An improved algorithm for the bilateral assignment problem

We are concerned with a variation of the assignment problem, where the assignment costs differ between assigners and assignees. We formulate this as a min-max optimization problem, present a surrogate relaxation approach to derive lower and upper bounds quickly, and show that the pegging test can be successfully applied to this problem. Next, we make use of the special structure of the assignment problem to shorten the computation time for pegging significantly. Finally, through numerical experiments we show that the developed method solves larger instances to optimality faster than conventional methods.