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This paper investigates two scheduling problems i.e., single machine scheduling problem with minimizing the number of tardy jobs and two machine flow shop scheduling problem with a common due date and minimizing the number of tardy jobs, in a stochastic setting in the class of nonpreemptive static list policies. It is assumed that the processing times of jobs are Gamma distributed stochastic variables. In previous results on these stochastic models, the strict condition– that all scale parameters are the same – is required. However, this condition may be difficult to be specified in real world problems. This paper presents new stochastic models for these two problems. Approximate deterministic problems are generated for these stochastic problems based on a new probability inequality, under mild conditions. The former stochastic models are special cases of our results. Keywords-stochastic scheduling; single machine scheduling; flow shop scheduling; tardy jobs

Minimizing the Number of Tardy Jobs with Gammadistributed Processing Times