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NTU Management Review Vol. 33 No. 3 Dec. 2023

among others.
A further extension for customer is to incorporate the time dependency of preference.
In many cases, once a service facility is built, it is open to customers throughout a day.
However, for a single facility, a customer may have different preferences over different

activity sessions in a day. For example, while several citizens may be willing to exercise
in a particular park, some may prefer to exercise in the morning while some may prefer
to do so in the evening. Suppose that a day is split into three activity sessions: morning,

afternoon, and evening. To calculate the total number of citizens that may exercise in
the park in a day, we cannot just multiply that number in any one of the three sessions
by three. Instead, a model with three activity sessions must be constructed to correctly
estimate the benefit of building that park. In short, taking the time factor into account is
needed to make a model much closer to reality.

One major motivating applications of our proposed model is to build public sport
facilities. With medical technology progressing and economic growth in recent years,
population aging has become a worldwide issue to be addressed. To improve the welfare

of an aging society, it is suggested for a government to increase the frequency and strength
of regular exercise of the elder (Laforge, Rossi, Prochaska, Velicer, Levesque, and
McHorney, 1999). To make this happen, constructing enough public sport facilities that
are appropriate to the elder is crucial. To make a good construction decision, the first step
is being able to estimate the benefit of building some facilities, which may be measured by

the number of elders using built facilities. An important feature of this problem is that the
government cannot specify a facility for a citizen; instead, each citizen will make her/his
own choice. Whether a construction plan may really benefit citizens cannot be determined

if customer is ignored. Note that typically one citizen only goes out for exercise once in
a day, different elders prefer different time for exercise, and a facility is generally open
throughout a day. Therefore, if the government neglects the elders’ time preferences
and assumes that all elders will compete for the capacitated facility at the same time,
the effective capacity of a facility becomes underestimated. Formulating a model that

includes time-dependent customer and multiple activity sessions in a day is thus required
for this construction plan. In addition, to the best of our knowledge, no previous study
simultaneously takes aforementioned factors into account. Therefore, our investigation

and consideration of a capacitated facility location problem along with customers’ time-

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