Transportation Simplex Method Calculator
Transportation simplex method calculator to minimize shipping cost from sources to destinations using linear programming.
Simplex Calculator
How Simplex Method Calculator Works
Enter the LP Problem
Type the objective function coefficients and every constraint row with its right-hand-side value.
Choose Maximize or Minimize
Pick your optimization goal. The tool builds the initial tableau with slack variables automatically.
Run the Pivot Iterations
The calculator identifies pivot column by Cj-Zj, computes ratios, performs elementary row operations until optimal.
Read the Optimal Solution
Final tableau displays optimal variable values, Zj row, and the maximum/minimum objective value.
Sample Simplex Tableau Output
Example tableau iteration for a 2-variable maximization problem
| Basis | x1 | x2 | s1 | s2 | RHS | Cj-Zj |
|---|---|---|---|---|---|---|
| x1 | 14 | 0 | 0 | 1 | 14 | 0 |
| x2 | 7 | 1 | 0 | 0 | 7 | 5 |
| Zj | 35 | 5 | 0 | 0 | 35 |
Solving Transportation Problems
The transportation problem is a special linear program that minimizes the total cost of shipping goods from several sources to several destinations subject to supply and demand constraints. This transportation simplex method calculator formulates the problem as a standard linear program and solves it with the simplex algorithm, showing each tableau iteration to the optimal shipping plan.
Why Use the Simplex Method Here
Although specialized techniques such as the MODI (u-v) and stepping-stone methods exploit the transportation structure, the general simplex method solves the same problem and clearly displays how the optimal cost is reached. Enter your cost objective and the supply and demand constraints to get the minimum total cost and the shipping quantities.
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Frequently Asked Questions
What is the transportation problem?
It is a linear programming problem that minimizes the cost of transporting goods from supply sources to demand destinations while satisfying all supply and demand limits.
Can the simplex method solve transportation problems?
Yes. A transportation problem is a linear program, so it can be solved with the standard simplex method, though the MODI and stepping-stone methods are specialized alternatives.
What are supply and demand constraints?
Supply constraints limit how much each source can ship; demand constraints require each destination to receive its required amount. Together they define the feasible shipping plans.
Is transportation a minimization problem?
Usually yes - the goal is to minimize the total shipping cost, though the same framework can maximize profit if costs are replaced by profits.
Does the calculator show steps?
Yes, it displays each simplex tableau iteration until the optimal, minimum-cost shipping plan is found.