An exact algorithm for identical parallel machine scheduling under scenarios

This paper discusses an uncertain identical parallel machine scheduling problem. Discrete scenario set is used to describe the uncertain processing times in actual production conditions. Objective of this problem is to minimize the mean makespan among all scenarios, which reflects solution optimality in uncertain environment. The concept of mean scenario is defined in this paper and is used to transform the model of mean makespan under scenarios into traditional deterministic identical parallel machine problem. The cutting plane algorithm is used on the basis of the mean scenario to solve the problem. The developed algorithm was applied in extensive test cases, involving different sizes and parameters. The computational results show that this proposed algorithm can solve this parallel machine model in reasonable time and can be applied in practical problems.