Analyze the transportation problem using multi-objective linear programming to minimize cost and distance

Abstract

The study addresses the classical transportation problem, which is central to operational research and logistics decision-making. Traditional transportation models often focus on minimizing costs under supply and demand constraints but tend to overlook the efficiency of network structures and alternative optimization strategies. This research seeks to determine whether transforming conventional transportation models into a multi-objective linear programming framework, while incorporating shortest path analysis, can yield more practical and cost-effective solutions. The research applies multi-objective linear programming techniques to three case studies from Union Food Industries Company, where commodities are transported from production sites to demand centers. Conventional allocation methods (Northwest Corner, Least-Cost, Vogel’s Approximation) were first applied to generate feasible initial solutions. These were then tested for optimality using the Modified Distribution Method. In parallel, the transportation models were reformulated as network optimization problems and solved using the shortest path method, allowing direct comparison between classical and network-based solution. The analysis demonstrated that shortest path optimization consistently reduced transportation costs compared to conventional methods. For example, in one case, the optimal cost decreased from $440 to $360 when applying shortest path modeling. The results also showed that while shortest path solutions sometimes initially violated feasibility conditions, minor adjustments restored balance without sacrificing optimality. Overall, the approach proved efficient, reliable, and computationally less complex than traditional iterative methods. Practically, the study highlights the potential of shortest path models to improve cost efficiency in transportation planning for industrial firms. Academically, it contributes to the field of operations research by integrating classical transportation theory with network-based optimization, offering a framework that balances multiple objectives while simplifying application. This work underlines the importance of modernizing transportation analysis to better support organizational decision-making