Two Stage Time Minimizing Transportation Problem with Restricted Flow

In this paper, a two stage time minimizing transportation problem (TSTMTP) with restricted flow is considered, in which the total availability of a homogeneous product at various sources is more than the total minimum requirement of the same at destinations. In the current problem, transportation takes place in two stages such that a fixed flow F₁(greater than or equal to the total minimum requirement at the destinations) is transported in the first stage and another fixed flow F₂ is transported in the second stage so as to meet the exact total requirement of the destinations. Each time the transportation from sources to destination is done in parallel. The objective is to find that feasible solution of Stage-I corresponding to which the optimal feasible solution (OFS) of Stage-II is such that the sum of the shipment times in Stage-I and Stage-II is minimum. A polynomial time iterative algorithm is proposed to solve the current problem.