Two-agent scheduling problem under fuzzy environment

The two-agent scheduling problem has a wide range of applications in real world. Although uncertainty is ubiquitous in real world, research of the two-agent scheduling problem under uncertain environment is rare. For applications where historical data is not abundant, investigation of this problem under fuzzy environment is necessary. This paper studies the two-agent scheduling problem under fuzzy environment. We assume that the processing time of each job and the weights that the agents assign to the jobs are fuzzy variables, and focus on the problem where the cost of one agent is the maximum weighted completion time of her jobs and the cost of the other agent is the sum of the weighted completion time of her jobs. Based on three different decision criteria, we present three concepts of schedule and three fuzzy programming models respectively. In order to solve the proposed models, we design a hybrid intelligent algorithm that integrates fuzzy simulation with genetic algorithm. Numerical experiments are given to show the effectiveness of the models and the algorithm.