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

ABSTRACT

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.

KEYWORDS:

• Horizontal cooperation
• cooperative game theory
• bi-allocation games
• multi-objective optimization
• core
• Traveling Salesman Problem

Additional information

Notes on contributors

Alf Kimms

Alf Kimms is a full professor for logistics and operations research at the Mercator School of Management, University of Duisburg–Essen. He graduated from the University of Kiel. His research interests include operations research, cooperative game theory, supply chain planning, revenue management, logistics, and production planning. He has published a large number of papers in high-ranked international journals. Currently, he is the president of the German OR society.

Igor Kozeletskyi

Igor Kozeletskyi received his master’s and Ph.D. in business administration from the Mercator School of Management, University of Duisburg–Essen. Currently, he works at Hermes, an international logistics service provider.