**InternationaleJournals**

**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 **t**_{ijk} 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 **m _{i}**

**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