Optimal Policies in Time-Varying Scheduling
This chapter addresses stochastic scheduling problems in which the processing times are varying during processing jobs. Two types of models, involving deteriorating processing times and learning effects respectively, are introduced and their solutions are studied. Section 9.1 deals with the model with deteriorating processing times. We formulate the mechanism of linear deterioration in Section 9.1.1, discuss the conditions for a job to be processible under deterioration and machine breakdowns in Section 9.1.2, derive the probabilistic features of the model with exponentially distributed uptimes and downtimes via Laplace transforms and differential equations in Section 9.1.3, and find optimal policies for minimizing the expected makespan in Section 9.1.4. The model with learning effects is discussed in Section 9.2. In Section 9.2.1 we consider optimal scheduling with learning effects but no machine breakdowns. The results are then extended to models with machine breakdowns in Section 9.2.2.
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