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VARIANT CONSTRAINT OF TIME DEPENDENT TIME MINIMIZATION ASSIGNMENT PROBLEM WITH MINIMIZE OBJECTIVE–A LEXISEARCH APPROACH

Animoni Nagaraju

SV Institute of Engineering and Technology, Eathbar pally, Moinabad, Hyderabad - 502504, A.P., India. Email: animoni_nagaraju@yahoo.co.in, svgi.org@gmail.com

 

ABSTRACT

            The variant constraint of time dependent time minimization assignment problem is a 3-dimensional assignment problem, where the time matrix tijk of size m x n gives the time required for job 'j' is to be carried out on machine 'i' at particular time 'k'. There are n jobs to be carried out when, only m (<<n) machines are available, with involved new constraint which p<n jobs are necessary to be done and n-p jobs are non necessarily processed on machines.

            And Each job has to be done only on one of the machine (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 number of jobs) and not more than miu (at most) jobs; thus, it is permissible that some jobs may have to go unprocessed i.e i=1m  miu  <=  n . With this idea we now formulate the objective is to minimize the total time required for processing the jobs on these machines at particular time.

Keywords: combinatorial optimization, Time minimizing assignment problem, time dependent tmap , Lexisearch, Alphabet table, Generalized assignment problem.

 


International eJournal of Mathematics and Engineering

Volume 4, Issue 3, Pages:  2170 - 2184