Question

The So's Hobby Shop carries a line of radio-controlled model racing cars. Average daily demand for the model cars is 100 with a standard deviation of 30. Unit inventory holding cost is estimated at $0.90/year. The shop purchases the model cars from one supplier. It is estimated that the ordering cost is $100 per order. The delivery lead time is 10 working days. Mr. So decides to use a Reorder Point System to control the inventory of the model cars and wants to achieve a service level of 90%. Assume 300 working days per year.

1. (3 points) Determine the optimal reorder point R and order quantity EOQ. (Hint: R = average demand during lead time + safety stock)

2. (3 points) Using the R and Q determined in part a), what is the average inventory in the shop? (Hint: average inventory = EOQ/2 + safety stock)

3. (4 points) Mr. So is considering a new supplier who can deliver the same line of model cars with a perfectly reliable lead time of only 3 working days. Estimate the potential annual savings in inventory holding cost by switching to this new supplier. (Hint: the saving = holding cost * reduction of average inventory)

Answer 1

a)

Daily Demand	µD	=		100
Standard Deviation of Daily Demand	σD	=		30
Working days per year	n	=		300
Annual Demand	D	=	n*µD	30,000
Lead Time (Days)	L	=		10
Desired Service level	α	=		90%
Z-value corresponding to Service Level	Zα	=	NORMSINV(α)	1.28
Safety stock	ss	=	ZασD √L	121
Reorder Point	R	=	µD*L + ss	1,121
Annual Holding Cost per Unit	H	=		$0.90
Ordering Cost per Order	S	=		$100
Optimal Order Qty	Q*	=	√(2SD/H)	2,582

Optimal reorder point, R = 1121

EOQ = 2582

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b)

Average inventory = EOQ/2 + Safety stock

= 2582/2 + 121

= 1412

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c)

New lead time, L = 3 days

Revised safety stock = 1.28*30*sqrt(3)

= 67

EOQ remains unchanged.

New average inventory = 2582/2+67

= 1358

Reduction in average inventory = 1412 - 1358

= 54

Savings = 54*0.9

= $ 48.6