Geoscience Reference
In-Depth Information
21.2.2.1
Modeling Capacity
Explicit modeling of capacity decisions is facilitated by a resource-based view
of facilities. For example, the capacity of a health center is determined by the
number of physicians assigned to that clinic. Similarly, the number of beds is
a significant determinant for hospital capacity. Many healthcare facility location
models consider the amount of resources in facilities also as decision variables. For
example, Güne¸sandYaman(
2009
) modeled the resource re-allocation problem for
a hospital network with beds as resources. Oliveira and Bevan (
2006
), Griffin et al.
(
2008
), Zhang et al. (
2009
,
2010
) and Güne¸setal.(
2014
) modeled the staff in each
facility as a decision variable. In addition, these models can incorporate the decision
about the services to offer in each facility (cf. Oliveira and Bevan
2006
;Griffinetal.
2008
). With R denoting the set of resource types and S the set of service types, such
a model can be built by defining resource sets R
s
R required to serve demand for
service s
2
S. To this end, let
sr
be the amount of resource r that is utilized to serve
a patient requiring service s. Then, the decisions concerning the capacity (number
of patients that can be served) for service s in location i, q
is
, and the amount of
resource r in location i,
w
ri
, are modeled by the following constraints:
X
sr
q
is
w
ri
8
i
2
I;r
2
R
(21.10)
s2SWr2R
s
X
d
j
x
ijs
q
is
8
i
2
I;s
2
S
(21.11)
j2J
X
x
ijs
D
1
8
j
2
J;s
2
S;
(21.12)
i2I
where x
ijs
is a binary variable defining the assignment of patients for service s from
district j to the facility at location i.
In some cases, there may be restrictions on the minimum number of patients
assigned to a facility. In general, such restrictions are motivated by economies of
scale arguments. For healthcare services, there may also be regulations on minimum
number of patients assigned to a physician because for some specialties (such as
mammography interpretation or surgery), regular practice is important to maintain
high service quality. See Verter and Lapierre (
2002
), Güne¸sandYaman(
2009
),
Mestre et al. (
2012
), Güne¸setal.(
2014
) for examples on how to incorporate such
type of constraints.
21.2.2.2
Assumptions on Allocation
The classical p-median formulation assumes that when x
ijs
D
1, all the population
in district j is served from the facility at location i for service s. This single
assignment assumption may be appropriate when it is desired to provide the same
