An improved algorithm for two stage time minimization assignment problem

The paper develops a technique to solve two stage time minimization assignment problem dealing with the allocation of n jobs to n persons in two stages where $$n_1$$n1 out of n jobs are primary jobs and constitute Stage-I and rest of the jobs are secondary jobs constituting Stage-II. It is assumed that each person can be assigned to one job only and each job is to be done by exactly one person. Further, in a particular stage, all the jobs are commenced simultaneously. Stage-II jobs are commenced only after Stage-I jobs are finished and the objective is to find an assignment which minimizes the total completion time of Stage-I and Stage-II jobs. Numerical examples are provided to support the theory. The proposed algorithm has been coded in MATLAB and tested on different problems with n varying from 10 to 100.

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