Theoretical Approaches Parallel Identical Machines with Multi-Objective Functions

Authors

  • Fahim Mohammed Ibrahim Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.
  • Hanan Ali Chachan Department of Mathematics, College of Science, Mustansiriyah University, Baghdad, Iraq.
  • Ali A. D. Al-Zuky Department of Physics, College of Science, Mustansiriyah University, Baghdad, Iraq.

DOI:

https://doi.org/10.23851/mjs.v33i3.1149

Keywords:

multi-objective functions ,identical parallel machines , completion time, tardiness, earliness, dominance rules

Abstract

In this study, we propose multi-objective functions which consist of the sum of completion time, tardiness time and earliness time where Ci denoted the completion time of job (i), Ti=max{Ci-di,0}, denotes the tardiness of job  (i), Ei=max{di-Ci,0} be denoted the earliness of job (i).This problem is defined by  // In this paper, we will present some theoretical analysis discussion, and prove when we have a problem with scheduling n  jobs on two identical parallel machines (IPMSP).

Downloads

Download data is not yet available.

References

Garey, M. R., & Johnson, D. S. (1979). Computers and intractability (Vol. 174). San Francisco: freeman.

Alidaee, B., & Rosa, D. (1997). Scheduling parallel machines to minimize total weighted and unweighted tardiness. Computers & Operations Research, 24(8), 775-788.

CrossRef

[3] Azizoglu, M., & Kirca, O. (1998). Tardiness minimization on parallel machines. International Journal of Production Economics, 55(2), 163-168.

CrossRef

Yalaoui, F., & Chu, C. (2002). Parallel machine scheduling to minimize total tardiness. International journal of production economics, 76(3), 265-279.

CrossRef

Mokotoff, E. (2004). An exact algorithm for the identical parallel machine scheduling problem. European Journal of Operational Research, 152(3), 758-769.

CrossRef

Shim, S. O., & Kim, Y. D. (2007). Scheduling on parallel identical machines to minimize total tardiness. European Journal of Operational Research, 177(1), 135-146.

CrossRef

Nessah, R., Yalaoui, F., & Chu, C. (2008). A branch-and-bound algorithm to minimize total weighted completion time on identical parallel machines with job release dates. Computers & Operations Research, 35(4), 1176-1190.

CrossRef

Tanaka, S., & Araki, M. (2008). A branch-and-bound algorithm with Lagrangian relaxation to minimize total tardiness on identical parallel machines. International Journal of Production Economics, 113(1), 446-458.

CrossRef

Chiang, T. C., Cheng, H. C., & Fu, L. C. (2010). A memetic algorithm for minimizing total weighted tardiness on parallel batch machines with incompatible job families and dynamic job arrival. Computers & Operations Research, 37(12), 2257-2269.

CrossRef

Selvi. V (2014), Multi Objective Optimization Problems on Identical Parallel Machine Scheduling Using Genetic Algorithms, International Journal on Recent Researches in Science, Engineering & Technology, 2 (7) 112 - 122.

Wang, J. Q., & Leung, J. Y. T. (2014). Scheduling jobs with equal-processing-time on parallel machines with non-identical capacities to minimize makespan. International Journal of Production Economics, 156, 325-331.

CrossRef

German, Y., Badi, I., Bakir, A., & Shetwan, A. (2016). Scheduling to Minimize Makespan on Identical Parallel Machines. International Journal of Scientific & Engineering Research, 7(3), 353-359.

Chachan, H. A., & Hameed, A. S. (2019). Exact Methods for Solving Multi-Objective Problem on Single Machine Scheduling. Iraqi Journal of Science, 60(8), 1802-1813.

CrossRef

Kramer, A., Dell'Amico, M., Feillet, D., & Iori, M. (2020). Scheduling jobs with release dates on identical parallel machines by minimizing the total weighted completion time. Computers & Operations Research, 123, 105018.

CrossRef

Downloads

Key Dates

Published

25-09-2022

Issue

Section

Original Article

How to Cite

[1]
F. M. . Ibrahim, H. A. . Chachan, and A. A. D. . Al-Zuky, “Theoretical Approaches Parallel Identical Machines with Multi-Objective Functions”, Al-Mustansiriyah Journal of Science, vol. 33, no. 3, pp. 54–59, Sep. 2022, doi: 10.23851/mjs.v33i3.1149.

Similar Articles

1-10 of 126

You may also start an advanced similarity search for this article.