MOMIP: Multi-Objective Mixed Integer Programming

We live in a world full of trade-offs and quite often we only know comparably little about them. In almost every problem situation we encounter it is difficult to define the one and only goal to aim for, especially whenever more than one decision maker or stakeholder is involved. Thus, many if not all practical problems involve several and often conflicting objectives. Prominent examples are environmental concerns versus cost or customer satisfaction versus profitability.  Our research is mainly rooted in the fields of transportation, logistics, and supply chain management and many relevant problems arising in these fields can be modeled as mixed integer linear programs. Despite the fact that these problems are often comparably easy to formulate they are quite often very difficult to solve. In addition, whenever multiple conflicting objectives are of concern, it is usually not possible to identify one best solution with respect to all of the considered goals. Rather, a set of optimal compromise solutions exists which are “better” than the other possible solutions and incomparable among each other. Each such solution represents a possible trade-off. The computation of this set of optimal trade-off solutions is a complex task. All currently available exact methods have limitations. Either they are only applicable to problems with at most two objectives or they cannot describe the complete set of trade-off solutions. The kernel of this project is the development of efficient generic algorithms, using the branch-and-bound idea in a way that allows to exploit the multi-objective nature of the considered problems, and thus to close this gap for mixed integer linear programs with up to three objectives. In order to illustrate the applicability of our algorithms, we will use them to solve practical problems arising in sustainable supply chain management, disaster relief distribution planning and green vehicle routing.