Real-time scheduling of semi-urgent patients under waiting time targets

Semi-urgent patients arrive at an emergency department and visit the physician after triage. Patients right after triage should be served within a maximum allowable waiting time; whereas in-process patients need to be served as soon as possible to avoid adverse events. The physician must determine which one to be served next. To deal with this problem, a Markov decision process (MDP) is proposed for real-time scheduling. The wait of patients right after triage incurs a non-decreasing marginal waiting cost in their lateness, whereas the wait of in-process patients incurs linear cost function. The objective is to minimise the total weighted waiting cost. The properties of the MDP model are analysed. In the special case of long examination time and common treatment rate for all patients, we prove the multimodularity of the value function and the optimality of state-dependent threshold policies. Based on these properties, efficient heuristic policies and an approximate dynamic programming (ADP) policy are proposed. A threshold policy, which is defined by the function of expected tardiness of patients right after triage, is found to excel in all experiments, with average gaps less than 0.7% from the optimal control in small-size instances and 0.18% from ADP in real application.

[1]  Gayane Yenokyan,et al.  An Electronic Emergency Triage System to Improve Patient Distribution by Critical Outcomes. , 2016, The Journal of emergency medicine.

[2]  Jean Walrand,et al.  The c# rule revisited , 1985 .

[3]  Ping Cao,et al.  Determining the conditions for reverse triage in emergency medical services using queuing theory , 2016 .

[4]  Wallace J. Hopp,et al.  Complexity-Augmented Triage: A Tool for Improving Patient Safety and Operational Efficiency , 2013, Manuf. Serv. Oper. Manag..

[5]  Yang Wang,et al.  The equity of China’s emergency medical services from 2010–2014 , 2017, International Journal for Equity in Health.

[6]  Richard F. Hartl,et al.  Supply chain dynamics, control and disruption management , 2016 .

[7]  Mark E. Lewis,et al.  Dynamic control of a tandem system with abandonments , 2016, Queueing Syst. Theory Appl..

[8]  Maurice Queyranne,et al.  Dynamic Multipriority Patient Scheduling for a Diagnostic Resource , 2008, Oper. Res..

[9]  Wayne E. Smith Various optimizers for single‐stage production , 1956 .

[10]  Avishai Mandelbaum,et al.  Erlang-R: A Time-Varying Queue with Reentrant Customers, in Support of Healthcare Staffing , 2014, Manuf. Serv. Oper. Manag..

[11]  Randolph W. Hall,et al.  Modeling Patient Flows Through the Health care System , 2013 .

[12]  Mahesh Nagarajan,et al.  Patient Prioritization in Emergency Department Triage Systems: An Empirical Study of Canadian Triage and Acuity Scale (CTAS) , 2018 .

[13]  David Goldsman,et al.  Using simulation and optimisation to characterise durations of emergency department service times with incomplete data , 2016 .

[14]  J. V. Mieghem Dynamic Scheduling with Convex Delay Costs: The Generalized CU Rule , 1995 .

[15]  Xiaolan Xie,et al.  Optimal Dynamic Outpatient Scheduling for a Diagnostic Facility With Two Waiting Time Targets , 2016, IEEE Transactions on Automatic Control.

[16]  Junfei Huang,et al.  Control of Patient Flow in Emergency Departments, or Multiclass Queues with Deadlines and Feedback , 2015, Oper. Res..

[17]  J. Walrand,et al.  The cμ rule revisited , 1985, Advances in Applied Probability.

[18]  Chao Wang,et al.  Improving patient flow in emergency department through dynamic priority queue , 2012, 2012 IEEE International Conference on Automation Science and Engineering (CASE).

[19]  Oded Berman,et al.  Using Strategic Idleness to Improve Customer Service Experience in Service Networks , 2014, Oper. Res..

[20]  Martin L Puterman,et al.  Dynamic scheduling with due dates and time windows: an application to chemotherapy patient appointment booking , 2013, Health Care Management Science.

[21]  Henriëtte A Moll,et al.  Challenges in the validation of triage systems at emergency departments. , 2010, Journal of clinical epidemiology.

[22]  Qing Li,et al.  Multimodularity and Its Applications in Three Stochastic Dynamic Inventory Problems , 2014, Manuf. Serv. Oper. Manag..

[23]  Wallace J. Hopp,et al.  Patient Streaming as a Mechanism for Improving Responsiveness in Emergency Departments , 2012, Oper. Res..

[24]  Eva K. Lee,et al.  Transforming Hospital Emergency Department Workflow and Patient Care , 2015, Interfaces.

[25]  M. E. Hock Ong,et al.  Application of Queuing Analytic Theory to Decrease Waiting Times in Emergency Department: Does it Make Sense? , 2013, Archives of trauma research.

[26]  S. Zeger,et al.  The challenge of predicting demand for emergency department services. , 2008, Academic emergency medicine : official journal of the Society for Academic Emergency Medicine.

[27]  I. Adiri,et al.  A Dynamic Priority Queue with General Concave Priority Functions , 1979, Oper. Res..

[28]  Alan Scheller-Wolf,et al.  Managing nurse lines – practical challenges and the developing theory , 2015 .

[29]  Michael Christ,et al.  Modern triage in the emergency department. , 2010, Deutsches Arzteblatt international.

[30]  Soroush Saghafian,et al.  Operations research/management contributions to emergency department patient flow optimization: Review and research prospects , 2015 .

[31]  Ward Whitt,et al.  Coping with Time‐Varying Demand When Setting Staffing Requirements for a Service System , 2007 .

[32]  Wei Lam Sean Shao,et al.  APPLICATION OF QUEUING ANALYTIC THEORY TO DECREASE WAITING TIMES IN EMERGENCY DEPARTMENT: DOES IT MAKE SENSE? (LETTER) , 2013 .

[33]  Melvyn Sim,et al.  Data-Driven Patient Scheduling in Emergency Departments: A Hybrid Robust-Stochastic Approach , 2019, Manag. Sci..

[34]  James R. Jackson Some problems in queueing with dynamic priorities , 1960 .

[35]  Bruce L. Golden,et al.  Applying queueing theory to the study of emergency department operations: a survey and a discussion of comparable simulation studies , 2018, Int. Trans. Oper. Res..

[36]  Elia El-Darzi,et al.  Length of Stay-Based Patient Flow Models: Recent Developments and Future Directions , 2005, Health care management science.