Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
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Min-Max Regret Version of an m-Machine Ordered Flow Shop with Uncertain Processing Times

  • Park, Myoung-Ju (Department of Industrial and Management Systems Engineering, Kyung Hee University) ;
  • Choi, Byung-Cheon (School of Business, Chungnam National University)
  • Received : 2015.04.29
  • Accepted : 2015.05.08
  • Published : 2015.05.31
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Abstract

We consider an m-machine flow shop scheduling problem to minimize the latest completion time, where processing times are uncertain. Processing time uncertainty is described through a finite set of processing time vectors. The objective is to minimize maximum deviation from optimality for all scenarios. Since this problem is known to be NP-hard, we consider it with an ordered property. We discuss optimality properties and develop a pseudo-polynomial time approach for the problem with a fixed number of machines and scenarios. Furthermore, we find two special structures for processing time uncertainty that keep the problem NP-hard, even for two machines and two scenarios. Finally, we investigate a special structure for uncertain processing times that makes the problem polynomially solvable.

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References

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