simplex.object             package:boot             R Documentation

Linear Programming Solution Objects

Description:

     Class of objects that result from solving a linear programming
     problem using 'simplex'.

Generation:

     This class of objects is returned from calls to the function
     'simplex'.

Methods:

     The class '"saddle.distn"' has a method for the function 'print'.

Structure:

     Objects of class '"simplex"' are implemented as a list with the
     following components.

soln The values of 'x' which optimize the objective function under the
     specified constraints provided those constraints are jointly
     feasible.

solved This indicates whether the problem was solved.  A value of '-1'
     indicates that no feasible solution could be found.  A value of
     '0' that the maximum number of iterations was reached without
     termination of the second stage.  This may indicate an unbounded
     function or simply that more iterations are needed. A value of '1'
     indicates that an optimal solution has been found.

value The value of the objective function at 'soln'.

val.aux This is 'NULL' if a feasible solution is found. Otherwise it is
     a positive value giving the value of the auxiliary objective
     function when it was minimized.

obj The original coefficients of the objective function.

a The objective function coefficients re-expressed such that the basic
     variables have coefficient zero.

a.aux This is 'NULL' if a feasible solution is found. Otherwise it is
     the re-expressed auxiliary objective function at the termination
     of the first phase of the simplex method.

A The final constraint matrix which is expressed in terms of the
     non-basic variables.  If a feasible solution is found then this
     will have dimensions 'm1+m2+m3' by 'n+m1+m2', where the final
     'm1+m2' columns correspond to slack and surplus variables.  If no
     feasible solution is found there will be an additional 'm1+m2+m3'
     columns for the artificial variables introduced to solve the first
     phase of the problem.

basic The indices of the basic (non-zero) variables in the solution.
     Indices between 'n+1' and 'n+m1' correspond to slack variables,
     those between 'n+m1+1' and 'n+m2' correspond to surplus variables
     and those greater than 'n+m2' are artificial variables.  Indices
     greater than 'n+m2' should occur only if 'solved' is '-1' as the
     artificial variables are discarded in the second stage of the
     simplex method.

slack The final values of the 'm1' slack variables which arise when the
     "<=" constraints are re-expressed as the equalities 'A1%*%x +
     slack = b1'.

surplus The final values of the 'm2' surplus variables which arise when
     the "<=" constraints are re-expressed as the equalities 'A2%*%x -
     surplus = b2'.

artificial This is NULL if a feasible solution can be found.  If no
     solution can be found then this contains the values of the
     'm1+m2+m3' artificial variables which minimize their sum subject
     to the original constraints.  A feasible solution exists only if
     all of the artificial variables can be made 0 simultaneously. 

See Also:

     'print.simplex', 'simplex'

