Medical centers location and specialists’ allocation: a healthcare planning case study

Almeida, João Flávio de Freitas; Pinto, Luiz Ricardo; Conceição, Samuel Vieira; Campos, Francisco Carlos Cardoso de

doi:10.1590/0103-6513.20190006

João Flávio de Freitas Almeida ^* * joao.flavio@dep.ufmg.br

Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil

https://orcid.org/0000-0002-3884-217X

Luiz Ricardo Pinto

Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil

https://orcid.org/0000-0001-5082-9595

Samuel Vieira Conceição

Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil

https://orcid.org/0000-0002-8090-264X

Francisco Carlos Cardoso de Campos

Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brasil

https://orcid.org/0000-0003-2172-0181

* joao.flavio@dep.ufmg.br

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Figure 1
Demographic pyramid shows fast aging population of MG from 2000 to 2010 (Instituto Brasileiro de Geografia e Estatística, 2019).

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Figure 2
The 27 health units (Specialized Care Centers and a Medical Center) dispersed over the state area. Source: Software Tabwin 2019.

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Figure 3
Municipalities selected (43, 45, and 64) for patients’ displacement of at most 180, 120, and 80 km, respectively, to meet health care on medical centers. Municipalities in purple (scenarios 2 a 3) are exception requiring special treatment.

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Figure 4
Municipalities selected in black and green enable the patients’ displacement of at most 80 km to meet health care on medical centers. Municipalities in purple are exception requiring special treatment.

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Figure 5
Additional hiring of medical specialties for patients' maximum displacement of 80 km.

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Figure 6
Additional equipment for patients' maximum displacement of 80 km.

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Figure 7
Financial results of overall annual costs of 64 medical centers and equipment maintenance, and a comparison with social cost.

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Figure 8
Municipalities selected to operate 70, 60, and 50 medical centers. Since 27 health units (in black) are fixed and available, the state would have to install 43, 33, and 23 new CEM.

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Figure 9
Municipalities (70) selected in black (27 CEAE) and blue (43 CEM). Patients’ average displacement of 156 km. All municipalities demand are covered.

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Figure 10
Financial results of overall annual costs of 70 medical centers and equipment maintenance, and a comparison with social cost.

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Figure 11
Financial results of overall annual costs of 41 medical centers, equipment maintenance, and social cost.

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Figure 12
General view of the web-based system interface (text in Portuguese). Location and demand coverage of new 20 MRI scanners considering available MRI scanners on MG for a maximum distance of 150 km. (the connections show municipalities and services of the northern region of the state). Source: Nescon (2018).

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Figure 3
Municipalities selected (43, 45, and 64) for patients’ displacement of at most 180, 120, and 80 km, respectively, to meet health care on medical centers. Municipalities in purple (scenarios 2 a 3) are exception requiring special treatment.

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Figure 4
Municipalities selected in black and green enable the patients’ displacement of at most 80 km to meet health care on medical centers. Municipalities in purple are exception requiring special treatment.

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Figure 5
Additional hiring of medical specialties for patients' maximum displacement of 80 km.

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Figure 6
Additional equipment for patients' maximum displacement of 80 km.

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Figure 7
Financial results of overall annual costs of 64 medical centers and equipment maintenance, and a comparison with social cost.

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Figure 8
Municipalities selected to operate 70, 60, and 50 medical centers. Since 27 health units (in black) are fixed and available, the state would have to install 43, 33, and 23 new CEM.

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Figure 9
Municipalities (70) selected in black (27 CEAE) and blue (43 CEM). Patients’ average displacement of 156 km. All municipalities demand are covered.

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Figure 10
Financial results of overall annual costs of 70 medical centers and equipment maintenance, and a comparison with social cost.

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Figure 11
Financial results of overall annual costs of 41 medical centers, equipment maintenance, and social cost.

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Figure 12
General view of the web-based system interface (text in Portuguese). Location and demand coverage of new 20 MRI scanners considering available MRI scanners on MG for a maximum distance of 150 km. (the connections show municipalities and services of the northern region of the state). Source: Nescon (2018).

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Figure A1
MRIs procurement for scenario [3].

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Figure A2
CTs procurement for scenario [3].

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Figure A3
Mammograms procurement for scenario [3].

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Figure A4
Ultrasound procurement for scenario [3].

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Figure A5
Ultrasound Doppler procurement for scenario [3]. Specialists hiring suggestion for scenario [3].

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Figure A6
Andiology hiring suggestion for scenario [3].

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Figure A7
Cardiology hiring suggestion for scenario [3].

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Figure A8
Endocrinology hiring suggestion for scenario [3].

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Figure A9
Gynecology hiring suggestion for scenario [3].

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Figure A10
Mastology hiring suggestion for scenario [3].

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Figure A11
Nephology hiring suggestion for scenario [3].

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Figure A12
Ophthalmology hiring suggestion for scenario [3].

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Figure A13
Pediatrics hiring suggestion for scenario [3].

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Figure A14
Urology hiring suggestion for scenario [3].

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Table 1
Input parameters of the facility location and resource allocation model.

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Table 2
Input variables of the facility location and resource allocation model.

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Table 3
Proposed sequence for installing medical centers in MG, and improve CEAE’s capacity.

