Geoscience Reference
In-Depth Information
this case, the customers' requests for service have a probabilistic behavior and
a facility or equipment may be busy when a new request arrives. This is the
topic addressed in Chap. 17. In the current chapter, we focus on aspects emerging
from uncertainty associated with the parameters of a facility location problem. We
show how uncertainty can be embedded in the models built for supporting the
decision making process. For illustrative purposes, we consider several well-known
facility location problems. We focus on discrete models. This is motivated by the
practical relevance that such models have acquired in the recent decades due to
many successful applications of facility location theory to areas such as logistics,
transportation and routing (see Chap.
1
).
In the following sections we assume that the reader is familiar with basic
concepts from robust and stochastic optimization. Important references in these
fields include Birge and Louveaux (
2011
) and Shapiro et al. (
2009
) (for stochastic
programming) and Kouvelis and Yu (
1997
) and Ben-Tal et al. (
2009
) (for robust
optimization).
The remainder of this chapter is organized as follows. In the next section, we
discuss general aspects related with uncertainty. In Sect.
8.3
, we address robust
facility location problems. In Sect.
8.4
, we focus on stochastic programming models.
Section
8.5
is devoted to chance-constrained problems. In Sect.
8.6
we discuss some
challenges and give suggestions for further reading. The chapter ends with a short
conclusion.
8.2
Uncertainty Issues
Basic information underlying a facility location problem includes demand levels,
travel time or cost for supplying the customers, location of the customers, presence
or absence of the customers, and price for the commodities. Uncertainty may occur
in one or several of these parameters.
One crucial aspect when dealing with uncertainty regards its representation.
First, uncertain parameters may be discrete or continuous. Second, if probabilistic
information is available, the uncertain parameters can be represented through
random variables. In this case, using the well-known characterization proposed by
Rosenhead et al. (
1972
), we say that we are making a decision under risk and we can
resort to stochastic programming models and methods for dealing with the problem.
If this is not the case, we are making a decision under uncertainty and a robustness
measure is usually considered for evaluating the performance of the system. It is
important to note that the existence of a probabilistic description for the uncertainty
does not prevent the use of some robustness measures, as it will be detailed in the
next section.
