Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

linopt::Transparent::phaseI_tableau

Start an ordinary phase one of a 2-phase simplex algorithm

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.

Syntax

linopt::Transparent::phaseI_tableau(tableau)

Description

linopt::Transparent::phaseI_tableau explicitly starts an (ordinary) phase one of the simplex algorithm , i.e. rows associated with infeasible basic variables are multiplied with -1 and another identity matrix with new slack variables is added to the given tableau. As soon as an optimal tableau with relative costs 0 is found the calculation can be continued with linopt::Transparent::clean_basis and the second phase of the simplex algorithm (linopt::Transparent::phaseII_tableau).

Examples

Example 1

The first simplex tableau is created and the first phase of the simplex algorithm is started:

t := linopt::Transparent([{x + y >= 2}, x, NonNegative]);
t := linopt::Transparent::phaseI_tableau(t)

We can see that a new slack variable, slk2, was added to the tableau. And if we now execute linopt::Transparent::simplex we can see that we have just finished the first phase of the simplex algorithm:

linopt::Transparent::suggest(t);
t := linopt::Transparent::simplex(t):
linopt::Transparent::suggest(t)

We continue the simplex algorithm by executing linopt::Transparent::clean_basis, linopt::Transparent::phaseII_tableau and linopt::Transparent::simplex. Observe in this special case linopt::Transparent::clean_basis is not necessary:

t := linopt::Transparent::clean_basis(t):
t := linopt::Transparent::phaseII_tableau(t):
t := linopt::Transparent::simplex(t);
linopt::Transparent::suggest(t)

delete t:

Parameters

tableau

A simplex tableau of domain type linopt::Transparent

Return Values

Simplex tableau of domain type linopt::Transparent.

References

Papadimitriou, Christos H; Steiglitz, Kenneth: Combinatorial Optimization; Algorithms and Complexity. Prentice-Hall, 1982.

Nemhauser, George L; Wolsey, Laurence A: Integer and Combinatorial Optimization. New York, Wiley, 1988.

Salkin, Harvey M; Mathur, Kamlesh: Foundations of Integer Programming. North-Holland, 1989.

Neumann, Klaus; Morlock, Martin: Operations-Research. Munich, Hanser, 1993.

Duerr, Walter; Kleibohm, Klaus: Operations Research; Lineare Modelle und ihre Anwendungen. Munich, Hanser, 1992.

Suhl, Uwe H: MOPS - Mathematical OPtimization System. European Journal of Operational Research 72(1994)312-322. North-Holland, 1994.

Suhl, Uwe H; Szymanski, Ralf: Supernode Processing of Mixed Integer Models. Boston, Kluwer Academic Publishers, 1994.

Was this topic helpful?