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 focuses on transportation, logistics and supply chain management, and many problems in this area can be modeled as mixed-integer linear programs. Although these problems can often be formulated comparatively easily, they are 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 of these solutions 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.
Additional information about the research project is available here: