A novel DEA model for hospital performance evaluation based on the measurement of efficiency, effectiveness, and productivity

Ghahremanloo, Mohammad; Hasani, Aliakbar; Amiri, Maghsoud; Hashemi-Tabatabaei, Mohammad; Keshavarz-Ghorabaee, Mehdi; Ustinovičius, Leonas

doi:10.2478/emj-2020-0001

Figures & Tables

Efficiency scores of hospitals in the period 2016 to 2018

Effectiveness scores of hospitals in the period 2016 to 2018

Productivity scores of hospitals in the period 2016 to 2018

Definition of sets, parameters, and variables

		DESCRIPTION
Sets	i ∈ I = {1,2,...,m}	Inputs
	r ∈ R = {l,2,...,s}	Outputs
	t ∈ G = {1,2,...,t}	Goals
	j ∈ D = {l,2,...,n}	DMUs
Parameters	xij${{x}_{ij}}$	i-th input of j-th DMU
	yrj${{y}_{rj}}$	r-th output of j-th DMU
	gtj${{g}_{tj}}$	t-th target of j-th DMU
	xio${{x}_{io}}$	i-th input of DMUo
	yro${{y}_{ro}}$	r-th output of DMUo
	gto${{g}_{to}}$	t-th target of DMUo
Variables	μj,λj${{\mu }_{j}},{{\lambda }_{j}}$	Dual variables of the problem
	β$\beta $	The variable added for linearization
	ti−${{t}^-_{i}}$	Total maximum of input losses
	tr+$t_{r}^{+}$	Total maximum of outputs that should have been produced with regard to the inputs, but they are not actually produced
	St−$S_{t}^{-}$	Total maximum of target deficiencies
	Sr+$S_{r}^{+}$	Total maximum of outputs that should have been produced with regard to the target values, but they are not actually produced
	ϕ$\phi $	Efficiency of DMU_o
	θ$\theta $	Effectiveness of DMU_o

Efficiency, Effectiveness and Productivity scores of hospitals in 2017

HOSPITALS	EFFICIENCY	EFFECTIVENESS	PRODUCTIVITY	μ_j	t1−$t_{1}^{-}$	t2−$t_{2}^{-}$	t3−$t_{3}^{-}$	t1+$t_{1}^{+}$	t2+$t_{2}^{+}$	λ_j	s1−$s_{1}^{-}$	s2−$s_{2}^{-}$	s1+$s_{1}^{+}$	s2+$s_{2}^{+}$
DMU₁	0.073	0.934	1.007	μ₅ = 0.566	0	26.19	12.80	47.17	68.22	λ₅ = 0.342 λ₈= 0.592	0	4.04	0	0
DMU₂	0.418	0.771	1.189	μ₅ = 1.265	3.26	0	31.16	31.76	49.76	λ₅ = 0.581 λ₈= 0.175	1.26	0	0	0
DMU₃	0.433	0.841	1.275	μ₅ = 0.697	54.02	0	72.02	23.42	48.41	λ₅ = 0.564 λ₈= 0.278	0	8.28	0	0
DMU₄	1	0.805	1.805	μ₄= 1	0	0	0	0	0	λ₅ = 0.532 λ₈= 0.273	0	4.27	0	0
DMU₅	1	1	2	μ₅= l	0	0	0	0	0	λ₅= 1	0	0	0	0
DMU₆	0.138	0.894	1.031	μ₇ = 1	15.06	0	14.91	39.36	60.84	λ₅ = 0.320 λ₈= 0.574	0	9.62	0	0
DMU₇	1	0.674	1.674	μ₇ = 1	0	0	0	0	0	λ₅ = 0.524 λ₈= 0.011	11.72	0	0	0
DMU₈	1	1	2	μ₈ = 1	0	0	0	0	0	λ₈= 1	0	0	0	0
DMU₉	0.201	0.898	1.098	μ₅ = 0.600	0	33.85	37.27	36.10	62.46	λ₅ = 0.396 λ₈= 0.502	0	21.09	0	0
DMU₁₀	0.733	0.850	1.583	μ₇ = 1.493	26.13	0	39.75	8.18	20.96	λ₅ = 0.727 λ₈= 0.123	0	23.29	0	0
DMU₁₁	0.298	0.958	1.256	μ₅ = 0.736	0	33.11	24.55	38.54	67.56	λ₅ = 0.552 λ₈= 0.406	0	14.96	0	0
Mean	0.572	0.875	1.447	--	--	--	--	--	--	--	--	--	--	--

Efficiency, Effectiveness and Productivity scores of hospitals in 2018

HOSPITALS	EFFICIENCY	EFFECTIVENESS	PRODUCTIVITY	μ_j	t1−$t_{1}^{-}$	t2−$t_{2}^{-}$	t3−$t_{3}^{-}$	t1+$t_{1}^{+}$	t2+$t_{2}^{+}$	λ_j	s1−$s_{1}^{-}$	s2−$s_{2}^{-}$	s1+$s_{1}^{+}$	s2+$s_{2}^{+}$
DMU₁	0.071	0.967	1.038	μ₇ = 1.032	41.46	0	35.76	42.10	69.68	λ₅ = 0.368 λ₈= 0.599	0	3.47	0	0
DMU₂	0.437	0.870	1.307	μ₇ = 1.294	8.62	0	30.41	26.69	53.93	λ₅ = 0.670 λ₈= 0.152	4.07	0	0	0
DMU₃	0.449	0.846	1.296	μ₇ = 1.260	221.24		190.18	2.90	33.39	λ₅ = 0.615 λ₈= 0.231	0	5.87	0	0
DMU₄	1	0.797	1.797	μ₄ = 1	0	0	0	0	0	λ₅ = 0.549 λ₈= 0.248	0	3.08	0	0
DMU₅	1	1	2	μ₅ = 1	0	0	0	0	0	λ₅ = 1	0	0	0	0
DMU₆	0.129	0.916	1.045	μ₇ = 0.927	19.08	0	15.14	32.67	60.12	λ₅ = 0.315 λ₈ = 0.601	0	10.50	0	0
DMU₇	1	0.783	1.783	μ₇ = 1	0	0	0	0	0	λ₅ = 0.614	14.39	6.29	0	0
DMU₈	1	1	2	μ₈ = 1	0	0	0	0	0	λ₈ = l	0	0	0	0
DMU₉	0.201	0.913	1.113	μ₇ = 1.119	32.96	0	53.28	33.37	65.66	λ₅ = 0.453 λ₈= 0.460	0	18.88	0	0
DMU₁₀	0.636	0.829	1.465	μ₇ = 1.314	11.91	0	28.60	10.95	36.33	λ₅ = 0.685 λ₈= 0.143	0	23.89	0	0
DMU₁₁	0.264	0.985	1.294	μ₇ = 1.235	48.29	0	47.09	30.52	67.21	λ₅ = 0.510 λ₈= 0.475	0	18.32	0	0
Mean	0.562	0.900	1.467	--	--	--	--	--	--	--	--	--	--	--

Statistical data of hospitals for 2018

HOSPITALS	INPUTS			OUTPUTS		GOALS
HOSPITALS	X1${{X}_{1}}$	X2${{X}_{2}}$	X3${{X}_{3}}$	Y1${{Y}_{1}}$	Y2${{Y}_{2}}$	G1${{G}_{1}}$	G2${{G}_{2}}$
DMU₁	2274	1118	1233	88.58	51.57	85	46
DMU₂	421	251	247	73.78	80.64	85	61
DMU₃	542	156	365	76.26	75.31	85	67
DMU₄	240	118	161	71.90	67.77	85	62
DMU₅	347	126	148	88.90	117.13	85	74
DMU₆	1108	607	551	84.07	45.41	85	52
DMU₇	151	94	69	48.26	71.88	85	58
DMU₈	269	189	194	93.29	14.17	85	23
DMU₉	814	424	526	83.15	59.56	85	69
DMU₁₀	298	175	169	74.32	82.32	85	94
DMU₁₁	724	358	408	89.68	66.48	85	68

Statistical data of hospitals for 2017

HOSPITALS	INPUTS			OUTPUTS		GOALS
HOSPITALS	X1${{X}_{1}}$	X2${{X}_{2}}$	X3${{X}_{3}}$	Y1${{Y}_{1}}$	Y2${{Y}_{2}}$	G1${{G}_{1}}$	G2${{G}_{2}}$
DMU₁	2269	1106	1182	91.43	51.89	85	46
DMU₂	416	247	257	73.61	76.92	85	61
DMU₃	539	154	333	81.98	76.02	85	67
DMU₄	239	115	145	78.46	71.90	85	62
DMU₅	339	119	154	96.95	128.19	85	74
DMU₆	1098	603	561	87.48	48.76	85	52
DMU₇	149	90	69	51.94	67.38	85	58
DMU₈	264	185	201	98.41	13.59	85	23
DMU₉	808	418	515	87.76	57.59	85	69
DMU₁₀	296	160	170	82.59	94.83	85	94
DMU₁₁	711	344	393	93.46	76.25	85	68

Statistical data of hospitals for 2016

HOSPITALS	INPUTS			OUTPUTS		GOALS
HOSPITALS	X₁	X₂	X₃	Y₁	Y₂	G₁	G₂
DMU₁	2172	1128	1170	91.02	49.85	85	46
DMU₂	401	232	240	72.83	67.97	85	61
DMU₃	501	156	304	90.05	82.52	85	67
DMU₄	231	110	149	83.34	67.62	85	62
DMU₅	310	118	145	90.60	125.94	85	74
DMU₆	972	563	550	91.36	51.27	85	52
DMU₇	133	90	69	51.32	59.86	85	58
DMU₈	263	154	202	94.26	13.24	85	23
DMU₉	742	398	475	89.58	58.17	85	69
DMU₁₀	294	159	169	86.03	98.30	85	94
DMU₁₁	651	318	370	84.66	53.87	85	68

Summary of the techniques in HPE

AUTHOR(S)	TECHNIQUE(S) USED	APPLICATION
Bannick and Ozcan (1995)	DEA	Hospitals of the US Department of Defence
Ersoy et al. (1997)	DEA	Turkish acute general hospitals
Ouellette and Vierstraete (2004)	DEA	Hospital emergency services in Montreal
O'Neill et al. (2008)	DEA	Systematic review of previous studies
Weng et al. (2009)	DEA	Iowa Hospital Association (IHA)
(Yawe, 2010)	DEA	Hospital Performance Evaluation in Uganda
Chuang et al. (2011)	DEA and regression tree	Taiwan's HOSPITAL
Mitropoulos et al. (2015)	Stochastic DEA and Bayesian analysis	Greek public hospitals
Rezaee and Karimdadi (2015)	Multi-group DEA	Iranian hospitals
Prakash and Annapoorni (2015)	DEA	Hospitals of Tamil Nadu State in India
Gholami et al. (2015)	DEA	US hospitals
Rouyendegh et al. (2016)	DEA-FAHP	Hospitals in Turkey
Chowdhury and Zelenyuk (2016)	DEA with truncated regression	Hospital services in Ontario
Lobo et al. (2016)	DEA	Brazilian hospitals
Khushalani and Ozcan (2017)	Dynamic Network DEA	USA HOSPITAL
Kang et al. (2017)	DEA	USA HOSPITAL
Johannessen et al. (2017)	DEA and panel analysis	Norwegian hospitals
Chen et al. (2017)	DEA	Pennsylvania hospitals
Haghighi and Torabi (2018)	BWM and DEA	A real general HOSPITAL
Zare et al. (2018)	DEA-Game theory	Iran hospitals
Omrani et al. (2018)	Fuzzy Clustering DEA-Game theory	Iran hospitals
This Study	New DEA Model	Hospitals of Tehran

