Solving the Transportation Problem: Optimality, MODI, and Degeneracy

Finding the most cost-effective way to transport goods from multiple sources to various destinations is a classic logistical challenge. To achieve true cost minimization, you must go beyond basic feasible solutions and master optimality testing. This written course guides you through the core mathematical frameworks of the Transportation Problem, helping you formulate models, evaluate initial solutions, test for optimality, and systematically resolve degeneracy issues that arise in logistics scenarios. What you'll learn: Understand the mathematical foundation of transportation models and cost matrices; Formulate Initial Basic Feasible Solutions using classic allocation methods; Apply the Modified Distribution (MODI) method step-by-step to test for optimality; Identify and resolve degeneracy in transport tables using epsilon allocations; Analyze cost-minimization scenarios and interpret shadow prices for decision-making; Explore how these mathematical algorithms translate into modern linear programming solvers and computational models. We begin with fundamental definitions, cost matrix layouts, and initial feasibility methods. From there, you will progress to advanced optimality tests, step-by-step MODI calculations, and robust strategies for handling degenerate cases. This course is designed for beginners, logistics planners, and business analysts seeking a clear, foundational understanding of operations research optimization. Start reading today to master the mathematical mechanics of logistics optimization.