Maximizing the efficiency of residents operating room scheduling: a case study at a teaching hospital

Assad, Daniel Bouzon Nagem; Spiegel, Thais

doi:10.1590/0103-6513.20190025

Daniel Bouzon Nagem Assad ^* * danielbouzon@gmail.com

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, Brasil

Universidad Politécnica de Madrid, Madrid, España

http://orcid.org/0000-0003-3911-4323

Thais Spiegel

Universidade do Estado do Rio de Janeiro, Rio de Janeiro, RJ, Brasil

http://orcid.org/0000-0002-7801-8492

* danielbouzon@gmail.com

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Figure 1
Synthesis of operating room planning literature review. Source: adapted from Assad (2017)Assad, D. B. N. (2017). Planejamento e programação de cirurgias eletivas: estudo de caso em um hospital universitário (Master’s dissertation). Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro..

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Figure 2
Optimized planning steps for operation room management. Source: adapted from Barbagallo et al. (2015)Barbagallo, S., Corradi, L., de Ville de Goyet, J., Iannucci, M., Porro, I., Rosso, N., Tanfani, E., & Testi, A. (2015). Optimization and planning of operating theatre activities: an original definition of pathways and process modeling. BMC Medical Informatics and Decision Making, 15(1), 38. http://dx.doi.org/10.1186/s12911-015-0161-7. PMid:25982033.
http://dx.doi.org/10.1186/s12911-015-016... .

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Table 1
Optimizing hospital processes models: classifications and categories.

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Table 2
Decision levels and type of problems in operating room planning.

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Table 3
Synthesis of literature review on MSSP.

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Table 4
Minimum amount of procedures defined by the current legislation.

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Table 5
Classification of procedures regarding category and size.

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Table 6
Relation between types of surgery and necessary inputs.

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Table 7
Amount of surgery instruments available at the CME.

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Table 8
Number of residentes by type.

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Table 9
Statement of Master Surgical Schedule model indexes.

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Table 10
Statement of Master Surgical Schedule model variables.

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Table 11
Statement of Master Surgical Schedule model parameters.

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Table 12
Weights and business rules by scenario.

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Table 13
Model results by scenario.

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Classifications	Categories
Type of model	Computer simulation
	Descriptive
	Analytical
Type of problem	Process Design
	Capacity problem
	Scheduling problem
Kind of department	Operating room
	Inpatient
	Outpatient
	Imaging diagnosis
	Other
Objective of study	Designing a model
	Comparing models
	Using a model
	Critiquing/ proposing a model
Outcome measures	Waiting times
	Needed capacity
	Cost
	Utilization
	others
Validated in practice	Yes/no
Generic	Yes/no

Decision level	Planning horizon	Type of problem	Decisions taken
Strategic	1 year	Case mix Problem (CMP)	Decide which surgeries will be offered by the hospital
Tactical	1, 2 or 3 months	Master Surgical Schedule Problem (MSSP)	Define which surgeon (or specialty) will be allocated in which rooms in a time horizon.
Operational Off-line	Week or day	Surgical Case Assigment Problem (SCAP)	Allocate each surgeon to each surgery on days defined by the MSSP and define order of execution.
Operational Online	Hours	Rescheduling	Rescheduling when unplanned events occur (dealing with real time variabilities).

