Student Transportation Now Inc. (STN) has a single supply depot that stocks and
ID: 354851 • Letter: S
Question
Student Transportation Now Inc. (STN) has a single supply depot that stocks and ships small maintenance items and replacement parts used by technicians that maintain STN’s fleet of 45,000 school buses across 600 locations. All this activity combines to create normally distributed daily demand for all items at the depot, including these three popular requests:
Average Daily
Standard Deviation in Daily Demand
Lead Time (constance in days)
STN Depot's Reorder Point
3-inch red reflectors
22
7
5
130
8-way flasher control unit
5
1
2
15
Condenser fan motor
15
2
2
35
1. Considering the reorder point policy set by the STN supple depot, how much safety stock is implied for each one of these three items?
2. Considering the reorder point policy set by the STN supple depot, which item is the safest from stockouts?
3. What should STN change the condenser fan motor reorder point to, if it was service level of 85.54% for that item?
4. Suppose the 2-inch red reflectors’ manufacturer has announced changes that will reduce its lead time on requests from the STN supply depot from 5 days to 4 days. If STN does not change its reorder point for that item, what will happen to its service level after these changes, and what will the new service level be?
Average Daily
Standard Deviation in Daily Demand
Lead Time (constance in days)
STN Depot's Reorder Point
3-inch red reflectors
22
7
5
130
8-way flasher control unit
5
1
2
15
Condenser fan motor
15
2
2
35
Explanation / Answer
Answer to question 1:
Following formula for Safety stock may be noted:
Safety stock = Reorder point – Average daily demand x Lead time ( days )
Therefore ,
Safety stock for 3 inch red reflectors = 130 – 22 x 5 = 130 – 110 = 20
Safety stock for 8 way flasher control unit = 15 – 5 x 2 = 15 – 10 = 5
Safety stock for Condenser fan motor = 35 – 15 x 2 = 35 – 30 = 5
Answer to question 2 :
Following to be noted :
Safety stock = Z value of instock probability x Standard deviation of daily demand x Square root ( Lead time )
Therefore :
For 3 inch red reflectors :
20 = Z x 7 x Square root ( 5 )
Or, 20 = Z X 7 X 2.236
Or, 20 = 15.65.Z
Or, Z = 1.28 ( rounded to 2 decimal places )
Corresponding in stock probability for Z = 1.28 as derived from standard normal distribution table is 0.89973
For 8 way flasher control unit :
5 = Z x 1x Square root ( 2 )
Or, 5 = 1.414.Z
Or, Z = 3.54 ( rounded to 2 decimal places )
Corresponding in stock probability for Z = 3.54 s derived from standard normal distribution table is 0.99980
For Condenser fan motor :
5 = Z x 2 x Square root ( 2 )
Or, 5 = Z x 2 x 1.414
Or, 5 = 2.828.Z
Or, Z = 1.77 ( rounded to 2 decimal places )
Corresponding in stock probability for Z = 1.77 as derived from standard normal distribution table is 0.96164
Out of above, 8 way flasher control unit has the highest in stock probability and therefore is safest from stockout
8 way flasher control unit is safest from stockout
Answer to question 3 :
Revised ins tock probability ( for service level 85.54 % ) = 0.8554
Corresponding Z value = NORMSINV ( 0.8554 ) = 1.0598
Hence safety stock = Z value x Standard deviation of daily demand x Square root ( Lead time ) = 1.0598 x 2 x 1.414 = 2.997
Reorder point for condenser fan motor
= Average daily demand x lead time ( Days ) + safety stock
= 15 x 2 + 2.997
=30 + 2.997
= 32.997 ( 33 rounded to nearest whole number )
REORDER POINT FOR CONDENSER FAN MOTORS = 33 UNITS
Answer to question 4:
For 3 inch red reflector , Since:
Reorder point
= Average daily demand x Lead time + Safety stock
= Average daily demand x Lead time(days) + Z valuexStd. Deviation of daily demand x Lead time ( days)
Therefore ,
130 = 22 x 4 + Z x 7 x Square root ( 4 )
Or, 130 = 88 + 14.Z
Or, 14.Z = 42
Or, Z = 3
Corresponding probability for Z = 3 as derived from standard normal table 0.99865The new service level therefore will = 0.99865 x 100 = 99.865 %
8 way flasher control unit is safest from stockout