A contractor has to supply 10000 bearings per day to a manufacturer, he can produce 25000 per day, holding cost is Rs. 0.02 per year, set up cost is Rs. 18. How frequently should production run be made

This is the standard batch production model with,

d = 10,000,

r = 25,000,

h = $\frac{2}{365}$ and

s = 1800.

$$Q* = \sqrt \frac{2sd}{h(1 - \frac{d}{r})}$$

$$Q* = \sqrt \frac{2 . 2800 . 10000}{\frac{2}{365} .\frac{15}{25}}$$

$$Q* = 104,642$$

$$T* = \frac{Q*}{d} = 10.46 is\ the\ time\ between\ production\ runs.$$