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Min-Max Regret Version of the Linear Time–Cost Tradeoff Problem with Multiple Milestones and Completely Ordered Jobs

Author

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  • Byung-Cheon Choi

    (Department of Business Administration, Chungnam National University, 79 Daehangno, Yuseong-gu, daejeon 305-704, Korea)

  • Myoung-Ju Park

    (Department of Industrial and Management Systems Engineering, Kyung Hee University, 1732, Deogyeong-daero, Giheung-gu, Yongin-si, Kyunggi-do 446-701, Korea)

Abstract

We consider a linear time–cost tradeoff problem with multiple milestones and uncertain processing times such that all jobs are completely ordered. The performance measure is expressed as the sum of total weighted number of tardy jobs and total crashing cost. The processing times uncertainty is described through two types of scenarios: discrete and interval scenarios. The objective is to minimize maximum deviation from optimality over all scenarios. For the discrete scenario case, we prove its NP-hardness, develop a pseudo-polynomial time approach, and present a polynomially solvable case. Finally, we show that the interval scenario case is also NP-hard.

Suggested Citation

  • Byung-Cheon Choi & Myoung-Ju Park, 2015. "Min-Max Regret Version of the Linear Time–Cost Tradeoff Problem with Multiple Milestones and Completely Ordered Jobs," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 32(05), pages 1-16.
    • Handle: RePEc:wsi:apjorx:v:32:y:2015:i:05:n:s0217595915500396
    DOI: 10.1142/S0217595915500396
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    Cited by:

    1. Geng, Zhichao & Yuan, Jinjiang, 2023. "Single-machine scheduling of multiple projects with controllable processing times," European Journal of Operational Research, Elsevier, vol. 308(3), pages 1074-1090.

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