Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely...

Although the normal distribution is a reasonable input distribution in many situations, it does have two potential drawbacks: (1) it allows negative values, even though they may be extremely improbable, and (2) it is a symmetric distribution. Many situations are modeled better with a distribution that allows only positive values and is skewed to the right. Two of these are the gamma and lognormal distributions, and @RISK enables you to generate observations from each of these distributions. The @RISK function for the gamma distribution is RISKGAMMA, and it takes two arguments, as in =RISKGAMMA(3,10).

The first argument, which must be positive, determines the shape. The smaller the argument, the more skewed the distribution is to the right; the larger the argument, the more symmetric the distribution is. The second argument determines the scale, in the sense that the product of the second argument and the first argument equals the mean of the distribution. (The mean above, when the arguments are 3 and 10, is 30.) Also, the product of the second argument and the square root of the first argument is the standard deviation of the distribution. (When the arguments are 3 and 10, it is
(10) = 17.32.) The @RISK function for the lognormal distribution is RISKLOGNORM. It has two arguments, as in =RISKLOGNORM(40, 10). These arguments are the mean and standard deviation of the distribution. Rework Example 11.2 for the following demand distributions. Do the simulated outputs have any different qualitative properties with these distributions than with the triangular distribution used in the example?

a. Gamma distribution with parameters 2 and 85

b. Gamma distribution with parameters 5 and 35

c. Lognormal distribution with mean 170 and standard deviation 60