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An integer programming approach to scheduling in a contaminated area


  • Sawik, Tadeusz


This paper presents a time-indexed integer programming formulation for scheduling dependent jobs executed by a team of workers in an area contaminated with radio-active or chemical materials. The dynamics of the harmful factor and the norms of organism recovery imply that each work period for a job should be immediately followed by a rest period for the worker executing this job and the length of the rest period depends on the start time of the corresponding work period. The problem is modeled as an NP-hard problem of scheduling on unrelated parallel processors with start time dependent processing times and different objective functions: maximum or total completion time and maximum or total tardiness. The special case of scheduling jobs executed by a single worker is also considered. Numerical examples and some computational results are reported.

Suggested Citation

  • Sawik, Tadeusz, 2010. "An integer programming approach to scheduling in a contaminated area," Omega, Elsevier, vol. 38(3-4), pages 179-191, June.
  • Handle: RePEc:eee:jomega:v:38:y:2010:i:3-4:p:179-191

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    References listed on IDEAS

    1. Wang, F. -K. & Lee, W., 2001. "Learning curve analysis in total productive maintenance," Omega, Elsevier, vol. 29(6), pages 491-499, December.
    2. Wang, Ji-Bo & Xia, Zun-Quan, 2006. "Flow shop scheduling with deteriorating jobs under dominating machines," Omega, Elsevier, vol. 34(4), pages 327-336, August.
    3. Cheng, T. C. E. & Ding, Q. & Lin, B. M. T., 2004. "A concise survey of scheduling with time-dependent processing times," European Journal of Operational Research, Elsevier, vol. 152(1), pages 1-13, January.
    4. Janiak, Adam & Kovalyov, Mikhail Y., 2006. "Scheduling in a contaminated area: A model and polynomial algorithms," European Journal of Operational Research, Elsevier, vol. 173(1), pages 125-132, August.
    5. Gentzler, GL & Khalil, TM & Sivazlian, BD, 1977. "Quantitative models for optimal rest period scheduling," Omega, Elsevier, vol. 5(2), pages 215-220.
    6. Wang, Ji-Bo, 2007. "Single-machine scheduling problems with the effects of learning and deterioration," Omega, Elsevier, vol. 35(4), pages 397-402, August.
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    Cited by:

    1. Delorme, Xavier & Dolgui, Alexandre & Kovalyov, Mikhail Y., 2012. "Combinatorial design of a minimum cost transfer line," Omega, Elsevier, vol. 40(1), pages 31-41, January.
    2. Rakes, Terry R. & Deane, Jason K. & Paul Rees, Loren, 2012. "IT security planning under uncertainty for high-impact events," Omega, Elsevier, vol. 40(1), pages 79-88, January.
    3. Shi, Yuhui & Reich, Daniel & Epelman, Marina & Klampfl, Erica & Cohn, Amy, 2017. "An analytical approach to prototype vehicle test scheduling," Omega, Elsevier, vol. 67(C), pages 168-176.
    4. Karapetyan, Daniel & Mitrovic Minic, Snezana & Malladi, Krishna T. & Punnen, Abraham P., 2015. "Satellite downlink scheduling problem: A case study," Omega, Elsevier, vol. 53(C), pages 115-123.
    5. Li, Deng-Feng, 2011. "Linear programming approach to solve interval-valued matrix games," Omega, Elsevier, vol. 39(6), pages 655-666, December.


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