Calculator
Example data table
This sample matches the default values loaded when the page first opens.
| Source \ Destination | Destination 1 | Destination 2 | Destination 3 | Destination 4 | Supply |
|---|---|---|---|---|---|
| Source 1 | 8 | 6 | 10 | 9 | 35 |
| Source 2 | 9 | 12 | 13 | 7 | 50 |
| Source 3 | 14 | 9 | 16 | 5 | 40 |
| Demand | 30 | 25 | 35 | 35 | 125 |
Formula used
The transportation model minimizes total cost across all routes while satisfying every source supply and destination demand restriction.
Objective function: Minimize Z = ΣΣ(cij × xij)
Supply constraints: For each source i, Σxij = Supplyi
Demand constraints: For each destination j, Σxij = Demandj
Non-negativity: xij ≥ 0 for every route.
This page builds an initial feasible plan with Vogel Approximation or Northwest Corner, then improves it using the MODI method until all reduced costs are non-negative.
How to use this calculator
- Choose the number of sources and destinations, then build the matrix.
- Enter supply for each source and demand for each destination.
- Type the unit transportation cost for every route in the matrix.
- Select an initial feasible method if you want a different starting plan.
- Click Solve Problem to display results above the form.
- Review the allocation matrix, reduced costs, iteration history, and graph.
- Download the solution table as CSV or PDF when needed.
FAQs
1. What does this transportation solver do?
It finds a low-cost shipping plan that satisfies every source supply and every destination demand. The tool builds a feasible allocation, improves it, and reports the final transportation cost.
2. What if total supply and total demand are unequal?
The calculator automatically balances the model by adding a dummy source or dummy destination with zero transportation cost. That keeps the mathematical model solvable without changing real route costs.
3. Which starting methods are included?
You can start with Vogel Approximation for a stronger initial plan or Northwest Corner for a simple baseline. Both are then refined by the optimization step.
4. What does the MODI method improve?
MODI tests unused routes through opportunity costs. If a route can reduce the total cost, the method pivots shipments through a closed loop and updates the plan.
5. What does the opportunity cost matrix show?
It shows reduced costs for each route. Negative values indicate a possible cost-saving route, while non-negative values confirm the final plan is optimal for the current model.
6. Can I solve fractional shipment quantities?
Yes. Inputs accept decimals for costs, supply, and demand. The solver works with continuous quantities, so it can represent loads, pallets, tons, or any comparable units.
7. Why are dummy rows or columns visible in results?
They appear only when the original model is unbalanced. Dummy allocations absorb surplus supply or unmet demand mathematically, helping you see where imbalance existed.
8. When should I export the result?
Export when you need a shareable record, a review document, or spreadsheet-ready values. The CSV is useful for analysis, while the PDF is better for reporting.