Stochastic Single-Machine Scheduling With Learning Effect

Learning is ubiquitous in the modern scheduling environment. While the deterministic scheduling problems with known processing time and learning rate have been extensively studied, limited work exists to address the problems with both learning effect and uncertainty. In this paper, the single-machine scheduling problem with random nominal processing time and/or random job-based learning rate is studied, with the objective of minimizing the expected total flow time and expected makespan. Several optimal policies are obtained: first, the shortest expected processing time is optimal when only the nominal processing time is random; second, when the job-based learning rate is random, the optimal policy can be obtained by solving an assignment problem with random assignment cost. Computational study is conducted to offer insights on the behavior of optimal policy. The expected value of perfect information (EVPI) is calculated as the difference between the expected objective value found by the optimal policy, and the expected objective value with perfect information. EVPI offers a practical way for decision makers to quantify the incentive and benefit of reducing uncertainty for the addressed problem. The results show that the performance of optimal policy will be negatively impacted by high variation of random parameters.