Mahmoud M. El-Sherbiny

Step Fixed-charge transportation problem (SFCTP) is considered to be one of the versions of Fixed-charge transportation problem (FCTP) where the fixed cost is incurred for every route that is used in the solution. This is considered to be an NP-hard problem since the cost structure causes the value of the objective function to behave like a step function. In this paper three formulae are proposed to construct intermediate coefficient matrix as a base for finding an initial solution for SFCTP. The proposed formulae overcome the drawbacks of one of the earlier proposed formulae, which fails to address the cases when load units become equal to or greater than the minimum of the supplies and demand for particular route. In addition, the achieved initial solution for the SFCTP is considered to be the best as compared to the initial solution achieved by the earlier proposed formulae in the literature. In order to confirm the superiority of the proposed formulae, forty problems with different sizes have been solved to evaluate and demonstrate the performance of the proposed formulae and to compare their performance with the earlier proposed formulae.