Authors	Objective of the model	Constraints considered	Type of data utilized	Planning horizon	Formulation of the optimization model ¹ 1 Optimization models may be formulated in diferent ways, among which stand out the following: integer programming (IP), mixed integer linear programming (MILP), integer quadratic programming (IQP), and mixed integer non-linear programming (MINLP);	Type of solution ² 2 Depending on the complexity of the modeling and/or the size of the model, finding the optimal solution, considering all combinations of the feasible solutions space (exact solution) may result in very long resolution times. To avoid long solution times, many authors propose faster solution methods (heuristics), that disconsider part of the feasible solutions space to obtain a solution (not necessarily the optimal one).
Persson & Persson (2007)Persson, M., & Persson, J. A. (2007). Optimization modelling of hospital operating room planning: Analyzing strategies and problem settings. In Operational Research for Health Policy: Making Better Decisions, 31st Annual Conference of the European Working Group on Operational Research Applied to Health Services (pp. 137). Bern, Switzerland: Peter Lang International Academic Publishers.	Minimize costs related to not operating on a patient considering their priority	sugery room, human resources, and beds	Real data	Weekly	MILP	Exact
Van Oostrum et al. (2008)Van Oostrum, J. M., Van Houdenhoven, M., Hurink, J. L., Hans, E. W., Wullink, G., & Kazemier, G. (2008). A master surgical scheduling approach for cyclic scheduling in operating room departments. OR-Spektrum, 30(2), 355-374. http://dx.doi.org/10.1007/s00291-006-0068-x. http://dx.doi.org/10.1007/s00291-006-006...	Minimize room allocation and peaks of bed occupation	sugery room, human resources, and beds	Real data	Weekly	MILP	Heuristic
Beliën et al. (2009)Beliën, J., Demeulemeester, E., & Cardoen, B. (2009). A decision support system for cyclic master surgery scheduling with multiple objectives. Journal of Scheduling, 12(2), 147-161. http://dx.doi.org/10.1007/s10951-008-0086-4. http://dx.doi.org/10.1007/s10951-008-008...	Minimize the peak of bed occupation	sugery room, human resources, and beds	Real data	Weekly	MILP and IQP	Exact and heuristic
Wang et al. (2010)Wang, Y., Tang, J., & Qu, G. (2010). A genetic algorithm for solving patient-priority-based elective surgery scheduling problem. In Y. Wang, J. Tang, & G. Qu. Life system modeling and intelligent computing (pp. 297-304). Berlin: Springer. http://dx.doi.org/10.1007/978-3-642-15597-0_33. http://dx.doi.org/10.1007/978-3-642-1559...	Maximize prioritary surgeries controlling staff workload	sugery room and human resources	Real data	Weekly and offline daily	MILP	Heuristic
He et al. (2012)He, B., Dexter, F., Macario, A., & Zenios, S. (2012). The timing of staffing decisions in hospital operating rooms: incorporating workload heterogeneity into the newsvendor problem. Manufacturing & Service Operations Management: M & SOM, 14(1), 99-114. http://dx.doi.org/10.1287/msom.1110.0350. http://dx.doi.org/10.1287/msom.1110.0350...	Minimize costs related to human resources (nursing)	sugery room and human resources (nursing)	Real data	Weekly	MILP	Exact
Day et al. (2012)Day, R., Garfinkel, R., & Thompson, S. (2012). Integrated block sharing: a win–win strategy for hospitals and surgeons. Manufacturing & Service Operations Management: M & SOM, 14(4), 567-583. http://dx.doi.org/10.1287/msom.1110.0372. http://dx.doi.org/10.1287/msom.1110.0372...	Maximize revenue and staff satisfaction	sugery room and human resources	Real data	Biweekly	MILP	Heuristic
Jeang & Chiang (2012)Jeang, A., & Chiang, A. J. (2012). Economic and quality scheduling for effective utilization of operating rooms. Journal of Medical Systems, 36(3), 1205-1222. http://dx.doi.org/10.1007/s10916-010-9582-0. PMid:20814721. http://dx.doi.org/10.1007/s10916-010-958...	Minimize idle time and overtime	sugery room and human resources	Real data	Biweekly	MINLP	Exact
Paul & Jotshi (2013)Paul, J. A., & Jotshi, A. (2013). Efficient operating room redesign through process improvement and optimal management of scheduled and emergent surgeries. International Journal of Mathematics in Operational Research, 5(3), 317-344. http://dx.doi.org/10.1504/IJMOR.2013.053626. http://dx.doi.org/10.1504/IJMOR.2013.053...	Minimize room allocation	sugery room and human resources	Real data	Weekly and offline daily	MILP	Exact
Sufahani & Ismail (2014)Sufahani, S., & Ismail, Z. (2014). A real scheduling problem for hospital operation room. Applied Mathematical Sciences, 8(114), 5681-5688. http://dx.doi.org/10.12988/ams.2014.46413. http://dx.doi.org/10.12988/ams.2014.4641...	Level occupation between surgery rooms	sugery room and human resources	Real data	Weekly	MILP	Exact
Saadouli et al. (2014)Saadouli, H., Masmoudi, M., Jerbi, B., & Dammak, A. (2014, November). An optimization and Simulation approach for Operating Room scheduling under stochastic durations. In 2014 International Conference on Control, Decision and Information Technologies (CoDIT) (pp. 257-262). USA: IEEE. http://dx.doi.org/10.1109/CoDIT.2014.6996903. http://dx.doi.org/10.1109/CoDIT.2014.699...	Maximize amount of surgeries	sugery room and human resources	Real data	Weekly	MILP	Exact
Saadouli et al. (2015)Saadouli, H., Jerbi, B., Dammak, A., Masmoudi, L., & Bouaziz, A. (2015). A stochastic optimization and simulation approach for scheduling operating rooms and recovery beds in an orthopedic surgery department. Computers & Industrial Engineering, 80, 72-79. http://dx.doi.org/10.1016/j.cie.2014.11.021. http://dx.doi.org/10.1016/j.cie.2014.11....	Maximize amount of surgeries	sugery room, post-anesthesia recovery (PAR)	Real data	Weekly	MILP	Exact
Villarreal & Keskinocak (2016)Villarreal, M. C., & Keskinocak, P. (2016). Staff planning for operating rooms with different surgical services lines. Health Care Management Science, 19(2), 144-169. http://dx.doi.org/10.1007/s10729-014-9307-x. PMid:25366968. http://dx.doi.org/10.1007/s10729-014-930...	Minimize resource allocation (nursing)	budget	Real data	Yearly (48 weeks)	MILP	Heuristic
This article	Minimize resource allocation	Surgery room, human resources, equipment, blood bags	Real data	Annual	MILP	Exact

CNRM Resolution number 02/2006	Minimum amount of procedures to be performed by the professional to obtain the license to offer vascular surgery service
Classification of vascular surgery procedures	Procedures	Amount of surgeries throughout the year
Small size	Vascular accesses, arteriovenous fistulas, vascular radiology, small amputations and debridement	45
Medium size	Embolectomies; femoral-popliteal, femoral-femoral, axillo-femoral, iliac-femoral, distal grafts; venous surgeries; amputations, sympathectomies and vascular radiology.	60
Large size	Surgery of the carotid arteries, aneurysms, aortoiliac and femoral grafts, arterial reoperations	45
Total	-	150

Surgery size	Great categories – classification per blocks of surgery	Procedures	Arterial surgeries	Number of surgeries per year (CNRM Resolution number 02/2006)
Small	Varicose veins and veins	Venous surgeries		-
	Aorta	-	X
	Fistula	Vascular access	X
	Femoral	-	X
	Carotid	-	X
	Amputation	Amputation
	Endovascular	Vascular radiology
Subtotal	Small size	-	-	15
Medium	Varicose veins and veins	Venous surgeries		-
	Aorta	-	X
	Fistula	Vascular access	X
	Femoral	Femoral-popliteal, femoral-femoral, axillo-femoral, iliac-femoral, distal grafts	X
	Carotid	axillo-femoral	X
	Amputation	Amputation
	Endovascular	Vascular radiology
Subtotal	Medium size			20
Large	Varicose veins and veins	Venous surgeries		-
	Aorta	Axillo-femoral, surgery of the carotid arteries, aneurysms, aortoiliac and femoral grafts, arterial reoperations
	Fistula	Vascular access	X
	Femoral	Axillo-femoral, surgery of the carotid arteries, aneurysms, aortoiliac and femoral grafts, arterial reoperations	X
	Carotid	Axillo-femoral, surgery of the carotid arteries, aneurysms, aortoiliac and femoral grafts, arterial reoperations	X
	Amputation	Amputation
	Endovascular	Vascular radiology
Subtotal	Large size	-	-	15
Total	-	-	-	50

