Abstract
This paper addresses a scheduling problem with random processing time when the operating system is subject to stochastic failure. First, scheduling of a single job is reviewed and the expected cost rate is obtained. Single scheduling time and multiple scheduling times for one job are discussed and the expected cost functions are obtained to setup the optimal due date. Numerical example is given to demonstrate the scheme of multiple scheduling times. Next, the scheduling problems of N tandem jobs and N parallel jobs are formulated and the expected cost functions are also derived. The optimal scheduling times which minimize the expected cost functions are discussed analytically.
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