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'