Resource parametrization		Necessary resources									Time (in minutes)							Minimum amount of surgeries
Surgery size	Great categories – classification per blocks of vascular surgery	Phlebo-extractor	Advanced extracranial surgery	Advanced aorta surgery	Varicose Veins Box	Arteriovenous fistula Box	Femoral Box	Amputation Box	C-arm required for the procedure?	Blood bags required for the procedure?	Time of room preparation	Time of patient preparation	Surgery duration	Anesthetist required for the procedure?	R1 Doctor	R2 Doctor	R3 Doctor	R1 Doctor	R2 Doctor	R3 Doctor
Small	Varicose veins and veins	X			X						20	0	45	-	X	X	X	10	0	0
	Aorta			X					X	X	20	0	-	-		X	X	0	0	0
	Fistula					X					20	0	60	-	X	X	X	20	0	0
	Femoral	X					X		X	X	20	0	150	X	X	X	X	5	15	0
	Carotid		X						X		20	0	-	-		X	X	0	0	0
	Amputation							X			20	0	40	-	X	X	X	10	0	0
	Endovascular (Laparoscopy)					X	X		X		20	0	60	-		X	X	0	10	15
Medium	Varicose veins and veins	X			X						20	20	75	X	X	X	X	10	5	0
	Aorta			X					X	X	20	20	-	-		X	X	0	0	0
	Fistula					X					20	20	110	X	X	X	X	20	0	0
	Femoral	X					X		X	X	20	20	210	X	X	X	X	10	15	15
	Carotid		X						X		20	20	135	X		X	X	0	15	10
	Amputation							X			20	20	50	X	X	X	X	10	0	0
	Endovascular (Laparoscopy)					X	X		X		20	20	135	-		X	X	0	10	20
Large	Varicose veins and veins	X			X						20	90	105	X	X	X	X	5	5	0
	Aorta			X					X	X	20	90	240	X		X	X	0	15	5
	Fistula					X					20	90	110	X	X	X	X	5	5	0
	Femoral	X					X		X	X	20	90	210	X	X	X	X	5	10	5
	Carotid		X						X		20	90	135	X		X	X	0	5	10
	Amputation							X			20	90	90	X	X	X	X	5	5	0
	Endovascular (Laparoscopy)					X	X		X		20	90	165	X			X	0	0	10

CME – Surgery instruments	Amount available at CME
Phlebo-extractor	1
Advanced extracranial surgery	2
Advanced aorta surgery	2
Varicose Veins Box	5
FAV Box	2
Femoral Box	3
Amputation Box	2

Type of resident	Number of residents	Minimum frequency of weekly allocation
R1 Doctor	2	3
R2 Doctor	2	3
R3 Doctor	2	3

Indexes	Meaning	Domain	Sub indexes
ar	arterial surgery	AR = [2:5] C = [1:7] D = [1:250] E = [1:1] R = [1:3] M = [1:7] P = [1:3] R = [1:3] S = [1:2]
s	Surgery
d	Day		ar
e	Equipment
i	Resource
m	Material
z	Surgery size		s, e
c	Class (group) of residents
r	Room

Variables	Meaning and type	Type
$A c C l S u_{c, s, z}$	Number of surgeries (s) of size (z) performed by residents of type (c) in the year	Integer
$A n S u_{s, z}^{r, d}$	Decision of allocating an anesthetist to perform surgery (s) of size (z) in room (r) on day (d)	Binary
$A n D a y^{r, d}$	Decision of allocating an anesthetist in room (r) on day (d)	Binary
$A u x A n^{r, d}$	Auxiliary variable created to associate variables $A n S u_{s, l}^{r, d}$ and $A n D a y^{s, d}$	Integer
$A u x E q_{e}^{r, d}$	Auxiliary variable created to associate variables $E q S u_{e, s, l}^{r, d}$ and $E q D a y_{e}^{r, d}$	Integer
$A u x C l_{r}^{d}$	Auxiliary variable created to associate variables $C l S u_{c, s, l}^{r, d}$ and $C l D a y_{r}^{d}$	Integer
$E q S u_{e, s, z}^{r, d}$	Decision of allocating equipment (e) in surgery (s) of size (z) in room (r) on day (d)	Binary
$E q D a y_{e}^{r, d}$	Decision of allocating equipment (e) in room (r) on day (d)	Binary
$M a t S u_{m, s, z}^{r, d}$	Decision of allocating surgical material (m) in surgery (s) of size (z) in room (r) on day (d)	Binary
$C l S u_{c, s, z}^{r, d}$	Decision of allocating a resident of type (c) to perform surgery (s) of size (z) in room (r) on day (d)	Binary
$C l D a y_{r}^{d}$	Decision of allocating any resident of type (r) on day (d)	Binary
$R o o m^{r, d}$	Decision of allocating or blocking room (r) on day (d) for the surgical service	Binary
$B l o o d S u_{s, z}^{r, d}$	Decision of allocating blood bag in surgery (s) of size (z) in room (r) on day (d)	Binary

