Engineering Optimization: Theory and Practice, Fourth Edition

662 Stochastic Programming

11.22 S. S. Rao and C. P. Reddy, Mechanism design by chance constrained programming,

Mechanism and Machine Theory, Vol. 14, pp. 413–424, 1979.

Review Questions

11.1 Define the following terms:

(a)Mean

(b)Variance

(c)Standard deviation

(d)Probability

(e)Independent events

(f)Joint density function

(g)Covariance

(h)Central limit theorem

(i)Chance constrained programming

11.2 Match the following terms and descriptions:

(a)Marginal density function Describes sum of several random variables

(b)Bivariate distribution Described by probability density function

(c)Normal distribution Describes one random variable

(d)Discrete distribution Describes two random variables

(e)Continuous distribution Described by probability mass function

11.3 Answer true or false:

(a)The uniform distribution can be used to describe only continuous random variables.

(b)The area under the probability density function can have any positive value.

(c)The standard normal variate has zero mean and unit variance.

(d)The magnitude of the correlation coefficient is bounded by one.

(e)Chance constrained programming method can be used to solve only stochastic LP

problems.

(f)Chance constrained programming permits violation of constraints to some extent.

(g)Chance constrained programming assumes the random variables to be normally dis-

tributed.

(h)The design variables need not be random in a stochastic programming problem.

(i)Chance constrained programming always gives rise to a two-part objective function.

(j)Chance constrained programming converts a stochastic LP problem into a determin-

stic LP problem.

(k)Chance constrained programming converts a stochastic geometric programming

problem into a deterministic geometric programming problem.

(l)The introduction of random variables increases the number of state variables in

stochastic dynamic programming.

11.4 Explain the notationN(μ,σ).