com.numericalmethod.suanshu.optimization.constrained.linearprogramming.simplex.pivoting
Class NaiveRule

java.lang.Object
  com.numericalmethod.suanshu.optimization.constrained.linearprogramming.simplex.pivoting.NaiveRule

All Implemented Interfaces:

SimplexPivoting

Direct Known Subclasses:

SmallestSubscriptRule

public class NaiveRule
extends java.lang.Object
implements SimplexPivoting

This is the rule found on p. 49.

One simple rule is to choose the column with the most negative reduced cost. This gives the biggest decrease in z per unit increase in the entering variable. However, since we cannot tell how much we can increase the entering variable until we perform the ratio test, it is not generally true that this choice leads to the best decrease in z on this step, among all possible pivot columns.

It does not prevent cycling, and should be used only for testing purpose.

Nested Class Summary

Nested classes/interfaces inherited from interface com.numericalmethod.suanshu.optimization.constrained.linearprogramming.simplex.pivoting.SimplexPivoting

SimplexPivoting.Pivot

Constructor Summary

NaiveRule()

Method Summary

SimplexPivoting.Pivot	findPivot(Tableau table) Compute the next swapping indices.
int	pricing(Tableau table) pivot column selection (pricing): We choose the column with most negative reduced cost (last entry in the column).
int	ratioTest(Tableau table, int s) pivot row selection (Ratio test): The pivot row is the smallest basic variable index, r, such that row r satisfies -h(r) / H(r,s) = min {-h(i) / H(i,s) | H(i,s) < 0}

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

NaiveRule

public NaiveRule()

Method Detail

pricing

public int pricing(Tableau table)

pivot column selection (pricing): We choose the column with most negative reduced cost (last entry in the column).

Specified by:

pricing in interface SimplexPivoting

Parameters:

table -

Returns:

the pivot column

ratioTest

public int ratioTest(Tableau table,
                     int s)

pivot row selection (Ratio test): The pivot row is the smallest basic variable index, r, such that row r satisfies -h(r) / H(r,s) = min {-h(i) / H(i,s) | H(i,s) < 0}

Specified by:

ratioTest in interface SimplexPivoting

Parameters:

table -

s -

Returns:

the pivot row

findPivot

public SimplexPivoting.Pivot findPivot(Tableau table)
                                throws LpProblem.Unbounded

Description copied from interface: SimplexPivoting

Compute the next swapping indices.

Specified by:

findPivot in interface SimplexPivoting

Returns:

a Pivot for column-row swapping; null if table already optimal

Throws:

LpProblem.Unbounded