A feasible flow-based iterative algorithm for the two-level hierarchical time minimization transportation problem

The THTMTP (two-level hierarchical time minimization transportation problem) is an important problem arising in industries. In literature, there are only two approaches with shortcomings to solve the problem. In this paper, the THTMTP is formulated as a mathematical model applicable to the case in which the total available supply at the sources is no less than the total demand at the destinations. A feasible flow-based iterative algorithm named THTMTP-A is proposed to solve the THTMTP by constructing network with lower and upper arc capacities. It is proved that the THTMTP-A algorithm can find the optimal solution to the THTMTP in a polynomial time. The proposed THTMTP-A algorithm has good performance in terms of computer implementation, computational time and required memory for computation, and hence overcomes successfully the shortcomings of the two existing approaches. Computational experiments validate that the THTMTP-A algorithm is an efficient and robust method to solve the THTMTP, and can serve as efficient tool to solve other related optimization problems.