A New Algorithm For The Initial Feasible Solutions Of Fixed Charge Transportation Problem

Abstract

Fixed Charge Transportation Problem (FCTP) is known as an NP-hard problem. Therefore, algorithms are developed to find the approximate solution of this problem. The success of these algorithms depends on the choice of initial feasible solutions. In this study, a new algorithm is proposed for the initial feasible solutions of FCTP. In the proposed algorithm, firstly, for each cell in the matrix of the given inputs of the problem, when the entire product corresponding to this cell is transported, its cost is calculated and a new cost matrix is created. Then, the rows or columns of this cost matrix are randomly selected and the least cost cell in the selected row or column is found and the value of the variable corresponding to this cell of the initial solution is determined. The proposed algorithm is explained on the example.