Question

Question 29. Consider a distributor of TV sets that orders from a manufacturer and sells to retailers. Suppose the distributor of the TV sets is trying to set inventory policies at the warehouse for one of the TV set models. Assume that whenever the distributor places an order for TV sets, there is a fixed ordering cost of $4673 which is independent of order size. The cost of a TV set to the distributor is $15 and annual inventory holding cost is 15% of the product cost. Lead time is 2.5 weeks. Historical data of the past 12 months' sales is given as Month Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sales 179 117 140 175 141 140 147 169 99 180 205 202 The distributor wants to ensure 89% service level. Calculate the order quantity, reorder level and the average inventory kept by the distributor.

Answer 1

Fixed ordering cost = $4673
Holding cost(H) = 15%
Lead time = 2.5 weeks
Cost of a TV (S)= $15
Order Quantity
We are given with the past 12 months data
Total year demand (D)= 1894 units
Order Quantity = Sq.root of (2DS/H)
Order Quantity = Square root of (2X 1894 X 15/15*0.15)
Order Quantity = 159 units
Reorder Level
Reorder Level = Average demand during lead time + Safety Stock
Lead time = 2.5 weeks
Annual demand = 1894 units
Assuming 52 week in a year
Per week demand = 1894/52
Per week demand = 36 units
Average demand during lead time = 2.5 weeks X Per week demand
Average demand during lead time = 2.5 X 36 units
Average demand during lead time = 90 units
Standard Deviation		D =	157.83333
Month	Demand	Di-D	(Di-D)^2
Sep	179	21	448
Oct	117	(41)	1,667
Nov	140	(18)	318
Dec	175	17	295
Jan	141	(17)	283
Feb	140	(18)	318
Mar	147	(11)	117
Apr	169	11	125
May	99	(59)	3,461
Jun	180	22	491
Jul	205	47	2,225
Aug	202	44	1,951
			11,700
Standard Deviation = square root of (11700/(n-1))
Standard Deviation = square root of (11700/(12-1))
Standard Deviation = 32.61
Standard Deviation = 33
Safety Stock = Z * Standard deviation
value of Z at 89% service level is 1.227 (from normal distribution table)
Safety stock = 1.227*33
Safety stock = 40 units
Reorder Level = Average demand during lead time + Safety Stock
Reorder Level = 90+40
Reorder Level = 130 units
Average inventory
Average inventory = 1894/12
Average inventory = 158 units