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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.
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