linopt::Transparent::autostep

Perform the next simplex step

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Syntax

linopt::Transparent::autostep(tableau)

Description

linopt::Transparent::autostep(tableau) performs the next step of the simplex algorithm. This is the same step that linopt::Transparent::suggest would suggest for the given simplex tableau tableau.

Normally linopt::Transparent::autostep returns the next simplex tableau. If the calculation of the simplex algorithm is finished linopt::Transparent::autostep returns a set containing a solution of the given linear program described by tableau.

Examples

Example 1

The ordinary simplex tableau of a given linear program is created:

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

The next two steps of the simplex algorithm are executed for the given simplex tableau:

linopt::Transparent::autostep(t);
linopt::Transparent::autostep(%)

delete k, t:

Example 2

The ordinary simplex tableau of a given linear program is created:

k := [{x + y >= -1, x + y <= 3}, x + 2*y, NonNegative]:   
t := linopt::Transparent(k)

If the end of the simplex algorithm is reached, linopt::Transparent::autostep returns a solution of the given linear program:

linopt::Transparent::suggest(t), 
linopt::Transparent::autostep(t)

delete k, t:

Parameters

tableau

A simplex tableau of domain type linopt::Transparent

Return Values

Simplex tableau of domain type linopt::Transparent or a set which contains the solution of the linear program.

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.