Question

Morgan Ltd is a retailer of Juice barrels. The company has an annual demand of 74,000 barrels. The barrels cost $20 each. Fresh supplies can be obtained immediately but ordering cost and the cost of carriage inwards are $300 per order. The annual holding cost of holding one barrel in inventory is estimated to be $2. The economic order quantity has been calculated to be 7,000 x 12 barrels.

The suppliers introduce a quantity discount of 3% (.97)  on orders of at least 9,000 barrels and 4% on orders of at least 10,000 barrels.

Calculate to determine whether the least cost order quantity is still the EOQ of 7,000 barrels

Answer 1

Solution:

Re-calculate the EOQ by applying a discount:

EOQ = $\sqrt{\frac{2DS}{H} }$

9000 barrels = 0.97

10,000 barrels and above = 0.96

Use discount of 0.97 for EOQ:

EOQ = $\sqrt{\frac{2\times 74,000}{2\times 20\times 0.96} } = 1,070$ units

Derive total costs:

Total costs = Ordering costs + Holding costs + Inventory costs

Ordering costs (1070) = $\frac{74,000}{1,070} \times300 = 20,748$

Ordering costs (9000) = $\frac{74,000}{9,000} \times300 = 2,466$

Ordering costs (10,000) = $\frac{74,000}{10,000} \times300 = 2,220$

Holding costs (1,070) = $2\times20\times\frac{1,070}{2} = 21,400$

Holding costs (9,000) = $2\times20\times0.97\times\frac{9,000}{2} = 174,600$

Holding costs (10,000) = $2\times20\times0.96\times\frac{10,000}{2} = 192,000$

 

Inventory costs (1,070) = $20\times74,000 = 1,480,000$

Inventory costs (9,000) = $20\times0.97\times74,000 = 1,435,600$

Inventory costs (10,000) = $20\times0.96\times74,000 = 1,420,800$

 

Total costs (1) = 20,748 + 21,400 + 1,480,000 = 1,522,148

Total costs (2) = 2,466 + 174,600 + 1,435,600 = 1,612,666

Total costs (3) = 2,220 + 192,000 + 1,420,800 = 1,615,020

 

The least cost order quantity, the EOQ = 1,070 barrels