A hybrid genetic algorithm for scheduling jobs sharing multiple resources under uncertainty

This study addresses the scheduling problem where every job requires several types of resources. At every point in time, the capacity of resources is limited. When necessary, the capacity can be increased at a cost. Each job has a due date, and the processing times of jobs are random variables with a known probability distribution. The considered problem is to determine a schedule that minimises the total cost, which consists of the cost incurred due to the violation of resource limits and the total tardiness of jobs. A genetic algorithm enhanced by local search is proposed. The sample average approximation method is used to construct a confidence interval for the optimality gap of the obtained solutions. Computational study on the application of the sample average approximation method and genetic algorithm is presented. It is revealed that the proposed method is capable of providing high-quality solutions to large instances in a reasonable time.