Question

(EOQ calculations​) A downtown bookstore is trying to determine the optimal order quantity for a popular novel just printed in paperback. The store feels that the book will sell at four times its hardback figures. It​ would, therefore, sell approximately 3 comma 000 copies in the next year at a price of​ $1.50. The store buys the book at a wholesale figure of​ $1. Costs for carrying the book are estimated at ​$0.30 a copy per​ year, and it costs ​$10 to order more books.

a. Determine the EOQ.

b. What would be the total costs for ordering the books​ 1, 4,​ 5, 10, and 15 times a​ year?

c. What questionable assumptions are being made by the EOQ ​model?

Answer 1

a) Economic Order Quantity (EOQ) formula is given by:

((2*A*O)/C)^1/2

where,

A: Annual Quantity Demanded

O: Ordering Cost/ order (Fixed Cost)

C: Carrying Cost per order per year (Interest Rate)

therefore, EOQ in this question: ((2*3000*10)/0.3)^1/2 = 447 copies per order (approx)

b) Total Cost= Ordering Cost + Carrying Cost + Purchase Cost

Ordering cost= cost per order* no. of orders

Carrying cost= (copies per order/2)*carrying cost per copy per year

Purchase Cost= purchase price per copy * annual demand

No.of orders	Copies per order (Annual demand/No. of orders)	Average inventory (copies per order/2)	Total Ordering Cost (no. of orders*10)	Total Carrying Cost(avg inventory*0.30)	Total Purchase Cost (annual demand* $1/copy)	Total Cost (Order +Carrying+Purchase Cost)
1	3000/1 =3000	1500	10	450	3000	3460
4	3000/4 =750	375	40	112.5	3000	3152.5
5	3000/5 =600	300	50	90	3000	3140
10	3000/10 =300	150	100	45	3000	3145
15	3000/15 =200	100	150	30	3000	3180

c) Questionable assumptions made by the EOQ model:

1. Demand for the particular product will stay consistent throughout the year, i.e 3000 copies as per the question. This is a limitation because this may not be true in practical life. Incase of demand fluctuations, a Company will have to constantly review and update its EQO which becomes quite a task

2. The EOQ model assumes that replenishment of stock is not a problem at all and is made immediately as per the EOQ schedule. This might not hold true in real life as it also depends on warehouse feasibility, manpower at the factories and other supply side constraints. Basically it doesn't take into account supply lead times

3. It assumes that the purchase price ($1/copy) will remain constant throughout the year. A Firm might have to pay lesser or higher cost for purchasing the product during the year owing to various external factors.

3.