Minimizing value-at-risk in single-machine scheduling

Atakan, Semih and Bülbül, Kerem and Noyan, Nilay (2017) Minimizing value-at-risk in single-machine scheduling. Annals of Operations Research, 248 (1-2). pp. 25-73. ISSN 0254-5330 (Print) 1572-9338 (Online)

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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. In practice, this assumption implies that the random parameters in the problem are represented by their point estimates in the scheduling model. The resulting schedules may perform well if the variability in the problem parameters is low. However, as variability increases accounting for this randomness explicitly in the model becomes crucial in order to counteract the ill effects of the variability on the system performance. In this paper, we consider single-machine scheduling problems in the presence of uncertain parameters. We impose a probabilistic constraint on the random performance measure of interest, such as the total weighted completion time or the 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. We propose a Lagrangian relaxation-based scenario decomposition method to obtain lower bounds on the optimal VaR and provide a stabilized cut generation algorithm to solve the Lagrangian dual problem. Furthermore, we identify promising schedules for the original problem by a simple primal heuristic. An extensive computational study on two selected performance measures is presented to demonstrate the value of the proposed model and the effectiveness of our solution method.
Item Type: Article
Uncontrolled Keywords: single-machine scheduling; stochastic scheduling; value-at-risk; probabilistic constraint; stochastic programming; scenario decomposition; cut generation; dual stabilization; K-assignment problem.
Subjects: T Technology > T Technology (General) > T055.4-60.8 Industrial engineering. Management engineering
T Technology > T Technology (General) > T055.4-60.8 Industrial engineering. Management engineering > T57.6-57.97 Operations research. Systems analysis
Divisions: Faculty of Engineering and Natural Sciences > Academic programs > Industrial Engineering
Faculty of Engineering and Natural Sciences
Depositing User: Kerem Bülbül
Date Deposited: 10 Sep 2017 12:45
Last Modified: 10 Sep 2017 12:45

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