Network Simplex Method Calculator
Network simplex method calculator for minimum-cost flow and network linear programming problems solved with the simplex algorithm.
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 |
Network Flow as Linear Programming
Network problems - such as minimum-cost flow, shortest path, and assignment - can be written as linear programs with flow-balance constraints at each node. The network simplex method is a specialized, efficient version of the simplex algorithm for these problems. This calculator solves the linear-programming formulation with the standard simplex method and shows each tableau.
When to Use It
Use it to minimize the total cost of sending flow through a network subject to capacity and balance constraints. Enter the cost objective and the node/arc constraints to get the optimal flow and total cost with full tableau steps.
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Frequently Asked Questions
What is the network simplex method?
It is a specialized version of the simplex algorithm designed for network flow problems, exploiting the network structure for greater efficiency.
What problems does it solve?
Minimum-cost flow, transportation, assignment, and shortest-path problems can all be formulated and solved as network linear programs.
How is a network problem written as an LP?
Each arc has a flow variable and a cost; each node has a flow-balance constraint requiring inflow to equal outflow plus supply or demand.
Is it faster than the standard simplex method?
For network-structured problems the network simplex method is typically much faster because it uses spanning-tree bases instead of a full tableau.
Does this tool show the steps?
Yes, it solves the linear-programming formulation and displays each simplex tableau to the optimal solution.