A heuristic approach to minimize expected makespan in open shops subject to stochastic processing times and failures

Many real world situations exist where job scheduling is required. This is the case of some entities, machines, or workers who have to execute certain jobs as soon as possible. Frequently what happens is that several workers or machines are not available to perform their activities during some time periods, due to different circumstances. This paper deals with these situations, and considers stochastic scheduling models to study these problems. When scheduling models are used in practice, they have to take into account that some machines may not be working. That temporal lack of machine availability is known as breakdowns, which happen randomly at any time. The times required to repair those machines are also random variables. The jobs have operations with stochastic processing times, their own release times, and there is no precedence between them. Each job is divided into operations and each operation is performed on the corresponding specialized machine. In addition, in the problems considered, the order in which the operations of each job are done is irrelevant. We develop a heuristic approach to solve these stochastic open-shop scheduling problems where random machine breakdowns can happen. The proposed approach is general and it does not depend on the distribution types of the considered random input data. It provides solutions to minimize the expected makespan. Computational experiences are also reported. The results show that the proposed approach gives a solid performance, finding suitable solutions with short CPU times.