Techniques for finding a list of solutions with increasing costs for the semi-assignment problem

This paper tackles the problem of finding the list of solutions with strictly increasing cost for the Semi-Assignment Problem. Four different algorithms are described and compared. The first two algorithms are based on a mathematical model and on a modification of Murty’s algorithm, which was designed to find the list of solutions for the classical assignment problem. The third approach is a heuristic that quickly finds a list of solutions, but is not guaranteed to find the best possible ones. As the fourth approach, we present a new algorithm based in Murty’s approach, adding symmetry cuts in order to avoid the generation of assignments with the same cost, previously found in the searching tree. The results show that our proposal finds the exact list of solutions, and considerably reduces the computation times in comparison with the other exact approaches.