Handbook of Civil Engineering Calculations

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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:


  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 pro-
    cedure 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 val-
    ues.
    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

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.



  1. 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.


TABLE 30. Frequency Distribution


Orders received per week Weekly shipping capacity

Number Relative Median Number Relative Median
of units frequency value of units frequency value
3000-3099 0.05 3050 3300-3349 0.15 3325
3100-3199 0.10 3150 3350-3399 0.30 3375
3200-3299 0.35 3250 3400-3449 0.35 3425
3300-3399 0.25 3350 3450-3499 0.20 3475

3400-3499 0.15 (^3450) Total L0 0
3500-3599 0.10 3550
Total 1.00

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