Multi-objective optimisation models for the travelling salesman problem with horizontal cooperation

This paper considers a horizontal logistics cooperation in which multiple companies jointly solve their logistics optimisation problem. To capture the individual partner interests in the logistics optimisation model, we allow each individual partner to set its own set of objectives. In such a situation, the question arises whether only these individual partner objectives should be considered during the optimisation of the collaborative optimisation problem (the partner efficiency approach), or whether a set of coalition objectives should be defined first (the coalition efficiency approach). This paper investigates the merits and drawbacks of both approaches by applying them to a collaborative variant of the well-known travelling salesman problem with soft time windows (coltspstw). Our results confirm that, even in a situation in which each partner has multiple, possibly conflicting objectives, joining a horizontal logistics coalition can be beneficial for all partners. We further conclude that the coalition efficiency approach is able to find good quality solutions with less calculation time, but lacks robustness. The partner efficiency approach, on the other hand, is able to provide the decision maker with a better Pareto front approximation for the individual partner interest, at the expense of a higher complexity.