OTHER ALGORITHMS FOR LINEAR PROGRAMMING:CONCLUSIONS

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CONCLUSIONS

The dual simplex method and parametric linear programming are especially valuable for postoptimality analysis, although they also can be very useful in other contexts.

The upper bound technique provides a way of streamlining the simplex method for the common situation in which many or all of the variables have explicit upper bounds. It can greatly reduce the computational effort for large problems.

Mathematical-programming computer packages usually include all three of these pro- cedures, and they are widely used. Because their basic structure is based largely upon the simplex method as presented in Chap. 4, they retain the exceptional computational effi- ciency possessed by the simplex method.

Various other special-purpose algorithms also have been developed to exploit the spe- cial structure of particular types of linear programming problems (such as those to be dis- cussed in Chaps. 9 and 10). Much research continues to be done in this area.

Karmarkar’s interior-point algorithm initiated another key line of research into how to solve linear programming problems. Variants of this algorithm now provide a power- ful approach for efficiently solving some very large problems.

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