Two-level solid transportation problem

Motivated by the hierarchical system in transportation problems, this paper discusses a two-level time minimization solid transportation problem (2l-STP) in which the transportation of different kinds of products is done in two phases depending upon the preferences of various transportation links. Due to the hierarchical structure of the transportation system, the whole set of source-destination links is divided into two disjoint sets namely Level-1 (preferred links) and Level-2 (non-preferred links). To solve the problem, an iterative algorithm is proposed that solves a restricted solid transportation problem at each iteration. The proposed algorithm uses the technique of sensitivity analysis to solve intermediate restricted problems which makes the algorithm computationally efficient. A two-dimensional two-level transportation problem is discussed as a special case of two-level solid transportation problem. The study is supported by theoretical results and numerical examples.