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

6. Conclusion

In this study, we consider a capacitated facility location problem with time-dependent
preferences. Inspired by previous literature, we reformulate the problem into a single-

level mixed integer problem with the objective to maximize the total number of customers
served. Since the problem is NP-hard, we develop two greedy-based heuristic algorithms
with maximum flow network and flow estimation, respectively. The latter is significantly
more time efficient. Through our numerical study, we find that our second algorithm can

provide near-optimal solutions in reasonable much shorter time.
There are several ways to extend this study. In particular, one decision that is missing
in our model is for the decision maker to determine the equipment/services to be delivered
in each facility. For example, if the decision maker is building sport facilities, it is the

job of this decision maker to allocate the limited space to basketball courts, swimming
pools, fitness rooms, etc., which certainly will affect potential customers’ preference over
different facilities. Extending our model and algorithm to include this feature will make
them more applicable in practice. Another research direction is to investigate the proposed

algorithm from a more theoretical perspective to see whether there is a worst-case
performance guarantee. An investigation on this may generate analytical contributions to
the literature of discrete optimization.

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