##### Question

In: Operations Management

# The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units

The assumptions of the production order quantity model are met in a situation where annual demand is 3650 units, the setup cost is $50, holding cost is$12 per unit per year, the daily demand rate is 10 and the daily production rate is 100. The production order quantity for this problem is approximate.

## Solutions

##### Expert Solution

For above data, production order quantity can be calculated by,

$$\sqrt{2 * K * D / h *(1-x)}$$

where,

$$\mathrm{K}=$$ Setup cost

$$\mathrm{D}=$$ Annual demand

$$\mathrm{h}=$$ Holding cost

$$\mathrm{x}=\mathrm{d} / \mathrm{p}$$ (daily demand rate/ daily production rate)

Hence, in this case,

production order quanity $$=\sqrt{2 * 50 * 3650 / 12 *(1-10 / 100)}=184$$ (rounding off)