Weekly Physician Scheduling for Emergency Departments with Time-Varying Demands of Patients with Revisits

doi:10.16183/j.cnki.jsjtu.2020.328

Abstract

Abstract:

To solve the flexible scheduling problem of emergency departments, a method based on the queuing theory and the fluid model for approximating the patient waiting length of a time-varying queuing system with returns for a given scheduling plan is proposed. A mixed-integer programming model, which considers the real constraints of physician scheduling, is then proposed and solved by using a tabu search algorithm. Numerical experiments show that the proposed method can effectively approximate the waiting queue length of patients and the scheduling plan computed by the proposed algorithm can effectively reduce the total waiting queue length of patients.

Key words: emergency departments, time-varying demands of patients with revisits, flexible scheduling, weekly physician scheduling problem, queuing theory

CLC Number:

F224

WANG Zixiang, WU Zerui, LIU Ran. Weekly Physician Scheduling for Emergency Departments with Time-Varying Demands of Patients with Revisits[J]. Journal of Shanghai Jiao Tong University, 2022, 56(2): 242-252.

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References 24

[1]	LIU R, XIE X L. Physician staffing for emergency departments with time-varying demand[J]. INFORMS Journal on Computing, 2018, 30(3):588-607. doi: 10.1287/ijoc.2017.0799 URL
[2]	BAUM R, BERTSIMAS D, KALLUS N. Scheduling, revenue management, and fairness in an academic-hospital radiology division[J]. Academic Radiology, 2014, 21(10):1322-1330. doi: 10.1016/j.acra.2014.05.009 URL
[3]	BARD J F, SHU Z C, LEYKUM L. A network-based approach for monthly scheduling of residents in primary care clinics[J]. Operations Research for Health Care, 2014, 3(4):200-214. doi: 10.1016/j.orhc.2014.08.002 URL
[4]	BOWERS M R, NOON C E, WU W, et al. Neonatal physician scheduling at the university of Tennessee medical center[J]. Interfaces, 2016, 46(2):168-182.
[5]	FÜGENER A, BRUNNER J O, PODTSCHASKE A. Duty and workstation rostering considering preferences and fairness: A case study at a department of anaesthesiology[J]. International Journal of Production Research, 2015, 53(24):7465-7487. doi: 10.1080/00207543.2015.1082667 URL
[6]	BRUNI R, DETTI P. A flexible discrete optimization approach to the physician scheduling problem[J]. Operations Research for Health Care, 2014, 3(4):191-199. doi: 10.1016/j.orhc.2014.08.003 URL
[7]	BRUNNER J O, BARD J F, KOLISCH R. Midterm scheduling of physicians with flexible shifts using branch and price[J]. IIE Transactions, 2010, 43(2):84-109. doi: 10.1080/0740817X.2010.504685 URL
[8]	朱华波, 唐加福, 宫俊. 具有I²型路由策略的门诊多阶段排队系统中护士优化配置方法[J]. 信息与控制, 2014, 43(2):217-222.
	ZHU Huabo, TANG Jiafu, GONG Jun. Nurse staffing and allocation in multistage queuing network model with I² patient routing in outpatient department[J]. Information and Control, 2014, 43(2):217-222.
[9]	PUENTE J, GÓMEZ A, FERNÁNDEZ I, et al. Medical doctor rostering problem in a hospital emergency department by means of genetic algorithms[J]. Computers & Industrial Engineering, 2009, 56(4):1232-1242. doi: 10.1016/j.cie.2008.07.016 URL
[10]	GENDREAU M, FERLAND J, GENDRON B, et al. Physician scheduling in emergency rooms[M]//Practice and Theory of Automated Timetabling VI. Berlin, Germany: Springer, 2006: 53-66.
[11]	FÜGENER A, BRUNNER J O. Planning for overtime: The value of shift extensions in physician scheduling[J]. INFORMS Journal on Computing, 2019, 31(4):732-744. doi: 10.1287/ijoc.2018.0865 URL
[12]	GREEN L V, KOLESAR P J, SOARES J. Improving the SIPP approach for staffing service systems that have cyclic demands[J]. Operations Research, 2001, 49(4):549-564. doi: 10.1287/opre.49.4.549.11228 URL
[13]	刘强, 谢晓岚, 刘冉, 等. 面向动态时变需求的急诊科医生排班研究[J]. 工业工程与管理, 2015, 20(6):122-129.
	LIU Qiang, XIE Xiaolan, LIU Ran, et al. Shifts scheduling method for physicians in emergency department with time-varying demand[J]. Industrial Engineering and Management, 2015, 20(6):122-129.
[14]	GREEN L, KOLESAR P. The pointwise stationary approximation for queues with nonstationary arrivals[J]. Management Science, 1991, 37(1):84-97. doi: 10.1287/mnsc.37.1.84 URL
[15]	AHMED M A, ALKHAMIS T M. Simulation optimization for an emergency department healthcare unit in Kuwait[J]. European Journal of Operational Research, 2009, 198(3):936-942. doi: 10.1016/j.ejor.2008.10.025 URL
[16]	ZELTYN S, MARMOR Y N, MANDELBAUM A, et al. Simulation-based models of emergency departments: Operational, tactical, and strategic staffing[J]. ACM Transactions on Modeling and Computer Simulation, 2011, 21(4):24.
[17]	EL-RIFAI O, GARAIX T, AUGUSTO V, et al. A stochastic optimization model for shift scheduling in emergency departments[J]. Health Care Management Science, 2015, 18(3):289-302. doi: 10.1007/s10729-014-9300-4 pmid: 25270574
[18]	XIAO G L, DONG M, LI J, et al. Scheduling routine and call-in clinical appointments with revisits[J]. International Journal of Production Research, 2017, 55(6):1767-1779. doi: 10.1080/00207543.2016.1237789 URL
[19]	INGOLFSSON A, AMANUL HAQUE M, UMNIKOV A. Accounting for time-varying queueing effects in workforce scheduling[J]. European Journal of Operational Research, 2002, 139(3):585-597. doi: 10.1016/S0377-2217(01)00169-2 URL
[20]	LIU Y N, WHITT W. Stabilizing customer abandonment in many-server queues with time-varying arrivals[J]. Operations Research, 2012, 60(6):1551-1564. doi: 10.1287/opre.1120.1104 URL
[21]	WHITT W. Fluid models for multiserver queues with abandonments[J]. Operations Research, 2006, 54(1):37-54. doi: 10.1287/opre.1050.0227 URL
[22]	YOM-TOV G B, MANDELBAUM A. Erlang-R: A time-varying queue with reentrant customers, in support of healthcare staffing[J]. Manufacturing & Service Operations Management, 2014, 16(2):283-299.
[23]	希利尔F S, 利伯曼 G J. 运筹学导论[M]. 胡运权, 等, 第9版. 北京: 清华大学出版社, 2010.
	HILLIER F S, LIEBERMAN G J. Introduction to operation research [M]. HU Yunquan, et al, 9th ed. Beijing: Tsinghua University Press, 2010.
[24]	CHEN G, GOVINDAN K, YANG Z Z, et al. Terminal appointment system design by non-stationary M(t)/E_k/c(t) queueing model and genetic algorithm[J]. International Journal of Production Economics, 2013, 146(2):694-703. doi: 10.1016/j.ijpe.2013.09.001 URL

