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linopt::Transparent::phaseI_tableau -- start an ordinary phase one of a 2-phase simplex algorithm

Introduction

linopt::Transparent::phaseI_tableau(tableau) starts an (ordinary) phase one of the 2-phase simplex algorithm on the given simplex tableau tableau.

Call(s)

linopt::Transparent::phaseI_tableau(tableau)

Parameters

tableau - a simplex tableau of domain type linopt::Transparent

Returns

a simplex tableau of domain type linopt::Transparent.

Related Functions

linopt::Transparent, linopt::Transparent::autostep, linopt::Transparent::convert, linopt::Transparent::clean_basis, linopt::Transparent::dual_prices, linopt::Transparent::phaseII_tableau, linopt::Transparent::result, linopt::Transparent::simplex, linopt::Transparent::suggest, linopt::Transparent::userstep

Details

Example 1

The first simplex tableau is created and the first phase of the simplex algorithm is started:

>> t := linopt::Transparent([[x + y >= 2], x, NonNegative]);
   t := linopt::Transparent::phaseI_tableau(t)
                  +-                                   -+
                  |  "linopt", "restr", slk[1],  x,  y  |
                  |                                     |
                  |    "obj",     0,       0,    1,  0  |
                  |                                     |
                  |   slk[1],     -2,      1,   -1, -1  |
                  +-                                   -+
      
              +-                                           -+
              |  "linopt", "restr", slk[2], slk[1],  x,  y  |
              |                                             |
              |    "obj",     -2,      0,      1,   -1, -1  |
              |                                             |
              |   slk[2],     2,       1,     -1,    1,  1  |
              +-                                           -+

We can see that a new slack variable, slk[2] was added to the tableau. And if we now execute linopt::Transparent::simplex we can see that we have just finished the first phase of the simplex algorithm:

>> linopt::Transparent::suggest(t);
   t := linopt::Transparent::simplex(t):
   linopt::Transparent::suggest(t)
                                 slk[2], x
      
                  "linopt::Transparent::phaseII_tableau"

We continue the simplex algorithm by executing linopt::Transparent::clean_basis, linopt::Transparent::phaseII_tableau and linopt::Transparent::simplex. Observe in this special case linopt::Transparent::clean_basis is not necessary:

>> t := linopt::Transparent::clean_basis(t):
   t := linopt::Transparent::phaseII_tableau(t):
   t := linopt::Transparent::simplex(t);
   linopt::Transparent::suggest(t) 
                   +-                                 -+
                   |  "linopt", "restr", slk[1], x, y  |
                   |                                   |
                   |    "obj",     0,       0,   1, 0  |
                   |                                   |
                   |      y,       2,      -1,   1, 1  |
                   +-                                 -+
      
                                  OPTIMAL
>> delete t:
     

Background

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