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Mathematical model bounds for maximizing the minimum completion time problem

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This paper focuses on the parallel machine scheduling problem related to maximizing the minimum completion time. This problem affects several industrial applications. The application of this problem in real life is very impressive. This paper is based on the development of new lower bounds for the exact solution of the studied problem. It is shown in the literature that the problem is strongly NP-hard. The first developed lower bound is obtained by utilizing the probabilistic method to generate several solutions for the lower bound. The second is based on the knapsack problem with the iterative method. These numerical methods give new, better lower bounds.
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Bibliogr. 20 poz., tab.
  • Department of Computer Science and Information, College of Science at Zulfi, Majmaah University Majmaah, 11952, Saudi Arabia
  • MARS Laboratory, University of Sousse, Sousse, Tunisia
  • Department of Computer Science, Higher Institute of Computer Science and Mathematics of Monastir, University of Monastir, Monastir, 5000, Tunisia
  • Department of Computer Science, Higher Institute of Computer Science and Mathematics of Monastir, University of Monastir, Monastir, 5000, Tunisia
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  • [15] Jemmali, M. (2019). Budgets balancing algorithms for the projects assignment. International Journal of Advanced Computer Science and Applications (IJACSA), 10(11), 574-578.
  • [16] Jemmali, M., Melhim, L.K.B., Alharbi, S.O.B., & Bajahzar, A.S. (2019). Lower bounds for gas turbines aircraft engines. Communications in Mathematics and Applications, 10(3), 637-642.
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  • [20] Jemmali, M. (2021). Intelligent algorithms and complex system for a smart parking for vaccine delivery center of COVID-19. Complex & Intelligent Systems, 1-13.
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