An iterative algorithm for two level hierarchical time minimization transportation problem

• A two-level hierarchical time minimization transportation problem related to an industry project is discussed.
• Transportation takes place in two stages and objective is to minimize the sum of transportation time in two stages.
• A polynomial time iterative algorithm is proposed.
• At each iteration, the restricted version of a related cost minimization transportation problem is solved.

This paper discusses a two level hierarchical time minimization transportation problem, in which the whole set of source–destination links consists of two disjoint partitions namely Level-I and Level-II links. Some quantity of a homogeneous product is first shipped from sources to destinations by Level-I decision makers using only Level-I links, and on its completion the Level-II decision maker transports the remaining quantity of the product in an optimal fashion using only Level-II links. The objective is to find that feasible solution for Level-I decision corresponding to which the optimal feasible solution for Level-II decision maker is such that the sum of shipment times in Level-I and Level-II is minimum. A polynomial time iterative algorithm is proposed to solve the two level hierarchical time minimization transportation problem. At each iteration a lexicographic optimal solution of a restricted version of a related standard time minimization transportation problem is examined to generate a pair of Level-I and Level-II shipment times and finally the global optimal solution is obtained by selecting the best out of these generated pairs. Numerical illustration is included in support of theory.