Citation
Minimizing Value-at-Risk in the Single-Machine Total Weighted Tardiness Problem. In proceedings of the 5th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2011), 9-11 August 2011, Phoenix, Arizona, USA, pages 215-229, 2011.
Paper
Abstract
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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Bibtex
@INPROCEEDINGS{2011-215-229-P, author = {S. Atakan and B. Tezel and K. Bülbül and N. Noyan},
title = {Minimizing Value-at-Risk in the Single-Machine Total Weighted Tardiness Problem},
booktitle = {In proceedings of the 5th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2011), 9-11 August 2011, Phoenix, Arizona, USA},
year = {2011},
editor = {J. Fowler and G. Kendall and B. McCollum},
pages = {215--229},
note = {Paper},
abstract = {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.},
owner = {gxk},
timestamp = {2011.08.15},
webpdf = {2011-215-229-P.pdf} }