Geoscience Reference
In-Depth Information
In order to capture predictable variations in the parameters of a facility location
problem, we often have to consider a dynamic or time-dependent model. From a
practical point of view, this type of model can be quite relevant because it allows for
embedding other decisions, such as those related with (1) inventory management,
(2) opening new facilities and removing existing ones, and (3) adjustment of the
operating capacities (which, from a cost point of view is often better than opening
new facilities). Even when the underlying parameters do not induce a dynamic
model, some other conditions may do so. For instance, if a budget constraint exists
say, per year, for installing new facilities, then locating the facilities over time may
be unavoidable.
When facility location decisions are to be made over time, it is important to define
the
planning horizon
beforehand. This is the time frame for which the decision
maker wishes to plan. Only a few papers have investigated facility location problems
over an infinite planning horizon. In this case, a static or a finite-horizon decision is
usually sought that is “the best” for an infinitely long planning horizon. Some works
in this direction include Chand (
1988
) and Daskin et al. (
1992
). Nevertheless, in
most cases, decision makers assume a finite planning horizon (see the recent review
paper by Arabani and Zanjirani Farahani
2012
). This is the case we consider in this
chapter.
When working with dynamic models, we can make a distinction between
continuous and discrete-time models. In the first case, there are no specific moments
for implementing the decisions; the best timing for performing changes in the
system is itself a decision to make. Some works exploring this feature include
Drezner and Wesolowsky (
1991
), Orda and Rom (
1991
), Puerto and Rodríguez-Chía
(
1999
), and Zanjirani Farahani et al. (
2009
). In our opinion, continuous-time facility
location problems are better addressed in the context of optimal control. Therefore,
in this chapter we do not focus on this type of problems. Instead, we consider a
discrete-time setting in which we have several moments in time for implementing
the decisions. These moments induce a partition of the planning horizon into several
time periods.
Facility location problems are often classified, according to the location space,
as being continuous, on a network, or discrete (Hamacher and Nickel
1998
). In
recent years, due to successful applications of location theory to many areas, discrete
models have increasingly played a major role. For this reason, in this chapter, special
emphasis is given to this type of problems.
The remainder of the chapter is organized as follows: in Sects.
11.2
and
11.3
we
present a brief overview of continuous and network multi-period facility location
problems, respectively. In Sects.
11.4
and
11.5
we focus on discrete problems.
Section
11.6
is used for introducing the value of the multi-period solution. Finally,
in Sect.
11.7
, we discuss some challenges and future trends on the topic.
