One of the products sold by OfficeMax is a HewlettPackard De

One of the products sold by OfficeMax is a Hewlett-Packard DeskJet Z4480 printer. As purchasing manager, you have the following information for the printer: What is the economic order quantity for the printer? Calculate annual ordering costs and holding costs (ignoring safety stock) for the EOQ. What do you notice about the two? Suppose OfficeMax currently orders 120 printers at a time. How much more or less would OfficeMax pay in holding and ordering costs per year if it ordered just 12 printers at a time? Show your work. What is the reorder point for the printer? How much of the reorder point consists of safety stock? For parts (e) and (f), use the following formula to consider the impact of safety stock (SS) on average inventory levels and annual holding costs: (Q/2 +SS)H e) What is the annual cost of holding inventory, including the safety stock? How much of this cost is due to the safety stock? Suppose OfficeMax is able to cut the lead time to a constant 1 week. What would the new safety stock level be? How much would this reduce annual holding costs?

Solution

So we have the following data:

Average weekly demand = 60 printers

Standard deviation = 12 printers

Order lead time = 3 weeks

Item cost that we have = $120

Cost of order = $2

Yearly holding cost per printer = $48

Service level = 99% or z = 2.33

a)            EOQ for the system = (2* Annual usage unit)(order cost)/annual carrying cost)

= (2* 60*52 * 2/48) = 16.14 or 17 printers

b)            Annual holding cost = orders quantity * holding cost / 2 = 17 * 48/2 =$ 408

Annual Order cost = (Annual demand/ order quantity) *(order cost)

= (52*60/17)*2 = $367

We see that the holding cost is higher than the ordering cost for one year.

c)            In case of ordering of 50 printers

Annual holding cost = orders quantity * holding cost / 2 = 50 *48 /2 =$1200

Annual Order cost = (Annual demand/ order quantity) *(order cost)

= (52*60/50)*2 = $124.8

Annual holding cost increases significantly but ordering cost decreases.

d)            Reorder point = average demand + z * std deviation

We have 60 + 2.33*12 = 88 approx

Safety stock = 88 – 60 = 28 printers

e)            So we have the service level of 99% and z = 2.33

Reorder point = average demand + z * std deviation

So we have demand = 60 in three weeks that is 15 working days

So per day we have = 60/15 = 4

Reorder point = 15 + 2.33 * (0.5) = 16.165

Hence reorder point = 4* 16.165 = 65 approx.