Question

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 6,000 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 $0.15 a copy per year, and it costs $25 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

your Economic order quantity = square root of [(2 x demand x ordering costs) ÷ carrying costs]

Demand = 6000

Ordering cost = 25

Carrying cost = 0.15

1. EOQ is a quantity optimization model in which we find the optimum quantity to order by considering all variable cost and fixed associated with orders. Your total cost includes ordering cost and holding cost. Ordering cost / unit goes down with increase in order units and Holding cost goes up with increase of units. In between, their is a level, where total cost remain lowest. This is our EOQ value. Refer the below given diagram.

EOQ = squae root of {[ 2 * 6000 * 25 ] / 0.15 }

=> squae root of (2,000,000) = 1415 units

2.

a) Total cost of ordering of books for 1 unit = 25

b) Total cost of ordering of books for 4 unit = 25*4 = 100

c) Total cost of ordering of books for 5 unit = 25*5 = 125

d) Total cost of ordering of books for 10 unit = 25*10 = 250

e) Total cost of ordering of books for 15 unit = 25*15 = 375

3. questionable assumptions are given below:

a) Rate of demand is constant and the total demand is known in advance, which is impossible to be accurate.

b) Ordering cost is constant

c) Unit price of inventory is constant, as it varies over time with different vendors and due to inflation

d) Delivery time is constant, it depends on varies factors.

e) Replacement of defective units is instantaneous. Not possible.

f) Minimum stock level is zero, not happens generally, as minimum stock level remains.

g) restocking is made by the whole batch, not always.