Question

One of the products sold by OfficeMax is a Hewlett-Packard LaserJet 299 printer. As purchasing manager, you have the following information for the printer: i Click the icon to view the information for the printer. a. The EOQ is 21. (Enter your response rounded to the nearest whole number.) b. The annual ordering costs and holding costs (ignoring safety stock) for the EOQ is $ 988 . (Enter your response rounded to the nearest dollar.) c. Suppose Office Max currently orders 250 printers at a time. OfficeMax would pay $ less in holding and ordering costs per year if it ordered just 25 printers at a time. (Enter your response rounded to the nearest dollar.) More Info Average weekly demand (52 weeks per year): 51 printers Standard deviation of weekly demand: 13 printers Order lead time: 2 weeks Standard deviation of order lead time: O (lead times are constant) Item cost: $250 per printer Cost to place an order: $4 Yearly holding cost per printer: $46 Desired service level during reordering period: 99% (z = 2.33)

Answer 1

a. According to the formulae of Economic order quantity

2DS Q=V7 where: Q = EOQ units D = Demand in units (typically on an annual basis) S = Order cost (per purchase order) H = Holding costs (per unit, per year)

D= 51*52= 2652

S= 4

H= 48

Putting these values in formulae we get Q = 21 (approx.)

Hence Economic order quantity is 21 units.

b. Total number of orders in a year = (Total Demand/ EOQ) = (2652/ 21) = 126 (approx.)

Ordering cost = Total number or orders in a year * Cost to place an order = 126* 4 = $ 504

Holding cost = Avg. Inventory * Holding cost per unit per year

= (Order quantity/2) * Holding cost per unit per year

= (21/ 2) * 48

= $ 504

This also verifies EOQ model as Ordering cost = Holding cost.

Annual Holding cost and Ordering cost = 504 + 504 = $ 1008

c. Safety stock = z* Std. Dev. of Lead Time* Average Demand

= 2.33* 0 * 51 = 0

As safety stock is zero, the Same formula for Holding cost and Ordering cost are formula is unchanged from part b of this question.

Now first, let's calculate Annual ordering and holding costs when ordering 250.

Holding cost = (250/2)*48 = $ 6000

Ordering cost = (2652/250)*4 = $ 42 (approx.)

Total cost @ 250 order size = $ 6042

Now, let's calculate Annual ordering and holding costs when ordering 25.

Holding cost = (25/2)*48 = $ 600

Ordering cost = (2652/25)*4 = $ 420 (approx.)

Total cost @ 25 order size = $ 1020

Money saved when order size is reduced to 25 from 250 = 6042-1020 = $ 5022

PS - In case Safety stock is not zero, Average inventory level = (Safety stock + Order quantity/2) for holding cost calculation.