Abstract
This paper deals with a class of scheduling problems with uncertain job processing times and due dates. The uncertainty is specified in the form of discrete scenario set. A probability distribution in the scenario set is known. Thus the cost of a given schedule is then a discrete random variable with known probability distribution. In order to compute a solution the popular risk criteria, such as the value at risk and the conditional value at risk, are applied. These criteria allow us to establish a link between the very conservative maximum criterion, typically used in robust optimization, and the expectation, commonly used in the stochastic approach. Using them we can take a degree of risk aversion of decision maker into account. In this paper, basic single machine scheduling problems with the risk criteria for choosing a solution are considered. Various positive complexity results are provided for them.
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Acknowledgements
Mikita Hradovich was supported by Wrocław University of Science and Technology, Grant 0401/0086/16.
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Hradovich, M., Kasperski, A., Zieliński, P. (2018). Risk Averse Scheduling with Scenarios. In: Kliewer, N., Ehmke, J., Borndörfer, R. (eds) Operations Research Proceedings 2017. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-89920-6_58
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DOI: https://doi.org/10.1007/978-3-319-89920-6_58
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