Pareto Optimal Solutions of the Minimal Cost Minimal Time Assignment Problem

We propose an exact algorithm for calculation of a list of all Pareto optimal solutions of a biobjective assignment problem (AP) with a linear objective function (representing a cost criterion) and a non-linear bottleneck objective function (representing a time criterion). The method, along with all needed helper functions for its implementation, is described in details. We provide comprehensive examples that illustrate the results, and a graphical illustration of the presented algorithm that also gives a geometrical proof of the method. The correctness of the algorithms is proved, and their compu-tational complexity is shown. The presented algorithms can be adopted to solve the other standard biobjective AP with the first function being a linear one, and the second function being from the bottleneck type.