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Table 3 Description of indices, parameters & variables

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

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