Efficiency, Effectiveness and Productivity scores of hospitals in 2016

HOSPITALS	EFFICIENCY	EFFECTIVENESS	PRODUCTIVITY	μ_j	t1−$t_{1}^{-}$	t2−$t_{2}^{-}$	t3−$t_{3}^{-}$	t1+$t_{1}^{+}$	t2+$t_{2}^{+}$	λ_j	s1−$s_{1}^{-}$	s2−$s_{2}^{-}$	s1+$s_{1}^{+}$	s2+$s_{2}^{+}$
DMU₁	0.070	0.978	1.049	μ₅ = 0.568	0	24.41	12.48	44.07	67.84	λ₅ = 0.327 λ₈= 0.651	0	5.80	0	0
DMU₂	0.406	0.792	1.198	μ₅ = 0.646	0	39.62	26.17	22.15	47.39	λ₅ = 0.510 λ₈= 0.282	0	4.10	0	0
DMU₃	0.488	0.979	1.467	μ₅ = 0.790	54.46	0	67.09	17.75	50.16	λ₅ = 0.617 λ₈= 0.362	0	11.61	0	0
DMU₄	1	0.903	1.903	μ₄ = 1	0	0	0	0	0	λ₅ = 0.494 λ₈= 0.409	0	10.04	0	0
DMU₅	1	1	2	μ₅ = 1	0	0	0	0	0	λ₅ = 1	0	0	0	0
DMU₆	0.153	0.982	1.136	μ₅ = 0.580	0	35.70	17.64	35.65	63.56	λ₅ = 0.340 λ₈= 0.643	0	11.17	0	0
DMU₇	1	0.632	1.632	μ₇ = 1	0	0	0	0	0	λ₅ = 0.465 λ₈= 0.097	5.90	0	0	0
DMU₈	0.834	1	1.185	μ₄ = 0.008μ₅ = 0.050μ₇ = 0.281	0	0	14.23	0	20.95	λ₈ = l	0	0	0	0
DMU₉	0.214	0.966	1.180	μ₅ = 0.630	0	30.39	33.65	33.48	63.99	λ₅ = 0.403 λ₈= 0.563	0	23.89	0	0
DMU₁₀	0.758	0.942	1.701	μ₅ = 0.050μ₇= 0.281	0	42.20	28.36	0	19.12	λ₅ = 0.403 λ₈= 0.563	0	28.06	0	0
DMU₁₁	0.242	0.913	1.155	μ₅ = 0.587	0	19.61	18.30	29.51	58.85	λ₅ = 0.371 λ₈= 0.542	0	22.15	0	0
Mean	0.501	0.917	1.478	--	--	--	--	--	--	--	--	--	--	--

Names of evaluated hospitals

HOSPITALS	DMU_s
IMAM KHOMEINI HOSPITAL	DMU₁
AMIRALAM HOSPITAL	DMU₂
BAHARLOO HOSPITAL	DMU₃
BAHRAMI HOSPITAL	DMU₄
ARASH HOSPITAL	DMU₅
SHARIATI HOSPITAL	DMU₆
RAZI HOSPITAL	DMU₇
ROOZBEH HOSPITAL	DMU₈
SINA HOSPITAL	DMU₉
ZIYAIYAN HOSPITAL	DMU₁₀
CHILDREN'S MEDICAL CENTRE	DMU₁₁

Input and output indicators according to the research literature and expert opinion

	CRITERIA	DESCRIPTION	AUTHOR(S)
Input	Number of health workers (C₁)	Number of health workers working in the hospital including doctors, nurses and ...	Liao et al. (2019)
	Number of other staff (C₂)	Number of other staff working in hospital sub-units including Food and Drug Staff, Management, Service ...	Chowdhury and Zelenyuk (2016)
	Number of patient beds (C₃)	Numbers of beds specially designed for hospitalised patients or others in need of some form of health care.	Wang et al. (2016)
Output	Bed occupancy rate (C₄)	Calculated as the number of hospital bed days divided by the number of available hospital beds, multiplied by the number of days in a year.	Zhijun et al. (2014)
Output	Bed turnover rate (C₅)	Number of times that hospitalised patients used a hospital bed over a one-year period	Zhijun et al. (2014)

A novel DEA model for hospital performance evaluation based on the measurement of efficiency, effectiveness, and productivity

Figures & Tables

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Definition of sets, parameters, and variables

Efficiency, Effectiveness and Productivity scores of hospitals in 2017

Efficiency, Effectiveness and Productivity scores of hospitals in 2018

Statistical data of hospitals for 2018

Statistical data of hospitals for 2017

Statistical data of hospitals for 2016

Summary of the techniques in HPE

Efficiency, Effectiveness and Productivity scores of hospitals in 2016

Names of evaluated hospitals

Input and output indicators according to the research literature and expert opinion

Paradigm

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