Question

Consider a distributor of TV sets that orders from a manufacturer and sells to retailers. The distributor is trying to set an inventory policy for one of the TV models she sells. Assume that whenever the distributor places an order for this TV set, there is a fixed ordering cost of $500. The distributor buys this TV set for $250. The annual inventory holding cost for this TV set is 18% percent of the product cost. Replenishment time is four weeks.

The table below provides data on the number of TV sets sold to retailers in each of the last 12 months. Given that the distributor would like to ensure 97% service level—with a corresponding z-value of 1.88, what is the reorder point and the order quantity that the distributor should set?

Month	Sep.	Oct.	Nov	Dec	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug
Sales	200	152	100	221	287	176	151	198	246	309	98	156

[Hint: Given the above data, we can calculate the monthly average demand to be about 191 units and based on that we can calculate weekly average demand to be about 44 units (assuming 4.3 weeks in a month). Similarly, we can calculate monthly standard deviation of demand to be about 67 units and weekly standard deviation of demand to be 32 units. You can use the weekly demand and weekly standard deviation for your calculations below.]

1. What is the average demand during the leadtime?
   
   
2. What is the standard deviation of demand during the leadtime?
   
   
3. How many TV sets should the distributor order at a time?
   
   
   
4. What is the safety stock that the distributor should carry?
   
   
5. What is the reorder point that determines when the distributor should place another order?

Answer 1

Month	Sales	(Sales - Mean)^2
Sep.	200	81
Oct.	152	1521
Nov	100	8281
Dec	221	900
Jan	287	9216
Feb	176	225
Mar	151	1600
Apr	198	49
May	246	3025
Jun	309	13924
Jul	98	8649
Aug	156	1225
Total	2294	48696
Average demand	191.00

Monthly Standard deviation = Sqrt( (mean - Sales) ^2 / n-1) = sqrt (48696/11) = 66.53 = 67

Weekly standard deviation = 67 / (Sqrt 4.30) = 32

Weekly average demand = 191/4.3 = 44.41 = 44 units

Note - We are going to use rounded values calculated above.

Lead time is 4 weeks.

a) Average demand during lead time = 4 *Weekly demand = 4*44 = 176 units

b) Standard deviation of demand during lead time, Sd = Std deviation * sqrt (lead time) = 32 * sqrt (4) = 64

c) EOQ = sqrt(2DS/h)

where D = Annual demand , S = Order cost, H = Holding cost

EOQ = sqrt (2*2294*500/ 18%*250) =sqrt (2*2294*500/ 45) = 225.78 or 226 units

Note - If you take annual demand as 44*52 weeks = 2288 , the answer will be 225 units)

d) Safety Stock = Z * Standard deviation of demand during lead time

Z-score for 97% service level , = 1.88

Safety Stock = 32*1.88 = 60.16 or 60 units

e) Reorder point = Safety Stock + Average demand during lead time = 176 +60 =236