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A comparative analysis of MIP formulations for the multi-mode resource-constrained independent task scheduling problem

Author

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  • Maryam Al-Khatib

    (Qatar University)

  • Mohamed Haouari

    (Qatar University)

  • Mohamed Kharbeche

    (Qatar University)

Abstract

We consider the problem of scheduling independent multi-mode tasks with multiple renewable resource constraints, aiming to minimize the weighted sum of tardinesses. This problem commonly arises in the context of multiproject scheduling. We propose three pseudo-polynomial mixed-integer programming formulations and conduct a theoretical comparative analysis of their respective linear programming relaxations. We present the results of extensive computational experiments that provide evidence that a formulation based on Dantzig–Wolfe reformulation exhibits very good empirical performance consistently solving all instances with fewer than 30 tasks. In addition, it achieved an average success rate of 94.28% for instances with tasks ranging from 40 to 100, compared to other formulations that on average achieved success rates of 64.28% and 58.57%.

Suggested Citation

  • Maryam Al-Khatib & Mohamed Haouari & Mohamed Kharbeche, 2025. "A comparative analysis of MIP formulations for the multi-mode resource-constrained independent task scheduling problem," Operational Research, Springer, vol. 25(2), pages 1-21, June.
    • Handle: RePEc:spr:operea:v:25:y:2025:i:2:d:10.1007_s12351-025-00924-2
    DOI: 10.1007/s12351-025-00924-2
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    References listed on IDEAS

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