Minimizing value-at-risk in the single-machine total weighted tardiness problem
Atakan, Semih and Tezel, Birce and Bülbül, Kerem and Noyan, Nilay (2011) Minimizing value-at-risk in the single-machine total weighted tardiness problem. In: 5th Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA 2011), Phoenix, Arizona, USA
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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 paper, we consider the celebrated single-machine total weighted tardiness (TWT) problem in the presence of uncertain problem parameters. We impose a probabilistic constraint on the random TWT and introduce a 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) measure on the random TWT at a specified confidence level. Furthermore, we develop a lower bound on the optimal VaR that may also benefit alternate solution approaches in the future. In this study, we implement a tabu-search heuristic to obtain reasonably good feasible solutions and present results to demonstrate the effect of the risk parameter and the value of the proposed model with respect to a corresponding risk-neutral approach.
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