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Practice Questions: Process Analysis and Capacity Management
The Avis Company is a car rental company and is located 3 miles from the
Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the
airport every 2 min. The average traveling time (a round trip) is 20 min.
How many Avis buses are traveling to and from the airport?
The throughput rate is 30 buses per hour.
The throughput time is 20/60 =1/3 hours
TT = WIP/TR
TT*TR = WIP
30*1/3 = 10
10 buses are traveling to and from the airport.
The branch manager wants to improve the service and suggests
dispatching buses every 0.5 min. She argues that this will reduce the
average traveling time from the airport to Avis offices to 2.5 min. Is she
correct? If your answer is negative then what will the average traveling
This reduces the average waiting time, but has no effect on the average
traveling time. The average traveling time does not change and will
remain 20 min.
Safety regulations require that the time between airplane takeoffs (on the same
runway) will be at least 3 min. When taking off, the run time of an airplane
on the runway is 45 sec. Planes are on average waiting 4 min and 15 sec for
take-off. On average there are 15 plans taking off per hour.
How many planes are either on the runway or waiting to take off?
TR = 15 plans per hour.
TT = (0.75 +4.25)/60 = 1/12 of an hour
WIP = TT*TR = 15*1/12 = 1.25
In Children’s Hospital in Seattle there are on average 60 births per week.
Mother and child stay, on average, two days before they leave the hospital. In
Swedish hospital (also in Seattle), the average number of births per week is
210. Mothers and children stay in the hospital 2 days on average.
How many new mothers are staying in Children’s Hospital?
TR = 60 per week
TT = 2/7 weeks
WIP = TT *TR = 60*2/7 = 120/7 = 17.1
On average there are 17.1 new mothers in the Children’s hospital.
How many new mothers are staying in the Swedish Hospital?
TR = 210per week
TT = 2/7 weeks
WIP = TT *TR = 210*2/7 = 60
On average there are 60 new mothers in Swedish.
The directors of the two hospitals are negotiating unifying the children
wards of the two hospitals. They believe that by doing so they will be able
to reduce the number of new mothers staying in the hospital.
Are they correct? How many new mothers will stay, on average, in the
You may assume that the average number of births and the length of stay
of the new mothers will not change.
TR = 270per week
TT = 2/7 weeks
WIP = TT *TR = 270*2/7 = 540/7 = 77.1
On average there will be 77.1 new mothers in the unified hospital. No, it
will not decrease the total number of mothers in the hospital.
The manufacturer of TV sets observed that the higher the work in process the
higher the throughput rate, perhaps because when operators see a lot of WIP
they work faster. He also noticed that the relationship between WIP and
Throughput rate is:
Throughput rate (units per month) = 10,000 + 0.1WIP
The CEO of the TV Company knows that it is very important to have high
through put rate and he wants to achieve a through put rate of 20,000 units per
month. At the same time the CEO knows that long throughput time have a
negative impact on the performance of the company. He instructed the vice
president for Operation to reduce the throughput time to one month without
changing the throughput rate. When the company failed to achieve this goal
the vice president for operation was fired.
Can the firing of the vice president be justified? Explain your answer.
Suppose TR = 20,000 and TT = 1. Then WIP = TR*TT = 20,000 units.
But in this case
TR = 10,000 + 0.1WIP = 10,000+0.1*20,000 = 12,000 < 20,000.
Thus the firing was not justified.
To achieve the objective of TR = 20,000, the company must have WIP =
100,000. In this case the TT = 100,000/20,000 = 5month.