Attaining a good primal solution to the uncapacitated transportation problem

Abstract

Transportation of products from sources to destinations with minimal total cost plays an important role in logistics and supply chain management. The Uncapacitated Transportation Problem (UTP) is a special case of network flow optimization problem. The prime objective of this UTP is to minimize the total cost of transporting products from origins to destinations subject to the respective supply and demand requirements. The UTP consists of special network structure. Due to the special structure of this problem, the transportation algorithm is preferred to solve it. The transportation algorithm consists of two major steps: 1) Finding an Initial Feasible Solution (IFS) to TP and 2) Examining the optimality of this IFS. A better IFS generates a lesser number of iterations to obtain a Minimal Total Cost Solution (MTCS). Recently, Juman and Nawarathne (2019)’s Method was introduced to find an IFS to UTP. In this paper, the Juman and Nawarathne (2019)’s Method is improved to get a better IFS to a UTP. A comparative study on a set of benchmark instances illustrates that the new improved method provides better primal solutions compared to the Juman and Nawarathne (2019)’s Method. The proposed method is found to yield the minimal total cost solutions to all the benchmark instances