simplex.object             package:boot             R Documentation

_L_i_n_e_a_r _P_r_o_g_r_a_m_m_i_n_g _S_o_l_u_t_i_o_n _O_b_j_e_c_t_s

_D_e_s_c_r_i_p_t_i_o_n:

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

_G_e_n_e_r_a_t_i_o_n:

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

_M_e_t_h_o_d_s:

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

_S_t_r_u_c_t_u_r_e:

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

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

_s_o_l_v_e_d 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.

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

_v_a_l._a_u_x 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.

_o_b_j The original coefficients of the objective function.

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

_a._a_u_x 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.

_b_a_s_i_c 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.

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

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

_a_r_t_i_f_i_c_i_a_l 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. 

_S_e_e _A_l_s_o:

     'print.simplex', 'simplex'

