Stochastic flow shop scheduling with random machine breakdowns

This paper deals with scheduling problems in m machines permutation flow shop subject to random breakdowns. The processing time of each job on each machine is a random variable. The objective is to find a job schedule, which minimizes the expected makespan. The traditional studies on flow shop scheduling based on deterministic flows mostly can't adapt to the dynamic flows, and current works on stochastic scheduling problems with random machine breakdowns only consider one kind of production fashions. But in practical production, there are always many different production fashions in different workshops. Different formulas should be introduced for different production fashions. For improving the efficiency of scheduling scenarios in different workshops, two kinds of methods were advanced to deal with different random breakdowns. Genetic Algorithms were used to search the optimized schedule. Finally, some stochastic numerical examples were employed to illustrate the effectiveness of the algorithms