Efficient Solutions for Multi-criteria Sequencing Problem by Using Modified Algorithm

Authors

  • Adawiya A. Mohmood
  • Wasfaa E. Ahmed

DOI:

https://doi.org/10.24237/ASJ.02.02.716B

Abstract

For multi criteria sequencing problem on one machine, we propose a modified branch and bound algorithm (MBAB) to find efficient (pareto optimal) solutions in this paper. The criteria are total completion time ( ), total lateness ( ), and maximum tardiness (Tmax).  A collection of n independent tasks(jobs) has to be sequenced on one machine , tasks(jobs)j (j=1,2,3,…..,n) requires processing time Pj and due data dj . The MBAB algorithm depends on branch and bound technique. Applied examples are used to show applicability of MBAB algorithm. The MBAB algorithm is compared with complete enumeration method (CEM). Conclusions are formulated on the performance of the (MBAB) algorithm.

References

J. A. Hoogeveen, Minimizing maximum earliness and maximum lateness on a single machine,CWI,BS-R9001(1990)

S. French, sequencing and scheduling : An introduction to the mathematical of job shop , (John Wiley and Sons, New York,1982)

H. Hoogeveen, Invited review of Multicriteria scheduling, European Journal of Operational Research, 167,592-623(2005)

J. A. Hoogeveen, S. l. van de Veld, Minimizing total completion time and maximum cost simultaneously isolvable in polynomial time, operations Research Letters,17, 205-208(1995)

A. A. M. AI-Nuaimi, Multi-criteria Scheduling Mathematicalmodels, Exact and Approximation Algorithms, Ph.D. thesis University of AI-Mustansiriyah, college of Science, Dept. of Mathematics,(2014)

A. A. M. AI-Nuaimi, A proposed Algorithm to find efficient solutions for Multi-criteria problem, Journal of Engineering and Applied Sciences,14 (2),5547-5549(2019)

A. A. M. AI-Nuaimi, An Algorithm for solving three criteria Scheduling Problem on a Single Machine, Int. J. Agricult. Stat. Sci. 14(1), 271-273(2018)

A. A. M. AI-Nuaimi, Solving a multi-criteria problem in a nierarchical method. International Journal of Nonlinear Analysis and Applications, 13(1),2671-2674(2022)

A. I. Khames, Solving Multiobjective Sequencing Problem on one Machine, M.SC. Thesis, University of Diyala College of Science , Dep of Mathmatices, (2022)

Z. A. Lomnicki, A branch-and-bound algorithm for the exact solution of the three-machine scheduling problem, Oper. Res.quart.16, 89-100(1965)

Downloads

Published

2024-04-01

How to Cite

Adawiya A. Mohmood, & Wasfaa E. Ahmed. (2024). Efficient Solutions for Multi-criteria Sequencing Problem by Using Modified Algorithm. Academic Science Journal, 2(2), 404–412. https://doi.org/10.24237/ASJ.02.02.716B

Issue

Section

Articles