Discrete Location Problems with Flexible Objectives

Mathematical location theory is one of the most active fields in the area of Operations Research. This importance is on the one hand due to the multitude of interesting structural properties of these problems. On the other hand, mathematical location models have been used for decision support in a large number of practical applications. In most of these applications the set of possible locations is discrete and finite. Therefore, discrete location models should be applied to prepare decisions in such situations. In this book, basic mathematical location problems with a discrete decision space are addressed. The focus lies on problems with a flexible objective function, the so-called ordered median function. With this function, most decision criteria which have been considered in location theory (e.g., pull-, push-, and push-pull-objectives) can be incorporated in a unified approach. Moreover, mathematical models for new objectives (e.g., balancing objectives) become available. Location problems with this flexible objective function are called ordered median problems. Apart from the multitude of decision criteria that can easily be modeled, the main advantage of ordered median problems is that a feasible solution approach/implementation is feasible for all special cases as well. Throughout this work, several mixed-integer linear formulations for basic ordered median problems with and without capacity restrictions are presented. Based on these formulations, solution approaches are developed. The suitability for solving the ordered median problems is tested using extensive computational studies. Furthermore, the ordered median extension of the classical transportation problem is introduced and it is explained how the flexible ordered median function can be applied to different logistics problems (e.g., routing or scheduling problems).