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QUESTION
A contractor has to supply $10\,000$ bearings a day to an
automobile manufacturer. When he starts a production run, he can
produce $25\, 000$ bearings per day. The cost of holding one
bearing in stock for one year (365 days) is \pounds0.02 and the
set up cost for a production run is \pounds18. How frequently
should production runs be made?
ANSWER
This is the standard batch production model with $d=10,000,\
r=25,000,\ h=\frac{2}{365}$ and $s=1800$.
$$Q*=\sqrt{\frac{2sd}{h\left[1-\frac{d}{r}\right]}}=\sqrt{\frac{2.2800.10000}{\frac{2}{365}.\frac{15}{25}}}=104,642$$
$T*=\frac{Q*}{d}=10.46$ is the time between production runs.
A practical answer if $T*=10$ with $Q*=100,000$.
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