### EOQ with discounts

Bulk buying discounts may be available if the order quantity is above a certain size.

#### To calculate the best order quantity then we need to:

Calculate EOQ in normal way (and the costs)

Calculate costs at the lower level of each discount above the EOQ

Then choose the lowest cost option!

#### Illustration

Demand is 100 units per month. Purchase cost per unit £10. Order cost £20

Holding cost 10% p.a. of stock value.

**Required**

Calculate the minimum total cost with a discount of 2% given on orders of 350 and over

#### Solution

Calculate EOQ in normal way (and the costs)

Calculate costs at the lower level of each discount above the

EOQ

Sq root 2 x 20 x 1200 / 1 = 219

**Ordering Costs**

= Order cost per unit x (Annual Demand / Order amount)

= 20 x 1200 / 219

= 110**Holding Costs**

= Holding Cost per unit x (Order amount / 2)

= 1 x 219 / 2

= 110

= 220At discount level 350

**Ordering Costs**

= Order cost per unit x (Annual Demand / Order amount)

= 20 x 1200 / 350 = 69**Holding Costs**

= Holding Cost per unit x (Order amount / 2)

= 0.98 x 350 / 2 = 171.5

= 240.5240.5 is higher than 220 (it would be as EOQ is the best level)

However we now need to take into account the 2% price discount

Discount = 2% x 1200 x 10 = 240

Clearly with the discount being offered the company should take the discount and order at 350