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A Single-Machine Scheduling Problem with Uncertainty in Processing Times and Outsourcing Costs

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  • Myoung-Ju Park
  • Byung-Cheon Choi

Abstract

We consider a single-machine scheduling problem with an outsourcing option in an environment where the processing time and outsourcing cost are uncertain. The performance measure is the total cost of processing some jobs in-house and outsourcing the rest. The cost of processing in-house jobs is measured as the total weighted completion time, which can be considered the operating cost. The uncertainty is described through either an interval or a discrete scenario. The objective is to minimize the maximum deviation from the optimal cost of each scenario. Since the deterministic version is known to be NP-hard, we focus on two special cases, one in which all jobs have identical weights and the other in which all jobs have identical processing times. We analyze the computational complexity of each case and present the conditions that make them polynomially solvable.

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  • Myoung-Ju Park & Byung-Cheon Choi, 2017. "A Single-Machine Scheduling Problem with Uncertainty in Processing Times and Outsourcing Costs," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-8, March.
    • Handle: RePEc:hin:jnlmpe:5791796
    DOI: 10.1155/2017/5791796
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    Cited by:

    1. Shabtay, Dvir & Gilenson, Miri, 2023. "A state-of-the-art survey on multi-scenario scheduling," European Journal of Operational Research, Elsevier, vol. 310(1), pages 3-23.
    2. Federico Alonso-Pecina & José Alberto Hernández & José Maria Sigarreta & Nodari Vakhania, 2020. "Fast Approximation for Scheduling One Machine," Mathematics, MDPI, vol. 8(9), pages 1-18, September.

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