Minimizing the Expected Number of Tardy Jobs in Dynamic Flow Shop with Stochastic Due Dates

The problem of minimizing the expected number of tardy jobs in a dynamic m machine flow shop i.e., Fm�rj�E�∑Uj� is studied in this research. It is assumed that the jobs with deterministic processing times and stochastic due dates arrive dynamically and randomly to the flow shop cell. The due date of each job is assumed to be normally distributed with known mean and variance. A dynamic method is proposed for this problem by which the m machine stochastic flow shop problem is decomposed into m stochastic single machine sub-problems. Then, each sub-problem is solved as an independent stochastic single machine scheduling problem by a mathematical programming model. The proposed dynamic method is applied whenever a sub-problem is generated during the process. Comparison of the proposed method with Shortest Process Time (SPT) first rule, which is the most effective rule in literature for the proposed research problem, shows that the proposed method performs 23.9% better than SPT rule on average for industry-size scheduling problems.