Sensitivity Analysis in Stochastic Scheduling
C. Attanasio (TU Delft - Electrical Engineering, Mathematics and Computer Science)
D. Kurowicka – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J. Söhl – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Alvaro Piedrafita Postigo – Mentor (TNO)
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Abstract
Stochastic scheduling plays a fundamental role in understanding how uncertainty propagates in machine logistics. However, existing research lacks explicit treatment of exact gradients for the project duration with respect to specific task parameters. This thesis develops a framework to calculate the sensitivity of the project duration distribution in stochastic directed acyclic graphs (DAGs).
Initially, closed-form analytical expressions for the gradients of the expected project duration are derived under Gaussian assumptions. The research then extends this foundation through a Generalized Sensitivity Theorem, accommodating a broader class of probability distributions and enabling the use of shared parameters across multiple nodes. Furthermore, the framework is applied to analyze internal machine logistics and component waiting times. By introducing parameterized artificial delays, the study formulates an optimization approach to approximate Just In Time (JIT) behavior within stochastic environments.