# The Effects of Coefficient Variations on the Solution

## Abstract

There are three groups of parameters in a linear programming problem : the “technological” coefficients, *a*_{ ij } (representing, for example, machine time per unit of product) ; the constant terms on the right-hand sides of the restrictions, bi (e. g., capacity limits) ; and the coefficients in the linear preference function, *c*_{ j } (for example, unit profits). In practical applications of linear programming it is important to explore the *sensitivity* of the numerical solution with respect to changes in these parameters^{1,2}. Some of them may be subject to known variations in time—prices or cost elements change, machine times are reduced and capacities increased because of rationalization or technological change, output stipulations vary from period to period, etc.—or it may not be possible to determine them exactly but only within certain intervals. (When these variations are of a random nature, the coefficients should be thought of as probability distributions rather than numbers and the problem becomes a *stochastic programming problem*.)

## Keywords

Linear Programming Problem Machine Time Input Price Actual Price Ingredient Price## Preview

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## References

- 1.This is an example of what Samuelson has termed “comparative statics”, cf. P. A. Samuelson (1947), p. 257.Google Scholar
- 1.For a detailed treatment of parametric programming, see E. O. Heady and W. Candler (1958), Chs. 7, 9, and 16.Google Scholar