On controlling the total flow in two stage time minimizing transportation problem

Transportation Problem is an important aspect which has been widely studied in Operations Research domain. A good and efficient transport is a key factor in mass production where the goods can reach the consumer from the production site or factory which may be situated many miles away. It has been studied with the objective of minimizing cost and the time to simulate different real life problems. In this paper, we study a time minimizing transportation problem in which the exact total demand of the destinations cannot be satisfied in one go. Due to some reasons, only a particular amount less than the exact total demand, can be transported first and therefore, rest of the amount has to be transported later. It gives rise to a two stage time minimizing transportation problem in which the stage-I flow is restricted. The present study proposes an iterative algorithm which concentrates on minimizing the total time of transportation of both the stages. At each iteration, a pair of times of Stage-I and Stage-II is generated with Stage-II time strictly less than the Stage-II time of the previous iteration. The pair with the minimum sum of Stage-I and Stage-II times is considered as the optimal pair and the corresponding transportation schedule is considered as the optimal solution of the problem.