Operations research
Explainer
The Transportation Problem: Shipping at Least Cost
How do you move ore from three pits to two plants at the lowest cost?
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Lesson notes
Key points
- The transportation problem is a special LP that ships goods from supply points to demand points at minimum total cost.
- A problem is balanced when total supply equals total demand; otherwise you add a dummy source or destination with zero cost.
- An initial feasible plan comes from methods like Northwest Corner, Least Cost, or Vogel's Approximation, which usually starts closest to optimal.
- A non-degenerate basic solution uses exactly m plus n minus one occupied cells, which you then test for optimality with MODI.
Takeaway: Balance first, start with VAM, then improve to the cheapest plan.
Quick check: Basic cells needed for 3 sources and 4 destinations?
- 7
- 12
- 6
Transportation problemBalanced problemInitial solutionm + n − 1
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