Location Problems in Healthcare - Location Science - page 539

A simple participation function can be defined as follows: ij D 1 c ij =c max
if c ij is less than or equal to c max and ij D 0 otherwise, where c max is the pre-
determined maximum distance between a facility i 2 I and a district j 2 J that
can be covered by that facility. The total weighted participation function is the
following:

X X

d j ij x ij : (21.2)

i2I j2J

￿ Maximize equity in access. There is an increasing interest in incorporating equity

in healthcare facility location applications. Nevertheless, there is no agreement
on how to define equity, and various definitions have been used in the literature.
For a review of these definitions, see Marsh and Schilling ( 1994 ). Commonly
used equity objectives are: minimize the maximum distance that patients must
travel (Mitropoulos et al. 2006 ; Güne¸setal. 2014 ), minimize deviations from a
standard distance (Smith et al. 2009 , 2013 ), minimize differences of utilization
from a national norm (Oliveira and Bevan 2006 ), or minimize standard deviation
of the distribution of the allocated populations to healthcare facilities (Günes
et al. 2014 ).

All of these objectives are important, and it may be difficult to choose one
in realistic applications. Therefore, multi-criteria models have gained popularity
in recent years. We note that the equity criterion is commonly considered in
combination with the efficiency (access) criterion since the equity objectives alone
can produce undesirable solutions (Smith et al. 2013 ). The reader can refer to
Mayhew and Leonardi ( 1982 ), Cho ( 1998 ), Mitropoulos et al. ( 2006 ), and Smith
et al. ( 2009 , 2013 ) for examples on applications with bi-criteria equity-efficiency
objectives. Stummer et al. ( 2004 ) developed a multi-objective model to determine
the size and location of departments in facilities within a given network of hospitals.
The objectives considered are: minimize total access cost for patients, minimize
total cost of the network, minimize number of patients rejected due to low capacity,
and minimize total number of changes required in the network. Güne¸setal.
( 2014 ) considered the objectives of minimizing access cost for patients, maximizing
coverage, maximizing participation, and maximizing equity among physicians.
A common solution approach in multi-criteria problems is to construct efficient
solution sets to inform decision makers (cf. Stummer et al. 2004 ; Smith et al. 2013 ;
Güne¸setal. 2014 ). In bi-criteria problems, the efficient frontier can be found by
solving the problem with one of the objectives and then including the obtained
result for the objective value as a constraint while solving for the second objective
(cf. Ehrgott 2005 ; Smith et al. 2013 ). Another approach, which is not restricted to
the bi-criteria case, is to include all criteria in the objective function with different
weights. For example, Bruni et al. ( 2006 ) modeled the location of transplant centers
considering distance, waiting list, and maximum waiting list (as a proxy for equity)
with different weights in the objective.