Microsoft Office Tutorials and References

In Depth Information

approach will suggest a greater service capacity stock-out than the former, as evi-

denced by how the one sample graph extends far beyond the 2 sample. Additionally,

the one sample graph has many more incidences of 0 arrivals. Thus, the distortion

occurs for both extremes, high and low arrival values. Thus, the modeler must care-

fully consider the
reality
of the model before committing a sampling approach to

a worksheet. The one sample approach may be ﬁne, and certainly involves fewer

excel functions to calculate, but it may also lead to exaggerated results.

8.5.5 Sufﬁcient Sample Size

How many simulated days are sufﬁcient? Obviously, simulating one day and basing

all our analysis on that single sample would be foolish, especially when we can see

the high degree of variation of
Daily Totals
that is possible in Exhibit 8.18—a max-

imum of 28 and minimum of 5. In order to examine the model behavior carefully

and accurately, I have simulated a substantial number of representative
1
days. Even

with a sample size of 250 days, another 250 days can be recalculated by depressing

the F9 key. By recalculating and observing the changes in summary statistics, you

can determine if values are relatively stable or if variation is too great for comfort.

Also, there are more formal techniques for calculating an appropriate sample size

for speciﬁc
conﬁdence intervals
for summary statistics, like the mean. Conﬁdence

intervals provide some level of assurance that a sample statistic is indicative of the

true value of the population parameter that the statistic attempts to forecast.

Without going any further, notice the substantial utility offered by our simple

determination of demand over the 250 workday year in Exhibit 8.18. The work-

sheet provides excellent high level summary statistics that Inez can use for planning

capacity. Note that there is a substantial difference between the minimum and max-

imum
Daily Totals
, 5 and 28. Thus, planning for peak loads will not be a simple

matter given that the costs of servicing such demand will certainly include human

capital and capital equipment investments. Also of great interest are the average

number of daily arrivals, 18.0, and the standard deviation of arrivals, 3.9. An aver-

age of 18.0 is a stable value for the model, even after recalculating the 250 days

many times. But what is the variation of daily arrivals about that average? There

are several ways we can answer this question. First, we can use the average and the

standard deviation to calculate a
coefﬁcient of variation
of approximately 21.7%

(standard deviation/mean

=

(3.9/18.0). It is difﬁcult to make a general statement

related to the variation of demand, but we can be relatively certain that demand

varying one standard deviation above and below the mean, 13.9–21.9, will include

1
We want to select a sample of days large enough to produce the diverse behavior that is possible

from model operation. I have used 250 because it is a good approximation of the number of work

days available in a year if weekends are not counted. After simulating many 250 day periods, I

determine that the changes in the summary statistics (mean, max, min, and standard deviation)

do not appear to vary signiﬁcantly; thus, I feel conﬁdent that I am capturing a diversity of model

behavior. If you are in doubt, increase the simulated days until you feel secure in the results.

Search JabSto ::

Custom Search