Theoretical Approaches Parallel Identical Machines with Multi-Objective Functions
DOI:
https://doi.org/10.23851/mjs.v33i3.1149Keywords:
multi-objective functions ,identical parallel machines , completion time, tardiness, earliness, dominance rulesAbstract
In this study, we propose multi-objective functions which consist of the sum of completion time, tardiness time and earliness time where Cidenoted 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).
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.
[3] Azizoglu, M., & Kirca, O. (1998). Tardiness minimization on parallel machines. International Journal of Production Economics, 55(2), 163-168.
Yalaoui, F., & Chu, C. (2002). Parallel machine scheduling to minimize total tardiness. International journal of production economics, 76(3), 265-279.
Mokotoff, E. (2004). An exact algorithm for the identical parallel machine scheduling problem. European Journal of Operational Research, 152(3), 758-769.
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.
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.
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.
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.
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.
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.
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.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Al-Mustansiriyah Journal of Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC-BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.
