introducing us to the practical requirements of tour planning and transmitting several real world instances. This cooperation project was supported by ‘Innovationsstiftung Schleswig-Holstein’.

Notes

1 http://www.informatik.uni-kiel.de/~vsa/tsptw.html.