Question

A local discount store stocks toy race cars. Recently, the store has received the following discount schedule for these cars.  The annual demand for race case is 5000 cars, the ordering costs are $49 per order and the annual carrying costs are 20% percent of the unit price.

a.) Indicate the order quantity, price and total cost that will minimize total inventory costs.

Quantity                Price

1-699                       $5.00

700-1999 $4.80

2000 +                     $4.75

b.) Assume that the discount store would like to have a minimum 2% risk of stockout, and that the lead time varies with an average of 5 days and a standard deviation of 1 day.  The store is open 363 days per year.  Find the reorder point and amount of safety stock needed.

Answer 1

A.

Quantity	Price	Demand	Ordering cost	carrying cost	Order Size	Purchase cost	Holding cost	Ordering cost	Total cost
	P	D	K	h	Q= Sqrt(2*K*D/h)	PD	Q*h/2	D*K/Q		EOQ= Sqrt(2*K*D/h)
1-699	5	5000	49	1	700	25000.0	350.0	350.0	25700.00	700
	5	5000	49	1	1	25000.0	0.5	245000.0	270000.50
	5	5000	49	1	699	25000.0	349.5	350.5	25700.00
700-1999	4.8	5000	49	0.96	700	24000.0	336.0	350.0	24686.00	714.4345083
	4.8	5000	49	0.96	1999	24000.0	959.5	122.6	25082.08
	4.8	5000	49	0.96	714.4345083	24000.0	342.9	342.9	24685.86
	4.8	5000	49	0.96	714	24000.0	342.7	343.1	24685.86	Min
2000 +	4.75	5000	49	0.95	2000	23750.0	950.0	122.5	24822.50	718.1848465

So we see 714 units should be the order quantity

Price is $4.8 (TO minimize the total cost)