Question

1. The demand for a particular part called SKU 005 is 1,500 units a year. The cost of one SKU 005 is $50.00. It costs $60.00 to place an order SKU 005, and the user of SKU 005 has a per year inventory carrying cost of 25% of unit cost. Assume that there are 250 working days in the year where SKU 005 is used.

a. What is the combined annual holding and ordering cost of an order size of 200 units for SKU 005?

b. How many of SKU 005 should be ordered, to minimize combined ordering and holding cost?

c. The vendor who sells SKU 005 has just offered a 5% discount for orders of 500 or more. Now how many should be ordered?

d. Once the purchasing manager for SKU 005 places an order, it always takes the vendor 5 working days to deliver that order. What should the purchasing manager’s reorder point be?

e. Why are we concerned the ROP?

Answer 1

(1)

Given:

Annual Demand D = 1500 units

Unit cost C= $50

Carrying cost = 25%

Working days = 250 days

Order cost S = 60

Carrying cost per year H = Unit cost * Carrying cost % = 50 * 0.25 = 12.5

(a)

Q = lot size = 200

Annual holding and carrying cost = (D/Q*S) +[(Q/2) *H = (1500/200*60) + [(200/2) *12.5] = 450+1250 = 1700

(b)

(c)

Annual total cost for order of EOQ

(D/Q*S) +[(Q/2) *H + CD = (1500/120*60) + [(120/2) *12.5] +50*1500= 750+750+75000 = 76500

Annual total cost for order of 500 units

C = (50 – (0.05*50)] = 50 – 2.5 = 47.5

H = 0.25*47.5 = 11.875

(D/Q*S) +[(Q/2) *H + CD = (1500/500*60) + [(500/2) *11.875] +47.5*1500= 180+2968.75+71250 = 74398.75

Discount should be accepted.

(d)

Daily demand = 1500/250 = 6

Lead time = 5

Reorder point = Daily demand * Lead time = 6 * 5 = 30

(e)

Reorder point is necessary to reduce the risk of stock out.