Parameters	Meaning	Values
$d u r S u_{s, z}$	Duration of surgery (s) of size (z)	Table 6
$\underline{f C l w k}$	Minimum frequency of groups of residents per week	Table 12
$h a C l S u_{s, r, z}$	Resident's (c) habilitation to perform surgery (s) of size (z)	Table 6
$M$	Large number	100.000
$w e i g h t_{i}$	Weight assigned to each type of resource (i)	Table 12
$\bar{n A n w k}$	Maximum number of anesthetists available in the week	Table 12
$\underline{n S u Y r}$	Minimum number of surgeries year for each resident	Table 4
$\underline{n S u A r}$	Minimum number of arterial surgeries for each resident	Table 5
${\underline{n S u A r S z}}_{z}$	Minimum number of arterial surgeries per size for each resident	Table 5
${\underline{n S u S z}}_{z}$	Minimum number of surgeries of size for each resident	Table 4
${\underline{n S u C l}}_{c, s, p}$	Minimum number of surgeries (s) of size (z) for resident of type (c) established by the preceptor	Table 6
${\bar{n E q w k}}_{e}$	Maximum number of equipment (e) assigned in the week	Table 12
$n M a t_{m}$	Number of surgical materials (m) available at SMC	Table 7
$n C l_{c}$	Number of residents per type (c)	Table 8
$\bar{n r o o m w k}$	Maximum amount of rooms assigned in the week	Table 12
$n b l o o d$	Number of patients attended by hemotherapy service (blood) per day	1
$r S u A n_{s, z}$	Anesthetist-surgery relation (s,z)	Table 6
$r S u E q_{s, z, e}$	Surgery-equipment relation (s,z,e)	Table 6
$r S u M a t_{s, z, m}$	Surgery-material relation (s,z,m)	Table 6
$r S u b l o o d_{s, z}$	Surgery-blood relation (s,z)	Table 6
$t P r e p_{z}$	Preparation time for surgery of size (z)	Table 6
$t P r e r o o m$	Room preparation time	Table 6
$t r o o m$	Room time	540 minutes

Scenario	Weight, per allocative decision, related to:			Weekly allocation business rules
Scenario	Surgery room	Anesthe-tist	Equip-ment	Minimum Frequency	Maximum number of rooms	Maximum number of anesthetists	Maximum amount of equipment
1	10⁶	10³	1	0	10	10	10
2	1	10³	10⁶	0	10	10	10
3	10³	10⁶	1	0	10	10	10
4	1	10⁶	10³	0	10	10	10
5	10³	10³	1	0	10	10	10
6	1	10³	10³	0	10	10	10
7	1000	1	10³	0	10	10	10
8	1	1	1	0	10	10	10
9	10⁶	10³	1	3	8	8	8
10	10⁶	10³	1	3	8	7	6
11	10⁶	10³	1	3	8	4	6

Scenario results	Input data			Model answers
	Objective function	Model Size		Computational resource	General solutions	Sizing model answers
	Resource Criticality Order (Hierarchy)	# decision variables	# Constraints	Solution time (in seconds)	Gap (%)	Average usage (%)	# Rooms	# Anesthetists	# Equipment
1	Room; anesthetist; equipment	52,250	70,621	11.456.4	1.48	86.9	285	285	262
2	Equipment; anesthetist; room	52,250	70,621	10,026.2	0.03	73.3	339	274	200
3	Anesthetist; room; equipment	52,250	70,621	12,340.2	4.39	73.3	344	230	333
4	Anesthetist; equipment; room	52,250	70,621	10,178.3	4.39	69.1	364	230	310
5	Room and anesthetist; equipment	52,250	70,621	19,633.1	11.55	83.5	297	269	270
6	Anesthetist and equipment; room	52,250	70,621	68,774.9	12.19	70.1	354	278	200
7	Room and equipment; anesthetist	52,250	70,621	69,962.0	2.48	84.6	293	293	200
8	No hierarchy	52,250	70,621	106,748.5	10.44	84.9	290	280	200
9	Room; anesthetist; equipment	52,250	70,612	60,038.6	1.48	86.9	285	285	262
10	Room; anesthetist; equipment	52,250	70,612	60,051.3	1.83	86.6	286	286	254
11	Room; anesthetist; equipment	52,250	70,612	Infeasible solution

[1] * danielbouzon@gmail.com

Brasil

Brasil

Maximizing the efficiency of residents operating room scheduling: a case study at a teaching hospital

Abstract

Paper aims

Originality

Research method

Main findings

Implications for theory and practice