Initial Basic Feasible Solution Approach for Transportation Problem: Logarithmic Fermi Approximation

Transportation problems are considered as a fundamental topic in operations research. In large-scale and complex network structures, initial solutions provide cost effectiveness by influencing the quality and speed of algorithms. Transportation problems aim to balance supply-demand and minimize costs. Appropriate initial solutions save time by producing results close to the optimal solution. Using a single appropriate initial solution algorithm for balanced and unbalanced transportation problems can be more efficient. The new approach proposed in this study is called the Logarithmic Fermi Approach. To analyze the performance of the approach, P1 and P2 test problems with different cost ranges were generated. Analyses have shown that Logarithmic Fermi Method (LFM) and Karagül-Şahin Approximation Method (KSAM) stand out in balanced and unbalanced problems, while North-West Corner Method (NCW) demonstrates poor performance. In large-scale problems, Logarithmic Fermi Method (LFM) and Least Cost Method (LCM) algorithms have produced results close to the optimal solution. The proposed method has shown to have a competitive structure in the analyses.