An algorithm for the bottleneck generalized assignment problem

The authors discuss a bottleneck (or minimax) version of the generalized assignment problem, known as the task bottleneck generalized assignment problem (TBGAP). TBGAP involves the assignment of a number of jobs to a number of agents such that each job is performed by a unique agent, and capacity limitations on the agents are not exceeded. The objective is to minimize the maximum of the costs of the assignments that are made. The authors present an algorithm for solving TBGAP. The TBGAP algorithm is illustrated by an example and computational experience is reported. The algorithm is seen to be effective in solving TBGAP problems to optimality.