排班序号	排班时间
1	8:00—16:00
2	10:00—18:00
3	12:00—20:00
4	14:00—22:00
5	16:00—24:00
6	24:00—8:00

参数	取值
O	9
N	6
δ/h	1
μ₁/h^-1	10.93
μ₂/h^-1	2.5
c₂	10
P	0.55
α	3
C_max	2
C_min	0
F/h	50
G/h	10
θ	10
U	160
V	40

算例	l'	l'_APP1	ω₁/%	l'_APP2	ω₂/%
W1	1615.62	170.22	89.46	1637.66	1.36
W2	1153.52	150.41	86.96	1176.16	1.96
W3	1231.12	150.23	87.80	1247.16	1.30
W4	1841.30	355.43	80.70	1919.40	4.24
W5	2089.66	403.81	80.68	2159.41	3.34
平均	1586.24	246.02	85.12	1627.96	2.44

算例	z			t_CT/h	t_WT/h
算例	γ_TS	γ_REAL	ω₃/%	t_CT/h	γ_TS	γ_REAL	ω₄/%
W1	1728.25	2645.66	34.68	1.15	301.39	1352.63	77.72
W2	1707.35	2184.16	21.83	1.38	366.89	914.65	59.89
W3	1571.75	2255.16	30.30	1.32	234.52	997.01	76.48
W4	1782.22	2927.40	39.12	1.24	365.05	1574.81	76.82
W5	1819.63	3167.41	42.55	1.29	342.98	1813.71	81.09
平均	1721.84	2635.96	33.70	1.27	322.17	1330.56	74.40

算例	TS	GA			MIP1
算例	z	z	t_CT /h	ω₅/%	z	t_CT /h	ω₆/%
W1	1728.25	2119.20	7.55	22.62	1779.92	8.13	2.99
W2	1707.35	2059.93	6.93	20.65	2059.10	8.15	20.60
W3	1571.75	1947.97	6.78	23.94	3652.85	8.14	132.41
W4	1782.22	2337.01	7.23	31.13	1991.34	8.14	11.73
W5	1819.63	2294.19	7.41	26.08	4854.50	8.13	166.78
平均	1721.84	2151.66	7.18	24.88	2867.54	8.14	66.90