Task preference-based bottleneck assignment problem

The paper discusses a task preference-based bottleneck assignment problem in which there are n tasks that are divided into three phases in order of preference of performance of various tasks. The assignment problem is balanced with an equal number of agents and tasks. An agent can perform only one task and each task can be accomplished by exactly one agent. Tasks belonging to a particular phase cannot be commenced until the tasks of the previous phase have been completed. Given the performance time of each task by each agent, the aim is to find an assignment of agents to the tasks that minimize the total completion time of all tasks. The total completion time here refers to the sum of the overall completion times of three phases. An iterative algorithm for solving such a task preference-based bottleneck assignment problem is proposed in the paper. The proposed algorithm is validated with the help of theoretical results and numerical illustration. The algorithm has been coded in MATLAB and the computational results show that the algorithm performs well in terms of computing time for finding optimal assignments for task preference-based assignment problems of different sizes.