Branch and Bound Method to Solve The Sum of Two Objective Functions

  • Hussein Kamil Taher Department of Mathematics, College of Computer Sciences and Mathematics Thi-Qar University, Thi-Qar, Iraq
  • Al- Zuwaini Mohammed Kadhim Department of Mathematics, College of Computer Sciences and Mathematics Thi-Qar University, Thi-Qar, Iraq
Keywords: Single machine, Scheduling, number of early jobs, completion time

Abstract

In this paper, the problem of sequencing a set of n jobs on single machine was considered to minimize multiple objectives function (MOF). The objective  is to find the optimal  solution (scheduling) for n independent jobs to minimize the objective function consists of a sum  of  weighted number  of  early  jobs  and  total  weighted of completion time. This problem is strongly NP-hard and to resolve it we derived two lower bounds (LB1, LB2) and heuristic method to get an upper bound which are used in root node of branch and bound tree. Some special cases  and dominance rule were proposed and proved. Results of extensive computational tests show that the proposed (BAB) algorithm effective in solving problems with up to (30)  jobs in time less than or equal to (30) minutes.

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Published
2018-01-16
How to Cite
Taher, H., & Mohammed Kadhim, A.- Z. (2018). Branch and Bound Method to Solve The Sum of Two Objective Functions. Journal of Progressive Research in Mathematics, 13(1), 2151-2163. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1391
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Articles