Question

a coffee shop buys beans 3.2$ per bag, and it sells it for 5.25 $. this coffee shop sales are 21 bag per week. its annual inventory holding cost rate is 25% and it costs this coffee shop 20$ to place an order with the bean supplier. if the bean supplier offers a 7% discount on orders of 400 bags or more and 10% discount for 900 bags or more.

A) What is the optimal order quantity for the coffee shop?

Answer 1

We have the following values:

DEMAND = 1008(annual)

HOLDING COST = 25%

ORDERING COST = 20

Now to find the optimal order quantity, we need to adjust the EOQ value to fit the order quantity upon which the discounts are based:

If the EOQ value lies between the minimum and maximum quantity for a particular price, the value of the EOQ is used. If the EOQ is smaller than the quantity, the minimum quantity is used, and if the value of the EOQ is higher than the quantity, the maximum quantity value for a particular price is used. Now. based on the above assumptions, we can calculate individual values for EOQ since the holding cost is variable and adjust them according to the quantity which represents the adjusted Q value

EOQ = SQRT(2DS/H)

TOTAL COST OF INVENTORY = DEMAND * PRICE PER UNIT + ((ADJUSTED Q / 2) * HOLDING COST) + ((DEMAND / ADJUSTED Q) * ORDERING COST

The optimal order quantity is based on the lowest total inventory cost for a particular unit price and quantity, the quantity then becomes the optimal order quantity, and the corresponding TCI value becomes the inventory buying, ordering and holding cost.

NO.	FROM QUAN	TO QUAN	PRICE	HOLDING	EOQ	ADJUSTED Q	TOTAL COST OF INVENTORY
1	1	400	2.976	0.744	233	233	3173.007605
2	401	900	2.88	0.72	237	401	3097.674314

The answer is as follows:

OPTIMAL ORDER QUANTITY = 401

TOTAL COST OF INVENTORY = 3098