Modeling hospital infrastructure by optimizing quality, accessibility and efficiency via a mixed integer programming model

Table 3 Description of indices, parameters & variables

Notation	Description
Indices
d	Diagnosis group
f	Facility
p	Zip code area
q	Zip code area
Parameters
a _d	The slope of the (linear) volume-outcome relationship of diagnosis group d
b _d	The constant term of the (linear) volume-outcome relationship of diagnosis group d
EQ	Euros per QALY
ET	Travel expenses per time unit
M	Big number [1,000,000]
maxt _d	The maximum acceptable travel time for diagnosis group d
minu _f	Minimum utilization per facility f
NP _d	The number of patients per diagnosis group d
$N P p, d D$	The number of patients per diagnosis group d and zip code p
NV _d	The total number of visits per patient having diagnosis d
TT _p,q	The driving time from zip code p to zip code q
U _fd	The amount of resources each patient within diagnosis group d makes use of facility f
Dependent variables
Quality _d	Total quality achieved for diagnosis group d [euros]
Travel _d	Total travel costs made for diagnosis group d [euros]
NL _d	The number of locations treating diagnosis group d
Decision variables
X _p	Whether a health care location is established in zip code p
Z _q,d	Whether diagnosis group d is treated at potential hospital location with zip code q
Y _p,q,d	Whether for diagnosis group d patients from zip code p are assigned to potential hospital location with zip code q