Question

Teck is a Canadian metal mining and processing company with new investments in coal and oil. The company has several warehouses in Western Canada that store thousands of parts and supplies for the machines and equipment used in its mines and operations. The stocks in the warehouses are controlled using computers in the Vancouver head office. For spare parts, the EOQ/ROP model is used.

The following data is the usage of specific spare part during a nine-month period:

Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sept
2	5	10	4	12	0	8	16	4

Suppose that now is the end of September and the next reorder point is coming up. The forecast for October is 6.7 units. The part costs Teck $15/unit. Holding cost rate is 20 percent of unit cost per year. Ordering cost is $2/order (due to EDI connection with the supplier). Purchase lead time for this part is 20 days. Assume 30 days in a month.

1. What should the EOQ be? (Hint: Use the forecast for October multiplied by 12 to estimate next year’s demand.)
2. What is order cycle for EOQ calculated in part 1?
3. Calculate the total annual inventory control cost of the EOQ.
4. Suppose now this part is ordered seven at a time. What is the total annual inventory holding cost of new order quantity (seven)? Which option is better (Ordering as seven at a time or EOQ calculated in Part 1)
5. Suppose there was no variability in demand or lead time. Determine the reorder point.
6. Suppose a 95 percent lead time service level is required. The standard deviation of monthly demand is 5.14 units. Determine the reorder point.

Answer 1

	Demand (6.7*12)	D	80.4	Units/yr
	Order cost		2	/set up
	Part cost		15
	Holding cost Rate		20%
	Holding Cost		3
	Lead time		20	days
	Economic order quantity = square root of [(2 x demand x ordering cost) ÷ carrying costs]
1	EOQ	10.35374
2	Order Cycle = (EOQ/Annual demand)*Number of working days per year
	46.3600	Days	=(10.33/80.4)*(30*12)
3	Total inventory cost (EOQ/2)*part cost	77.65307
4	New order quantity	7
	Total inventory cost (7/2)*part cost	52.5
	Ordering EOQ is beter as total cost (ordering cost+holding cost) is less in case of EOQ
5	Per day demand (6.7/30)	0.223333
	Reorder point = Lead time demand = (20*per day demand)	4.466667
6	95% lead time service level	95%
	SD of monthly demand	5.14
	z @95% service level	1.65
	Safety stock (z*SD*root of lead time) Lead time in month (20/30)	6.924708
	Reorder point = Lead time demand+safety stock (4.466+37.92)	8.574708