A lexicographic approach for solving bi-criteria bottleneck assignment problems

The suitability of agents for tasks and ranked preference of tasks for agents play a significant role in problems where several agents are available to perform various tasks. The agents should be allocated to various tasks so that the corresponding assignment schedules must provide solution points on the Pareto front in the criteria space of the problem. This study discusses a bi-objective assignment problem of this kind, related to positioning players in a sports ground, and an algorithm based on a lexicographic technique is developed to solve this problem. The two objectives of the problem are to maximize the minimum suitability of players among positions and to minimize the maximum rank of positions among players, simultaneously. The proposed algorithm efficiently finds all the Pareto-optimal/non-dominated assignment schedules and hence, the solution points of the problem. This is an improved algorithm than the one available in the literature for this problem. A numerical example demonstrates the applicability of the proposed algorithm and shows less computational complexity than an existing algorithm.