Handbook of Civil Engineering Calculations

TABLE 30. Frequency Distribution
Experience indicates that this capacity may be expected to vary in the manner shown in
Table 30.
When the volume of daily orders exceeds the shipping capacity, sales will be lost;
when the reverse condition occurs, trucks will be idle. Lost sales are valued at $2.40 per
unit, which includes an allowance for partial loss of goodwill. Unused shipping capacity
is valued at $1.10 per unit. Applying the Monte Carlo technique, estimate the amount of
these losses if plan A is adopted.
Calculation Procedure:
STATISTICS, PROBABILITY, AND THEIR APPLICATIONS
1. Determine the average weekly losses
In Table 30, record the median value for each range, as shown in the third and sixth
columns. For convenience, apply only these median values in the calculations. This procedure
is equivalent to assuming, for example, that the volume of prospective sales varies
discretely from 3050 to 3550 units with an interval of 100 units between consecutive
values.
Analysis of Table 30 reveals that the excess of weekly shipping capacity over delivery
requirements may range between 425 units (3475 3050) and 225 units (3325
3550), and that it may assume any of the following values:
425 375 325 275 225
175 125 75 25 25
75 125 175 225
9.117
Orders received per week
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Weekly shipping capacity
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Number Relative Median Number Relative Median
of units frequency value of units frequency value
30003099 0.05 3050 33003349 0.15 3325
31003199 0.10 3150 33503399 0.30 3375
32003299 0.35 3250 34003449 0.35 3425
33003399 0.25 3350 34503499 ____ 0.20 3475
34003499 0.15 3450
Total 1.00
35003599 ____ 0.10 3550
Total 1.00
To evaluate the average weekly losses, it is necessary to evaluate the frequency with
which these values are likely to exist. The Monte Carlo technique is a probabilistic device
that circumvents the mathematical complexity inherent in a rigorous solution by resorting
to a set of numbers generated in a purely random manner. Tables of random numbers are
published in books listed in the references for this section.
2. Compute the cumulative frequency of the prospective sales
The cumulative frequency of each value of prospective sales is the relative frequency
with which orders of the designated magnitude, or less, are received. The results of this
calculation appear in Table 31.