Consideration of multiple objectives in horizontal cooperation with an application to transportation planning

This article contributes to the interface between mathematical programming and (cooperative) game theory. Using the well-known traveling salesman problem as a basis, we discuss situations where multiple players cooperate, which leads to a multi-objective optimization problem. The important issue that is new is that not only individual objectives of the players are considered but also a joint objective. Hence, a sharing problem is created, which must somehow be integrated into multi-objective optimization. From a game-theoretic view, we thus face a cooperative game with non-transferable, as well as transferable, utilities. This is an innovative problem setting, for which we propose a solution procedure. To succeed, we extend knowledge from cooperative game theory and propose a concept based on the core to tackle the sharing problem when non-transferable, as well as transferable, utilities are present. As a result, we obtain a mathematical programming–based procedure that solves the multi-objective optimization problem and computes fair shares. Similar settings may occur in a universe of applications, and the presented ideas may be adapted for those situations.