Robust job shop scheduling problem: Mathematical models, exact and heuristic algorithms

• In real world applications, the job shop schedules are contaminated with disruptions.
• Robust schedules should be able to absorb the predefined range of disruptions.
• We propose 2 robustness measures.
• We propose 2 exact and 2 heuristic methods to reach a robust solution.

Job shop scheduling problem is very important one in real application of many kind of industries. In the real world applications, there exist many different kinds of disruptions with different sizes. In this situation, beyond the optimality of the final solution, its ability to absorb disruptions is vital, so that the final solution remains feasible in the case of occurring predicted disruptions. In this paper a robust job shop scheduling problem under disruptions is considered. It is intended to generate robust schedules which are able to absorb a predefined range of disruptions. For this reason, two robustness indices are proposed and the related formulas for computing the required buffer times to reach the desired robustness level are proposed. For this purpose, four methods are proposed to solve the variant defined robust job shop scheduling problem, including (1) a mathematical model, (2) a Branch and Bound algorithm, (3) a beam search algorithm, and (4) a meta-heuristic algorithm based on the particle swarm optimization (PSO) method. The first and second methods result in optimum solution. As the size of the problem increases, the required time to find the optimum solutions raises, so that no solutions can be achieved in rational amount of time, e.g. one hour. Therefore, the third and fourth methods are proposed to find good solutions even for large-scale problem in a limited amount of time. Finally, the algorithms are compared using some randomly generated instances. The results show that each algorithm can outperform the others in different conditions.