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Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty

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  • Choi, Byung-Cheon
  • Chung, Kwanghun

Abstract

We consider the min-max regret version of a single-machine scheduling problem to determine which jobs are processed by outsourcing under processing time uncertainty. The performance measure is expressed as the total cost for processing some jobs in-house and outsourcing the rest. Processing time uncertainty is described through two types of scenarios: either an interval scenario or a discrete scenario. The objective is to minimize the maximum deviation from optimality over all scenarios. We show that when the cost for in-house jobs is expressed as the makespan, the problem with an interval scenario is polynomially solvable, while the one with a discrete scenario is NP-hard. Thus, for the discrete scenario case, we develop a 2-approximation algorithm and investigate when the problem is polynomially solvable. Since the problem minimizing the total completion time as a performance measure for in-house jobs is known to be NP-hard for both scenarios, we consider the problem with a special structure for the processing time uncertainty and develop a polynomial-time algorithm for both scenarios.

Suggested Citation

  • Choi, Byung-Cheon & Chung, Kwanghun, 2016. "Min–max regret version of a scheduling problem with outsourcing decisions under processing time uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 367-375.
    • Handle: RePEc:eee:ejores:v:252:y:2016:i:2:p:367-375
    DOI: 10.1016/j.ejor.2015.12.046
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    References listed on IDEAS

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    3. Lingfa Lu & Liqi Zhang & Jie Zhang & Lili Zuo, 2020. "Single Machine Scheduling with Outsourcing Under Different Fill Rates or Quantity Discount Rates," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(01), pages 1-15, January.
    4. Zhong, Xueling & Fan, Jie & Ou, Jinwen, 2022. "Coordinated scheduling of the outsourcing, in-house production and distribution operations," European Journal of Operational Research, Elsevier, vol. 302(2), pages 427-437.
    5. Lingfa Lu & Liqi Zhang & Jinwen Ou, 2021. "In-house production and outsourcing under different discount schemes on the total outsourcing cost," Annals of Operations Research, Springer, vol. 298(1), pages 361-374, March.

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