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

Byung-Cheon Choi and Kwanghun Chung

European Journal of Operational Research, 2016, vol. 252, issue 2, 367-375

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.

Keywords: Scheduling; Uncertainty; Outsourcing; Computational complexity (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:252:y:2016:i:2:p:367-375

DOI: 10.1016/j.ejor.2015.12.046

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