Interval Potential Method for Solving Transportation Problems Using Mathematical Programming

This study explores the interval variant of the potential method as an innovative approach for solving transportation problems within mathematical programming. Traditional methods often fail to address the complexities arising from parameter uncertainties, creating a knowledge gap in deriving reliable solutions under varying conditions. To bridge this gap, the interval potential method is proposed, utilizing interval matrices to define constraints and feasible solutions. The methodology involves constructing the initial transportation plan using the northwest corner method and applying interval analysis to account for data variability. A structured algorithm calculates directional potentials and checks the plan's acceptability, iteratively adjusting for optimal results. Numerical simulations demonstrate the robustness of the proposed method in solving transportation problems with uncertain parameters. Results confirm that this approach identifies optimal interval solutions while maintaining computational efficiency. The implications extend to various fields requiring reliable transportation and logistics optimization under uncertain conditions, such as supply chain management and resource allocation. This work contributes to the broader application of interval analysis in mathematical programming, providing a scalable solution for real-world challenges.