Distribution cost optimization: Comparison of NWC, MODI, and Stepping Stone methods in transportation problems
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Abstract
Solving transportation problems is essential in minimizing distribution costs in logistics and supply chains. Three classical methods North West Corner (NWC), Modified Distribution Method (MODI), and Stepping Stone are frequently used, but few studies offer a comprehensive comparison. This study fills this gap by evaluating their performance using simulated data representing real-world distribution scenarios. This study applies a structured comparative framework to analyze NWC (a cost-agnostic initial allocation technique), MODI (a dual-variable-based optimization approach), and Stepping Stone (a closed-loop path evaluation method). Each method was tested on a simulated cost matrix using Python. Evaluation metrics included total distribution cost, number of iterations, and computation time. The NWC method yielded a feasible but suboptimal solution with a cost of 540 units. Optimization using MODI reduced the cost to 425, while Stepping Stone further minimized it to 410 after three iterations. MODI showed greater computational efficiency, while Stepping Stone offered visual traceability of cost reductions. This study contributes methodologically by combining heuristic and iterative optimization techniques in one analytical framework. Practically, it provides decision-makers with insights into selecting appropriate solution methods based on trade-offs between simplicity, efficiency, and cost minimization.
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