A solution technique for capacitated two-level hierarchical time minimization transportation problem

Abstract

As a generalization of two-level hierarchical time minimization transportation problem (2HTMTP), capacitated two-level hierarchical time minimization transportation problem (C2HTMTP) is a vital issue due to the route shipping capacity finiteness in reality, and no research report on C2HTMTP is available owing to the intractability. Only 4 approaches with defects are available in the literature to resolve 2HTMTP, and they cannot be applied directly to C2HTMTP although their generalized versions can. In this paper, by creating mathematical model along with auxiliary models and constructing network with lower and upper arc capacities, C2HTMTP is transformed into a collection of searching feasible flow in the constructed network, and consequently 4 iteration algorithms, with two respectively derived from other two by applying binary search, are developed as C2HTMTP’s solution method basing feasible flow algorithm. It is proved that the 4 iteration algorithms find C2HTMTP’s optimum solution in a polynomial computation time. Because of sufficiently exploiting C2HTMTP’s intrinsic network flow structure, the 4 iteration algorithms hold the merits such as no memory overflow, easier implementation on computer, higher computation efficiency, and easier extension to the capacitated multilevel hierarchical time minimization transportation problem with level exceeding two, and successfully overcome the deficiencies of extant solving approaches to 2HTMTP. Computational experiments validate that as compared to extant best solving method for 2HTMTP, the 4 iteration algorithms are robust and efficient C2HTMTP’s solution method able to serve as a powerful tool to solve other related complex optimization problems, where in terms of computation time, when applied to solve 2HTMTP, three algorithms vastly outperform (even the worst performing one rivals) extant best solving approach to 2HTMTP, especially when applied to solve C2HTMTP, two fast descent algorithms are rivals ranking first and second (one performs better for small and medium scale instances, another performs better for large scale instances), and significantly outperform the ranking third algorithm with rival as extant best 2HTMTP’s solving algorithm’s generalized version and great superiority to the ranking last algorithm.