linopt::Transparent::autostep
--
perform the next simplex steplinopt::Transparent::autostep(
tableau)
perform the next step of the simplex algorithm for the given simplex
tableau tableau
.
linopt::Transparent::autostep(tableau)
tableau |
- | a simplex tableau of domain type
linopt::Transparent |
a simplex tableau of domain type linopt::Transparent
or
a set which contains the solution of the linear program.
linopt::Transparent
, linopt::Transparent::convert
,
linopt::Transparent::dual_prices
,
linopt::Transparent::phaseI_tableau
,
linopt::Transparent::result
,
linopt::Transparent::simplex
,
linopt::Transparent::suggest
,
linopt::Transparent::userstep
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
.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
.The ordinary simplex tableau of a given linear program is created:
>> k := [[x + y >= 2], x, NonNegative]: t := linopt::Transparent(k)
+- -+ | "linopt", "restr", slk[1], x, y | | | | "obj", 0, 0, 1, 0 | | | | slk[1], -2, 1, -1, -1 | +- -+
The next two steps of the simplex algorithm are executed for the given simplex tableau:
>> linopt::Transparent::autostep(t); linopt::Transparent::autostep(%)
+- -+ | "linopt", "restr", slk[1], x, y | | | | "obj", -2, 1, 0, -1 | | | | x, 2, -1, 1, 1 | +- -+ +- -+ | "linopt", "restr", slk[1], x, y | | | | "obj", 0, 0, 1, 0 | | | | y, 2, -1, 1, 1 | +- -+
>> delete k, t:
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)
+- -+ | "linopt", "restr", slk[1], slk[2], x, y | | | | "obj", 0, 0, 0, 1, 2 | | | | slk[1], 1, 1, 0, -1, -1 | | | | slk[2], 3, 0, 1, 1, 1 | +- -+
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)
OPTIMAL, {x = 0, y = 0}
>> delete k, t:
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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.
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