SmartBeans is Canada’s largest online retailer of fair-trade organic coffee, and

Question

SmartBeans is Canada’s largest online retailer of fair-trade organic coffee, and imports coffee beans from several countries. SmartBeans operates 300 days a year and sells an average of 150 pounds of Harar (Ethiopia) Fair Trade Organic beans a day. After ordering, beans are always shipped from Ethiopia within exactly 11 days. Annual holding costs per pound are estimated to be 15% of the per pound cost of beans. The ordering cost is $35 per order. The cost of a pound of green coffee beans is $7.

If SmartBeans orders in quantities of 1200 pound or more, it can get a 0.1% discount on the (entire) cost of beans. Should SmartBeans take the quantity discount? How much should SmartBeans order? Would your answer change if the discount is 0.1% per pound but only for orders in quantities of 3000 pounds or more?

Explanation / Answer

If SmartBeans orders in quantities of 1200 pound or more, it can get a 0.1% discount on the (entire) cost of beans. Should SmartBeans take the quantity discount? How much should SmartBeans order?

Regular Purchase price per unit, p=   $7

Purchase price per unit, p varies for different quantities of orders

Ordering cost, O=                $35 per order

Annual holding costs per pound are estimated to be 15% of the per pound cost of beans

Carrying cost per year, C = $ 7*0.15 =1.05

Annual Demand, d =            300*150 =45000

First let us find the optimal quantity (does not depend upon price)

Optimal order quantity, E.O.Q          

= SQRT(2 × Annual demand × Cost Per Order / Carrying Cost per unit per year)

= SQRT(2*45000*(35/1.05))

=1732.05

EOQ=1732.05

When discounts are offered, the optimum order quantity is

Here the discount quantity is below the EOQ. Hence the EOQ is the optimal order quantity. Also the economic order quantity is automatically eligible for quantity discount and Smart beans should order 1732.05 or 1733 pounds

Would your answer change if the discount is 0.1% per pound but only for orders in quantities of 3000 pounds or more?

Here the discount quantity is   above EOQ. Hence the optimal quantity can either be the EOQ or the minimum discount quantity above the EOQ level. We determine the optimal quantity by comparing the total annual costs at the different order quantities.

Step 1

For order quantity =1732.05 & Regular Purchase price, p=   $7,

Total annual cost= Purchase cost+ Inventory cost

= purchase cost+ ordering cost+ carrying cost

= p*d+   O* d/Q +   c * Q/2

= 7*45000    +    35 *( 45000/1732.05)    +      1.05* (1732.05/2)

= $ 316819

Step 1

For getting discount

Total annual cost

= Purchase cost+ Inventory cost

= purchase cost+ ordering cost+ carrying cost

= p*d+   O* d/Q +   c * Q/2

= 6.993*45000    +    35 *( 45000/3000)    +      1.04895* (3000/2)

= $ 316783

The total annual cost at discounted price is lower than when we buy at regular EOQ. Hence we buy at order quantity of 3000 per order.

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