Geoscience Reference
In-Depth Information
Recently, Hinojosa et al. (
2014
) considered a problem with location decisions
made at a tactical or operational level, i.e., location decisions are
ex post
decisions.
The multi-product problem considered in this paper arises in the context of logistics
systems. Like in some of the above problems, the available distribution channels
correspond to a decision made before demand is known and result from some
contract or option. Furthermore, due to the limited capacity at the facilities, the
distribution channels contracted in advance may turn out to be insufficient for
covering the demand that occurs. In this case, a penalty is incurred (corresponding,
e.g., to a “last minute” and thus more expensive contract, to an outsourcing action,
or simply to an opportunity loss cost). The location decisions correspond to the
“activation” of existing equipments or facilities from where the commodities will
be shipped to the customers. Accordingly, this becomes a decision that can be
made only after demand is revealed. The authors formulate the extensive form of
the deterministic equivalent and solve it for instances with a realistic size using a
general solver.
In all of the above models, the recourse function is the expected value of the
second-stage problem. As mentioned before, this conveys a neutral attitude of the
decision maker towards risk. Location decisions are often strategic and involve
significant investments. Accordingly, a risk-averse attitude towards risk cannot be
disregarded as a possibility to be considered. One way of capturing such attitude
consists of applying a Markowicz type of approach in which the recourse function
is expanded to include a variability measure. Taking, as an example, model (
8.26
)-
(
8.31
) this consists of defining
Q.y/
D
E
ŒQ.y;/
Va r
ŒQ.y;/:
(8.71)
Such a modeling framework in facility location is far from new (see Jucker and
Carlson
1976
). Nevertheless, this type of approach has a clear disadvantage: it often
results in a non-linear large-scale mixed-integer model. Different possibilities for
overcoming this drawback are discussed by Louveaux (
1993
).
Stochastic discrete facility location problems have attracted much attention in
the recent years. Some papers not mentioned so far include those by Ravi and Sinha
(
2006
), Lin (
2009
), Wang et al. (
2011
) and Kiya and Davoudpour (
2012
).
In the context of logistics with particular emphasis to logistics network design,
we can also observe an increasing attention paid to stochastic facility location
problems (see Chap.
16
for further details). We can refer, among others, to Aghezzaf
(
2005
), Listes and Dekker (
2005
), Mo and Harrison (
2005
), Romauch and Hartl
(
2005
), Pan and Nagi (
2010
), Fonseca et al. (
2010
), and Nickel et al. (
2012
).
Recently, Alumur et al. (
2012
) explored the possibility of using a robustness
measure within a stochastic programming modeling framework. The authors apply
the idea to a hub location problem. Uncertainty is associated with two sets of
parameters. In both cases, uncertainty can be captured by a finite set of scenarios.
For one set of parameters, probabilistic information is assumed to be known which
is not the case for the other set. The authors propose a so-called robust-stochastic
model: for each scenario associated with the parameters that have no probabilistic
