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MANAGEMENT SCIENCE MODELS AND TECHNIQUES 23

the construction the College is able to take a 20-year Cost ¼ 400 000 þ 0:25x
loan from the local bank (run by one of the College’s
Revenue = 2.50X
alumni). Under the terms of the loan, the College
would pay off the amount at a rate of E250 000 per
Breakeven occurs when cost ¼ revenue so we
year for 20 years. It is estimated that the car park
have:
would cost a further E150 000 per year to operate
and maintain regardless of how many cars used it. 400 000 þ 0:25x ¼ 2:50x
Students and staff using the car park during semes-
ter would be charged E1 for two hours parking. And solving for x gives x ¼ 177,777.8. For report-
Outside of semester, parking would be free. Initial ing purposes in practice we’d probably show this as
market research suggests that each car using the 177 800 or even 180 000. So, with the information
car park would stay on average for five hours. given, 180 000 cars a year would need to pay to
Semesters typically cover 25 weeks each year and use the car park for the project to breakeven. How-
ever, we can also provide some additional informa-
during semester the car park would be open from
tion that might help the President. Under the pro-
7.00 a.m. until 10.00 p.m. To offset pollution and
posal only cars using the car park during semester
carbon emissions, the College will contribute E0.25
would be charged. Semesters last 25 weeks so on
for each car using the car park to a carbon offset
average, we’d need around 7200 cars per week
scheme which will use the money for additional tree
(180 000 divided by 25) to breakeven. This also
planting. You have been asked about how many cars
equates to 1440 cars per day (assuming the College
would need to use the car park for it to breakeven.
operates five days per week). Clearly, at this stage
The President is also looking for any other advice
we’d need to go back to the President and ask
that you can offer.
whether the 1440 cars per day looked a realistic
Solution target. After all, we have no information on the size
of the College, the number of students attending per
Well, where to start? day, how many students travel by car and so on. We
It’s a typical, messy management science prob- can also go one stage further and speculate about
lem. There’s some data, we’ve been given a task the required size of the car park. With 1440 cars
which is fairly specific (work out breakeven for the required per day to breakeven, we know from the
car park) but we’ve also been given a fairly open- information given that each car stays an average of
ended remit in terms of any other advice we can five hours. That gives a total of 7200 hours of parking
offer. Clearly, in terms of Figure 1.2 we’re effectively each day (1440 x 5). The car park is open 15 hours
at the Modelling and Analysis stage so let’s do each day (from 7.00 a.m. until 10.00 p.m.) so divid-
what we can. We’ve been asked to determine the ing the total parking hours (7200) by the hours avail-
number of cars needed to use the proposed car able (15) the car park would require a minimum of
park for it to breakeven. Let’s collect together the 480 parking places. This is based on the assumption
data we have and build a basic breakeven model. that parking would be evenly spread through the 15
The College will incur two fixed costs if it goes hours the car park is open. This is an unrealistic
ahead with the project. There’s the annual repay- assumption but the only one we can make on the
ment to the bank of E250 000 and there’s the
information currently available. So, we’d need to
annual operating cost of E150 000. Both these
advise the President that it looks like the car park
costs remain constant, or fixed, no matter how
will need to be able to accommodate around 500
many cars use the car park. There’s also a variable
cars for breakeven. To summarize we can now
cost of E0.25 to the carbon offset scheme for each
inform the President that, based on the information
car using the car park. On the revenue side the available:
College will get E1 for every two hours of parking
during semester time with cars on average staying l The proposed car park will need around
for five hours. This equates to a revenue per car 180 000 cars a year paying an average of
per stay of E2.50. If we let x be the number of cars E2.50 per stay to break even.
using the car park over a year (the decision varia- l This equates to around 1440 cars per day
ble) we then have: during semester.

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