Simplex-Algorithm

Help: Solution

Display

Show LP relating to the simplex tableaus

Choosing “yes” will display the LP relating to the tableaus dealt with on this tab. This option is particularly useful if the original LP is not in standard form. Simplex tableaus describe an LP in canonical form which is based on the standard form. If necessary, the tool automatically transforms the LP to this form. Thus, the LP relating to the simplex tableau may differ from the original LP. In this case, the tool also displays the reverse transformations that are necessary, to obtain the solution of the original LP.

Tableau format

Most textbooks introduce a tableau format based on an LP's canonical form. This representation includes n unit vectors which are redundant given the information which variables constitute the basis. ORTOOL calls this form extensive form. There is no need for the softare to explicitly store the unit vectors and, in fact, ORTOOL does not.

The textbook by Neumann and Morlock (1993) introduces a tableau format that abstains from explicitly including the unit vectors. ORTOOL calls this the reduced form. It is more compact, closer to a machine representation and possibly more convenient for hand-written computations.

Deviating from Neumann and Morlock's representation, the reduced form also expands the tableau entries to integer numbers if fractions are choosen as display format. The joint denominator of the row's entries is shown on the left side as a multiplier to the base variable or objective function, respectively.

Number format

The tool performs all computations precisely in fractions. If the numerator and/or denominator of the coefficients become(s) large, the display may become quite unclear. Using decimal numbers for coefficients and solutions may improve readability.

Changing the number format option will also affect the tab “LP Properties”.

Pivot Rule

A set of different rules for determining the pivot column and row are offered.