203x Filetype XLS File size 0.05 MB Source: www.kellogg.northwestern.edu
Sheet 1: ATM
Supermarket ATM | |||||||
A chain of supermarkets has learned (from the collection of data over several | |||||||
months) that the daily weekday draw from the cash machine at its Tel Aviv store | |||||||
is normally distributed (and varies independently from day to day), with a mean | |||||||
of $15,000 and a standard deviation of $6,000. | |||||||
What is the probability that the Monday draw exceeds $18,000? | |||||||
They stock the cash machine on Mondays and Fridays (four days apart). On | |||||||
Monday, they put $75,000 in the machine. How likely is it that the machine will | |||||||
run dry before the Friday refill? | |||||||
$15,000 | mean daily draw | ||||||
$6,000 | std dev of daily draw | ||||||
$18,000 | Monday limit | ||||||
30.85% | Pr( Monday draw over limit ) | ||||||
4 | k (days before restocking) | ||||||
$60,000 | mean over k days | ||||||
$12,000 | standard deviation over k days | ||||||
$75,000 | limit | ||||||
10.56% | Pr( k-day draw is over limit ) | ||||||
Via simulation: | |||||||
$18,359 | Monday draw | ||||||
$20,814 | Tuesday draw | ||||||
$17,108 | Wednesday draw | ||||||
$5,803 | Thursday draw | ||||||
$62,084 | four-day draw | ||||||
0 | is the four-day draw over $75,000? | ||||||
$B$35 | $B$37 | monitored cell | |||||
$59,986 | 10.56% | mean | |||||
$11,968 | 30.73% | sample standard deviation | |||||
$6,858 | 0 | minimum | |||||
$112,838 | 1 | maximum | |||||
100,000 | 100,000 | number of simulation runs | |||||
$372 | 0.07% | margin of error (95% confidence) |
Feingeld Industries | |||||||
Once a year, in December, Feingeld Industries prints a product catalog for the | |||||||
coming year. The press run (done by an outside firm) costs them $7,000 (for | |||||||
setup), plus $10 per catalog. (At this point, they throw away any old catalogs.) | |||||||
Marketing estimates a need for 2000 catalogs over the next year, with a forecast | |||||||
standard error of 200 (i.e., one standard-deviation's-worth of uncertainty in the | |||||||
forecast is 200 units); actual demand is normally distributed. They also estimate | |||||||
a cost of $50 for each catalog request which cannot be immediately fulfilled. | |||||||
What is their “critical fractile ” for product catalogs? | |||||||
How many catalogs should they print this December? | |||||||
$7,000 | setup cost; irrevelant to problem | ||||||
$10 | variable cost per catalog | ||||||
2000 | mean demand for next year | ||||||
200 | standard deviation of demand | ||||||
$50 | cost of leaving a catalog order unfilled | ||||||
Assuming that, when a request cannot be immediately fulfilled, it | |||||||
$10 | per-unit cost of being "over" | is put on temporary hold and filled out of the next-December | |||||
$50 | per-unit cost of being "under" | publication run, then - one way or the other - $10 will be spent | |||||
fulfilling that request. The net cost difference between fulfilling it | |||||||
83.3% | critical fractile | immediately, and fulfilling it after a delay, is $50. | |||||
2193 | number of catalogs to print | ||||||
If requests which can't be fulfilled immediately are never fulfilled, | |||||||
the cost of being "under" would be $50-$10 = $40. | |||||||
Similarly, if fulfilling a delayed request with next-year's edition | |||||||
cancels out a request for that addition, the cost of being "under" | |||||||
is only $40. | |||||||
Accounting is a non-trivial subject! |
Demand for weekly newspaper | |||||||
Weekly newsstand sales of a local (weekly, nonsubscription) newspaper are | |||||||
normally distributed, with a mean of 6,000 and a standard deviation of 700. | |||||||
How likely is it that a press run of 7,000 copies will sell out? | |||||||
What total monthly sales (4 issues) could the newspaper publisher guarantee to | |||||||
a regular advertiser, while having a 90% chance of meeting the guarantee? | |||||||
6,000 | mean weekly sales | ||||||
700 | standard deviation | ||||||
7,000 | press run | ||||||
7.66% | Pr( press run insufficient ) | ||||||
4 | issues / month | ||||||
24,000 | mean monthly sales | ||||||
1,400 | monthly standard deviation | ||||||
90% | Pr( meet guarantee ) | ||||||
22,206 | sales that can be guaranteed |
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