Operations and Supply Chain Management The Core

356 OPERATIONS AND SUPPLY CHAIN MANAGEMENT
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A simple way to think about this is to consider how much risk we are willing to take
for running out of inventory. Let’s consider that the newsperson selling papers in the sales
stand had collected data over a few months and had found that, on average, each Monday
90 papers were sold with a standard deviation of 10 papers (assume that during this time
the papers were purposefully overstocked in order not to run out, so they would know what
“real” demand was). With these data, our newsperson could simply state a service rate that
is felt to be acceptable. For example, the newsperson might want to be 80 percent sure of
not running out of papers each Monday.
Recall from your study of statistics, assuming that the probability distribution associated
with the sales of the paper is normal, that if we stocked exactly 90 papers each Monday
morning, the risk of stocking out would be 50 percent, since 50 percent of the time we
expect demand to be less than 90 papers and 50 percent of the time we expect demand to
be greater than 90. To be 80 percent sure of not stocking out, we need to carry a few more
papers. From the “cumulative standard normal distribution” table given in Appendix E,
we see that we need approximately 0.85 standard deviation of extra papers to be 80 percent
sure of not stocking out. A quick way to find the exact number of standard deviations
needed for a given probability of stocking out is with the NORM.S.INV(probability)
function in Microsoft Excel: NORM.S.INV(0.8) = 0.84162. Given our result from Excel,
which is more accurate than what we can get from the tables, the number of extra papers
would be 0.84162 × 10 = 8.416, or 9 papers. (There is no way to sell 0.4 paper!)
To make this more useful, it would be good to actually consider the potential profit
and loss associated with stocking either too many or too few papers on the stand. Let’s say
that our newspaper person pays $0.20 for each paper and sells the papers for $0.50. In this
case, the marginal cost associated with underestimating demand is $0.30, the lost profit.
Similarly, the marginal cost of overestimating demand is $0.20, the cost of buying too many
papers. The optimal stocking level, using marginal analysis, occurs at the point where the
expected benefits derived from carrying the next unit are less than the expected costs for
that unit. Keep in mind that the specific benefits and costs depend on the problem.