Minimizing value-at-risk in single machine scheduling problems
Atakan, Semih (2012) Minimizing value-at-risk in single machine scheduling problems. [Thesis]
The vast majority of the machine scheduling literature focuses on deterministic problems in which all data is known with certainty a priori. This may be a reasonable assumption when the variability in the problem parameters is low. However, as variability in the parameters increases incorporating this uncertainty explicitly into a scheduling model is essential to mitigate the resulting adverse effects. In this thesis, we consider singlemachine scheduling problems in the presence of uncertain problem parameters. We impose a probabilistic constraint on the random performance measure of interest (such as the total completion time, total weighted completion time, and total weighted tardiness), and introduce a generic risk-averse stochastic programming model. In particular, the objective of the proposed model is to find a non-preemptive static job processing sequence that minimizes the value-at-risk (VaR) of the random performance measure at a specified confidence level. In this study, we propose a Lagrangian relaxation based decomposition strategy to obtain tight lower and upper bounds for the optimal VaR. In order to solve the Lagrangian dual problem we provide a stabilized cut-generation algorithm. We also present an extensive computational study on three selected performance measures to demonstrate the effectiveness of our solution methods and the value of the proposed model.
Repository Staff Only: item control page