Uncertain Programming Model For Machine Scheduling Problem

Machine scheduling problem is a hot spot in the feld of operational research. It iswidely applied in the feld of mathematics, system engineering and automatic manage-ment. The processing times are considered as random variables in traditional models.For lack of enough statistical data, some researchers suppose that the processing timesare fuzzy variables. However, fuzzy set theory can hardly explain many subjective un-certain phenomena. In order to deal with the subjective uncertain phenomena better,Liu proposed uncertainty theory and applied it to scheduling problem.The processing times are assumed to be uncertain variables with known uncer-tainty distributions in this paper. Generally speaking, there are two important objectivesin machine scheduling problem including the makespan and the maximum tardiness.The two objectives are integrated into one objective function in this paper.First, a satisfaction-maximization model is proposed within the framework of un-certainty theory. Furthermore, a hybrid intelligent algorithm is designed by integratinginverse uncertainty distribution method and genetic algorithm for solving the uncer-tain programming model. Finally, some numerical example is presented to show theefectiveness of the proposed model and algorithm.The main innovations of this paper are listed as follows,1. A model is proposed by considering the makespan and the maximum tardinessare optimized simultaneously under uncertainty;2. A hybrid intelligent algorithm is designed for solving the uncertain machinescheduling problem.