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Variant Of Time Minimization Assignment Problem For Three Machines Distance Minimum -A Lexi Search Approach

Nagaraju Animoni *, V. V. Hara Gopal^{1} , S. N. Narahari Pandit^{2}

*****Department of Mathematics, SV College of computer sciences , Eathabar pally, ,Moinabad, Hyderabad,502504, India. E.Mail: animoni_nagaraju@yahoo.co.in

^{1 Department of Statistics &CQM, Osmania University, Hyderabad-500007, India.
2 Center for Quantitative Methods, Osmania University, Hyderabad-500007, India
Abstract:
There are n jobs to be carried out and m (<<n) machines only are available, out of the n jobs k jobs are necessary to be done on the available machines. Consider time matrix (tij) of size m x n gives the time required for job j is carried out on machine ‘i’. Each job has to be done only on one of the machines (i.e. one can not start processing a job on one machine and halfway shift it to another machine). Also, each machine is required to process not less than mil (at least ) and not more than miu (at most) jobs; thus, it is permissible that some jobs may have to go unprocessed i.e . For this approach, we consider the objective is to minimize the distance between accumulate machine times, required for processing the jobs on the machines M1, M2 andM3.
It should be noted that if , some of the jobs will necessarily to be left unprocessed.
Keywords: Combinatorial optimization, Time minimizing assignment problem; Generalized assignment Problem, Lexi-Search Approach
International eJournal of Mathematics and Engineering
Volume 2, Issue 4, Pages: 1169 - 1178
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