On a standard time transportation problem

This paper studies a standard time transportation problem. Parallel transportation is done from all the sources but a source supplying goods to more than one destination can ship to another destination only after the earlier chosen destinations have been served. The aim is to minimize the maximum of the total time that the various sources take to serve the various destinations. A lexi-search algorithm is proposed to obtain a global optimal solution. A heuristic is also explained to obtain a near optimal starting upper bound on the value of the objective function. The lexi search is further facilitated by establishing some results in form of theorems and remarks.