Optimization Result
Final Allocation Table
Opportunity Cost Table
Iteration Summary
Calculator Input
Enter supply values, demand values, and a cost matrix. Each matrix row must match one source. Each matrix column must match one destination.
Example Data Table
This sample is already loaded in the calculator. It has three sources and four destinations.
| Source | Destination 1 | Destination 2 | Destination 3 | Destination 4 | Supply |
|---|---|---|---|---|---|
| Source 1 | 8 | 6 | 10 | 9 | 20 |
| Source 2 | 9 | 12 | 13 | 7 | 30 |
| Source 3 | 14 | 9 | 16 | 5 | 25 |
| Demand | 10 | 25 | 25 | 15 | 75 |
Formula Used
The transportation simplex method minimizes total shipping cost while satisfying supply and demand restrictions.
Subject to: Σ xᵢⱼ = Supplyᵢ
Subject to: Σ xᵢⱼ = Demandⱼ
xᵢⱼ ≥ 0
Here, cᵢⱼ is the cost from source i to destination j. The value xᵢⱼ is the shipped quantity. The calculator first builds an initial feasible plan. It then applies MODI opportunity costs. A negative opportunity cost shows that the current plan can improve.
How to Use This Calculator
- Enter all supply values in the first box.
- Enter all demand values in the second box.
- Enter the cost matrix with one row per source.
- Select the initial solution method.
- Press the calculate button.
- Review allocations, opportunity costs, and total cost.
- Download the CSV or PDF report if needed.
Transportation Simplex Method Guide
What This Calculator Does
A transportation problem appears when goods move from several sources to several destinations. Each source has limited supply. Each destination has required demand. Every route has a unit shipping cost. The goal is to find the cheapest shipment pattern. This calculator solves that task with a structured transportation simplex approach. It accepts custom supplies, demands, and route costs. It also balances unequal totals with a dummy row or column. That makes many real planning cases easier to test.
Why the Method Matters
Manual transportation tables can become slow. A small mistake may change the final cost. The calculator reduces that risk. It creates an initial basic feasible solution first. You can choose Vogel, least cost, or north-west corner. Vogel often gives a strong starting plan. Least cost is simple and cost focused. North-west corner is fast and mechanical. After the first plan, the tool checks improvement using opportunity costs.
Understanding the Result
The allocation table shows shipment quantities for each route. The total cost multiplies every allocation by its route cost. The opportunity table shows reduced costs. For a minimization problem, non-negative values mean the plan is optimal. A negative value means a better route pattern may exist. The calculator adjusts shipments along a closed loop. It repeats this process until no negative opportunity cost remains.
Practical Planning Use
This tool is useful for logistics, warehouse planning, assignment style shipping, and classroom examples. It can compare alternate cost tables quickly. It also helps explain how shipment plans change. Use clean numeric data for best results. Avoid mixing units in one model. Keep all supplies and demands in the same unit. Review dummy allocations carefully. Dummy routes often show unused supply or unmet demand balancing.
FAQs
1. What is a transportation simplex method calculator?
It is a tool that finds a low-cost shipment plan between sources and destinations. It uses supply, demand, and unit route costs to create and improve an allocation table.
2. What does the total minimum cost mean?
It is the sum of every shipped quantity multiplied by its route cost. A lower total means the shipment plan uses cheaper routes more efficiently.
3. Why does the calculator add a dummy row or column?
A dummy row or column balances unequal supply and demand. Dummy costs are usually zero. This makes the transportation table mathematically complete.
4. Which starting method should I choose?
Vogel is usually a strong choice because it uses penalty values. Least cost is simple. North-west corner is useful for learning the basic allocation process.
5. What is an opportunity cost table?
It shows whether unused routes can reduce the total cost. For minimization, negative opportunity costs suggest that the current plan can still improve.
6. Can this calculator handle unbalanced problems?
Yes. If total supply and total demand are different, the calculator balances the model automatically with a dummy source or destination.
7. What format should I use for the cost matrix?
Enter one row per source. Separate values with commas, spaces, or tabs. Each row must contain the same number of values as the demand list.
8. Can I export the result?
Yes. Use the CSV button for spreadsheet work. Use the PDF button for a clean report that includes allocation, opportunity costs, and iteration details.