(1.0)

(1.1)

(1.2)

(1.3)

(1.4)

(1.5)

(1.6)

(1.7)

(1.8)

(1.9)

(1.10)

(1.11)

(1.12)

(1.13)

(1.14)

(1.15)

(1.16)

(1.17)

Parameters	Description	Unit
$B_{i}$	Inhabitants on municipality i	Inhabitants
$B_{m i n}$	Minimum number of inhabitants for a candidate municipality	Inhabitants
$D_{i j}$	Distance between municipalities (i, j)	Km
$D M_{e i j}$	Maximum displacement (i,j) a patient can take to meet specialty e	Km
$J = N_{i}$	Candidate destinations of municipality i.	Municipality
$E_{j}$	Global efficiency of services provided on municipality j	Percent
$P_{j}$	Candidate municipality j that received a Medical Center	Binary
$H E_{i e}$	Demand of patients of municipality i by (full time equivalent) specialty e	FTE (40h)
$H Q_{i q}$	Demand of patients for exams on equipment q (ex/1000inhab/year)	Exams
$K Q_{i q}$	Available capacity of equipment q on municipality i	Exams
$K_{q}$	Nominal annual production capacity of equipment q	Exams
$K E_{i e}$	Availability of physicians of specialty e municipality i	Physicians
$F$	Minimum number of secondary health care facilities (Medical Centers)	Facilities
$P_{q}$	Minimum number of additional equipment of type q	Equipment
$C I$	Average annual cost of a Medical Center facility operations	Real (R$)
$C Q_{q}$	Average acquisition cost of equipment q	Real (R$)
$S_{e}$	Average annual salary of medical specialty e	Real (R$)
$C D_{i j}$	Average annual cost estimate of patients displacement from (i,j)	Real (R$)
$α_{e i j}$	Average demand decay estimate due distance increase (i,j)	Percent
$M_{e q}$	Matrix assignment defining if equipment q is used by specialty e	Binary

Variables	Description	Unit
$x_{e i j}$	If demand of municipality i is met by specialty e on municipality j	Binary
$y_{q i j}$	If demand of municipality i is met by equipment q on municipality j	Binary
$z_{j}$	Decide if candidate municipality j receive (or not) a healthcare unit	Binary
$w q_{q j}$	Number of equipment q to be acquired to municipality j	Integer
$w e_{e j}$	Number of FTE physicians of specialty e to be hired to municipality j	Integer

Sequence	Municipality	SVI	Sequence	Municipality	SVI
1º	Bom Despacho	0.18	36º	Unaí	0.288
2º	Extrema	0.185	37º	Sarzedo	0.31
3º	Araxá	0.187	38º	Pompéu	0.31
4º	Guaxupé	0.189	39º	Nanuque	0.32
5º	Nova Serrana	0.199	40º	Salinas	0.324
6º	João Monlevade	0.202	41º	Bocaiúva	0.331
7º	Timóteo	0.204	42º	Várzea da Palma	0.34
8º	Uberaba	0.206	43º	Guanhães	0.353
9º	Formiga	0.207	CEAE 1º	São Lourenço	0.164
10º	Passos	0.213	CEAE 2º	Santo Antônio do Monte	0.178
11º	Machado	0.216	CEAE 3º	Lavras	0.181
12º	Alfenas	0.217	CEAE 4º	Viçosa	0.187
13º	Ouro Fino	0.217	CEAE 5º	Patos de Minas	0.194
14º	Monte Carmelo	0.22	CEAE 6º	São João del Rei	0.201
15º	Ituiutaba	0.222	CEAE 7º	Itabirito	0.207
16º	Três Pontas	0.222	CEAE 8º	Muriaé	0.216
17º	Oliveira	0.224	CEAE 9º	Frutal	0.229
18º	Andradas	0.225	CEAE 10º	Sete Lagoas	0.233
19º	Uberlândia	0.225	CEAE 11º	Campo Belo	0.235
20º	Visconde do Rio Branco	0.226	CEAE 12º	Governador Valadares	0.243
21º	Piumhi	0.237	CEAE 13º	Patrocínio	0.246
22º	São Gotardo	0.241	CEAE 14º	Itabira	0.248
23º	Carangola	0.246	CEAE 15º	Juiz de Fora	0.248
24º	Ponte Nova	0.247	CEAE 16º	Manhuaçu	0.254
25º	Boa Esperança	0.248	CEM 17º	Pirapora	0.259
26º	Ouro Branco	0.251	CEAE 18º	Leopoldina	0.262
27º	Três Marias	0.253	CEAE 19º	Teófilo Otoni	0.302
28º	Congonhas	0.258	CEAE 20º	Janaúba	0.313
29º	Barão de Cocais	0.261	CEAE 21º	Diamantina	0.318
30º	Iturama	0.264	CEAE 22º	Taiobeiras	0.329
31º	Três Corações	0.27	CEAE 23º	Capelinha	0.337
32º	Belo Horizonte	0.276	CEAE 24º	Ribeirão das Neves	0.358
33º	Caratinga	0.276	CEAE 25º	Brasília de Minas	0.405
34º	Curvelo	0.277	CEAE 26º	Januária	0.426
35º	Paracatu	0.278	CEAE 27º	Jequitinhonha	0.442

Medical centers location and specialists’ allocation: a healthcare planning case study

Abstract