A Feasible Flow-based Algorithm for Solving Classic Assignment Problem with Bottleneck

Abstract

Classic assignment problem with bottleneck is a fundamental combinatorial optimization problem with numerous practical applications in diverse domains. In order to comprehensively explore the classic assignment problem with bottleneck and to develop efficient algorithm, a feasible flow-based algorithm is proposed for optimizing classic assignment problem with bottleneck. The bottleneck constraints are addressed by updating the bottleneck of the problem, and a feasible-flow approach is leveraged to efficiently identify optimal solutions within the network framework associated with such problems. To assess the effectiveness of our proposed algorithm, a comprehensive set of numerical experiments is carried out across various instances of classic assignment problem with bottleneck. Our numerical results demonstrate the superior performance of our algorithm, particularly when applied to problems with smaller cost scales, making it particularly suitable for addressing medium-sized to smaller-scale problems.