Operation Management
Q1: A manufacturer’s average work-in-process inventory for a certain part is 1,000 units. The workstation produces this part at the rate of 200 units per day. What is the average time a unit spends at this workstation? Inventory,
,
Throughput,
.
Thus,
Flow time,
.
A unit spends an average time of 5 days at this workstation.
Q2: The Wilcox Student Health Center has just implemented a new computer system and service process to “improve efficiency.” As pharmacy manager, you are concerned about waiting time and its potential impact on college students who “get no respect.” All prescriptions (Rxs) go through the following process: Drop-off ! Fill Rx !
Pick-up ! Cashier Assume that students arrive to drop-off Rxs at a steady rate of 2 Rxs per minute, with an average of one Rx per student. The average number of students in process (those who are waiting and those who are being served) at each station is:
Drop-off - 5 students
Pick-up - 3 students
Pay cashier - 6 students
On average, the Fill Rx station has 40 Rxs in process and waiting.
Because of this perceived long wait, 95% of the students decide to come back later for pick-up. They come back an average of 3 hours later. If the students choose to stay, their name is called as soon as the Rx is filled and they then enter the pick-up line. Assume that the system is operating at a steady state.
a) The flow diagram for the entire process:
Come
back later
95%
Start
Drop-off
End
5%
Pick-up
Cashier
100%
Flow paths for students
Fill Rx
Flow paths for prescriptions
b)
Drop-off
Fill Rx
Pick-up
Cashier
5 Rxs
40 Rxs
3 Rxs
6 Rxs
2 Rxs/min
2 Rxs/min
2 Rxs/min
2 Rxs/min
2.5 min
20 min
1.5 min
3 min
Table 1: Find Missing Data Using Little Law.
Average time in the pharmacy for those students who stay to pick-up their Rxs (see Table 1) = 2.5 + 20 + 1.5 + 3 = 27 minutes
c) Average time in the pharmacy for those students
,
Throughput,
.
Thus,
Flow time,
.
A unit spends an average time of 5 days at this workstation.
Q2: The Wilcox Student Health Center has just implemented a new computer system and service process to “improve efficiency.” As pharmacy manager, you are concerned about waiting time and its potential impact on college students who “get no respect.” All prescriptions (Rxs) go through the following process: Drop-off ! Fill Rx !
Pick-up ! Cashier Assume that students arrive to drop-off Rxs at a steady rate of 2 Rxs per minute, with an average of one Rx per student. The average number of students in process (those who are waiting and those who are being served) at each station is:
Drop-off - 5 students
Pick-up - 3 students
Pay cashier - 6 students
On average, the Fill Rx station has 40 Rxs in process and waiting.
Because of this perceived long wait, 95% of the students decide to come back later for pick-up. They come back an average of 3 hours later. If the students choose to stay, their name is called as soon as the Rx is filled and they then enter the pick-up line. Assume that the system is operating at a steady state.
a) The flow diagram for the entire process:
Come
back later
95%
Start
Drop-off
End
5%
Pick-up
Cashier
100%
Flow paths for students
Fill Rx
Flow paths for prescriptions
b)
Drop-off
Fill Rx
Pick-up
Cashier
5 Rxs
40 Rxs
3 Rxs
6 Rxs
2 Rxs/min
2 Rxs/min
2 Rxs/min
2 Rxs/min
2.5 min
20 min
1.5 min
3 min
Table 1: Find Missing Data Using Little Law.
Average time in the pharmacy for those students who stay to pick-up their Rxs (see Table 1) = 2.5 + 20 + 1.5 + 3 = 27 minutes
c) Average time in the pharmacy for those students