Job shop scheduling with stochastic processing time through genetic algorithm

This paper deals with job shop scheduling with stochastic processing time in normal distribution. The extended Giffler-Thompson procedure in the stochastic context is first presented and some operations on the stochastic processing time are defined. A new permutation-based representation method is then proposed, in which the substring related to each machine is a permutation. The conflict among the competing operations is eliminated by giving priority to the operation with the minimum gene value in the same permutation. An efficient genetic algorithm is proposed to minimize the maximum completion time of jobs. The proposed algorithm is tested on a set of benchmark problems and compared when it is endowed with different crossover and mutation. The computational results demonstrate the effectiveness of the proposed genetic algorithm.