A variant of time minimizing assignment problem

A time minimizing assignment problem dealing with the allocation of n jobs to m (> n) persons is considered in this paper. One job is to be allocated to exactly one person and each person does at least one job. All the persons start working on the jobs simultaneously. If a person is to do more than one job, he does them one after the other in any order. The aim of the present study is to find that feasible assignment which minimizes the total time for completing all the jobs. A lexi-search approach is proposed to find an optimal feasible assignment.