Geoscience Reference
In-Depth Information
in Table
17.2
, and include Aboolian et al. (
2009
), Berman and Drezner (
2007
),
Boffey et al. (
2010
), Drezner and Drezner (
2011
), Hamaguchi and Nakade (
2010
),
Marianov et al. (
2009
), Marianov and Serra (
2011
), and Wang et al. (
2002
).
Here “limited resources” means that the number of facilities to be located and the
total available service capacity are specified through constraints, rather than through
the objective function term (
17.47
). “Customer service” is typically defined as the
combination of travel and congestion costs; thus the objective function typically
includes terms (
17.45
)and(
17.46
). Since the congestion cost term (
17.46
) only
measures the aggregate congestion, some authors (see Boffey et al.
2010
;Marianov
et al.
2009
; Marianov and Serra
2011
and Wang et al.
2002
) impose service level
constraints to ensure that congestion is controlled at each facility. Service-objective
models assume inelastic demand, so the revenue term is missing in the objective
as all available customer demand is assumed to be “covered” (even though some
models do allow for demand losses due to congestion, these losses are controlled
through service level constraints). Thus, all customers must be assigned to facilities
and thus constraint (
17.55
) is specified as equality.
The models of this class are either of NR type (directed assignment, no customer
response) or AR type with distance-based utility function (customers travel to
the closest open facility). An interesting exception is the use of AR model with
proportional allocation and exponential utility (
17.29
) by Drezner and Drezner
(
2011
) (though they do not comment on the existence and uniqueness of the
equilibrium solution, it is in fact assured by the results cited earlier).
While the constraint set for service-objective models is quite similar to that
of coverage-oriented models (in fact, it is somewhat simpler since the coverage
constraints and, in some cases, service level constraints are missing), inclusion
of the congestion term in the objective leads to a non-linear model for which
finding exact solutions is problematic. This difficulty is further compounded when
the queues at the facilities are of multi-server type and/or have non-Markovian
service times: in these cases exact closed-form expressions for the congestion-
related performance measures are either not available, or are quite complex,
requiring a separate procedure to evaluate the congestion levels for each set of
values of the facility location and customer allocation decision variables. For this
reason, the proposed solution methods are all heuristic-based, typically employing
meta-heuristic approaches such as tabu search, simulated annealing, and genetic
algorithms.
Service-objective models become significantly more complicated when capac-
ities of facilities are allowed to be flexible (i.e., when
i
are not assumed to
be identical at all facilities). Most of the published models assume identical
capacities, with Aboolian et al. (
2009
) and Berman and Drezner (
2007
)being
notable exceptions.
