Enhanced linear programming model for optimizing unbalanced transportation problems

Abstract

This study develops improved approaches to solving freight transportation problems by considering three distinct transportation cases using real-world data. The main objective is to minimize total transportation costs from supply sources to demand destinations while determining optimal shipment quantities. The proposed models are designed to obtain efficient basic feasible solutions satisfying the required number of occupied cells, m+n−1, at the minimum possible cost. The models were implemented in MATLAB and LINGO and evaluated using a genetic algorithm (GA) and four statistical methods: the arithmetic mean (PAM), geometric mean (PGM), quadratic mean (PQM), and harmonic mean (PHM). The obtained results show that the proposed models can reduce total transportation costs while satisfying the relevant supply and demand constraints. Optimal shipment quantities were determined for each of the three transportation problems after balancing the corresponding supply and demand conditions. The results obtained using MATLAB, LINGO, the genetic algorithm, and the statistical methods were generally close, indicating the validity and effectiveness of the proposed models for solving balanced and unbalanced transportation problems at minimum total cost.