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Cardoso et al. ( 2012 ) proposed a simulation model based on a short term decision
tree and long term Markov model in order to predict annual demand for long term
care services over the next few years.
Location-allocation models are commonly used for healthcare facility planning.
In some applications, the assumption that some patients will patronize the desig-
nated facility may be realistic. This may be forced by regulations dictating that
patients must be served from the facilities they are assigned to. However, in many
health service systems, patients have free choice of where to get service from. If this
is the case, then a user-choice model defining patient behavior should be considered.
One approach is to assume that patients patronize each facility with a certain
probability that depends on its location as well as on other relevant factors. For
example, Oliveira and Bevan ( 2006 ) used a gravity model to define the probability
that patients in some district or region choose some hospital.
An alternative approach is to assume that patients patronize their first choice
given by an optimization model. It is common to assume that patients patronize the
closest facility, i.e., to use the closest assignment constraints in ( 21.14 ). However,
although the distance to a facility is very important, it is not the only factor
influencing the choice of users. In fact, the waiting time at a facility is another
important factor that can be considered. Capturing congestion and its effects on
patient preferences is an interesting aspect to improve realism in healthcare facility
location models. In this case, the number of people using a facility determines
the waiting time at the facility. Since waiting time, in turn, affects the number of
people using the facility, models should incorporate equilibrium constraints. In the
equilibrium, allocation should ensure that patients are assigned to their best choice
and do not want to switch facilities. One such example was proposed by Chao et al.
( 2003 ) where resource allocation decisions for a public hospital network are made
in order to minimize the waiting time at the facilities. The resulting allocation is
incentive compatible, i.e., it is also optimal from the perspective of the patients.
Zhang et al. ( 2009 ) modeled the location of preventive healthcare facilities where
patients choose the facility with minimum total service time. The latter is defined
as the sum of travel time and waiting time at the facility. In turn, the waiting time
at a facility can be modeled using steady-state equations found in queuing theory.
The resulting formulation proposed by Zhang et al. ( 2009 ) is highly nonlinear and
a heuristic approach was suggested in that paper. Zhang et al. ( 2010 ) proposed a bi-
level model with equilibrium constraints for a preventive healthcare facility network
design problem. The solution approach uses a gradient projection method and a tabu
search heuristic.
21.2.2.4
Assumptions on Facility Types and Patient Flows: Hierarchical
Models
In most countries, healthcare systems are organized in hierarchical structures. There
are different types of facilities, such as physicians' offices, community health
centers, specialty clinics, and general hospitals. Notice that there is a hierarchy
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