Discrete optimization: An Austrian view

After studying mathematics at the universities in Graz and Vienna and writing a PhD thesis in the field of uniform distribution of sequences (a subarea of analytical number theory), guided by Professor Edmund Hlawka at the university of Vienna, I became assistant at the Institute of Applied Mathematics of the Karl-Franzens University in Graz. The former head of this Institute, Professor Rudolf Albrecht, asked me to prepare classroom notes for the new field of integer programming. These notes were the basis for the first German book on Integer Programming (Burkard, 1972) which was published by Springer in Vienna. During the bibliographical search for these notes I came across the quadratic assignment problem (QAP) which fascinated me from the beginning. The QAP is a location model: let ai j denote the distances between possible sites for buildings and let bkl denote the flow between the buildings (e.g. the estimated number of persons which go weekly from an office building to a canteen). The classic Koopmans-Beckmann problem asks to minimize the total traffic. So we have to find a permutation φ of the index set {1, 2, . . . , n} such that