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.]
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
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