This tool solves linear programming problems using the dual simplex method. It automatically converts constraints, initializes variables, and finds the optimal solution. Outputs if the problem is unbounded or unfeasible.
Select Max or Min from the dropdown menu and enter the objective function. Ensure the objective function includes all variables from the constraints. Adding extra variables will cause misalignment. The objective converts "minimize" problems to "maximize" type. Refer to solution output for further information.
Enter constraints in the input fields. Add new constraints using the Add Constraint button or by pressing Enter. The tool supports ≤, ≥, and = constraints. Note that the solver converts "greater than or equal to" (≥) constraints to "less than or equal to" (≤) type, and "equals" (=) constraints to 2 seperate types. Afterwards, the problem is converted to the canonical form by introducing slack variables before the solution procedure. (Therefore no excess variables in principle.)
Click Solve to compute the solution. The results, including the optimal value and basic variables in the basis, will appear on the right. Also, the convention Maximize{cTx : Ax=b,x≥0} is specified with the parameters for the sake of completeness. If it is not possible to (or possible but could not found in built-in iteration limit) find the global maximum or global minimum of the feasible region, it is also reported.
This tool simplifies solving Linear programming (LP) problems efficiently, especially when dealing with infeasible origin in standard simplex. Utilizing the dual simplex for initialization instead of big-M method or 2-phase method, convergence is empiricaly made faster. The dual simplex method is particularly useful when the initial solution is infeasible, as it avoids the need for artificial variables or two-phase methods.
The revised simplex method is an efficient variant of the standard simplex algorithm, designed to reduce computational effort by maintaining and updating the inverse of the basis matrix in a compact form. Instead of recomputing the entire tableau at each iteration, it uses the product form of the inverse, which represents the basis inverse as a product of elementary matrices (E matrices). Each E matrix corresponds to a pivot operation and is defined by an eta vector (η), which captures the changes to the basis. This approach significantly reduces storage requirements and computational effort (not computational complexity, mathematically both are equivalent), especially for large-scale linear programming problems. By focusing only on the essential information needed for pivoting, the revised simplex method improves both speed and numerical stability, making it a preferred choice for solving complex optimization problems.
press enter to add constraint.