Facility Location Under Uncertainty - Location Science - page 194

8.6.3 Scenario Generation

In this chapter it has often been assumed that uncertainty can be represented by a set
of scenarios. In particular, it has been assumed that each scenario fully determines
all the uncertain parameters. In practice, defining the scenarios is itself a relevant
problem.
In some situations, scenarios are associated with driving forces (e.g., the political
conditions in a specific region, economic trends or some technological develop-
ments) which, in turn, influence the input of the model that supports the decision
making process. In this case, it is up to the decision maker to understand these
driving forces and the way they influence the input of the model. This understanding
leads to a complete definition of the scenarios. The reader should refer to Kouvelis
and Yu ( 1997 ) for a deeper discussion on this matter.
In other situations, namely in the context of stochastic programming, scenario
generation may be important either to instantiate large deterministic equivalent
models or to restrict the set of scenarios in a sampling approach used within a
solution procedure. The reader should refer to Dupacová et al. ( 2003 ), Høyland and
Wallace ( 2001 ), Di Domenica et al. ( 2007 ) and the references therein for further
details.
In the case of facility location problems, a short discussion on scenario generation
is presented by Kouvelis and Yu ( 1997 ) who discuss the issue in the context of a
network with uncertain node weights. Assuming a small set of possible values for
the demand of each node, one possibility is to take as a scenario each element of the
cartesian product of the sets for all nodes. Nevertheless, this is strongly discouraged
since the number of scenarios easily leads to intractable models. Instead, the
authors highlight that in many location problems the driving forces mentioned
above are the key element inducing uncertainty and thus should be identified and
taken into account. Typically, these forces induce high correlation between different
parameters. If a small number of such factors is identified, the number of scenarios
associated with them should be manageable.

8.6.4 Other Notes

One important research topic in facility location under uncertainty regards location-
inventory problems. These are problems in which location decisions are combined
with inventory management: uncertainty can hardly be disregarded in a realistic
modeling framework. This type of problems that was introduced by Daskin et al.
( 2002 ) and extended by Snyder et al. ( 2007 ) is of great relevance in complex systems
such as those arising in logistics. The reader should refer to Chap. 16 for further
details.