A stochastic programming model for outpatient appointment scheduling considering unpunctuality

Abstract Many papers on outpatient appointment scheduling assume that patients arrive on time. However, unpunctuality is a stochastic factor that is inevitable in practice, which leads to patients arriving out of order. A schedule may not be reasonable if a clinic neglects the influence of patient unpunctuality. This paper addresses the outpatient scheduling problem considering unpunctuality (OS-U) by developing a stochastic programming model. We compare the performance of the OS-U system with the strict-punctuality (OS-P) system. We illustrate that the model has an exact and unified formula for cases of patients arriving in the appointment order and arriving out of order. The OS-U problem is solved by using Benders decomposition combined with the sample average approximation (BD-SAA) technique to determine the global optimal set of appointment intervals with the goal of minimizing the weighted sum of all patient waiting times, doctor idle times, and overtime. Numerical experiments indicate that the appointment rule changes when considering unpunctuality, although the set of optimal appointment intervals still takes the shape of dome (interval width increases at first, then remains nearly constant and eventually decreases for the last patients). The OS-P system schedules the first two patients together at the start of a session, whereas the OS-U system schedules them with different appointment times and requires a longer slot between the first two patients if patients tend to arrive early rather than late. The variance of unpunctuality has little impact. The no-show probability has a greater influence on system performances in an OS-U system than those in an OS-P system.

[1]  Michel Mandjes,et al.  Appointment scheduling in tandem-type service systems , 2015 .

[2]  Michel Mandjes,et al.  Optimized appointment scheduling , 2014, Eur. J. Oper. Res..

[3]  Stephen R. Lawrence,et al.  Appointment Overbooking in Health Care Clinics to Improve Patient Service and Clinic Performance , 2012 .

[4]  Lawrence W. Robinson,et al.  A Comparison of Traditional and Open-Access Policies for Appointment Scheduling , 2010, Manuf. Serv. Oper. Manag..

[5]  Subhamoy Ganguly,et al.  Optimal Sequencing of Unpunctual Patients in High‐Service‐Level Clinics , 2016 .

[6]  Dieter Fiems,et al.  Computationally efficient evaluation of appointment schedules in health care , 2014, Eur. J. Oper. Res..

[7]  Emre A. Veral,et al.  Assessment of patient classification in appointment system design , 2008 .

[8]  L. Green,et al.  Reducing Delays for Medical Appointments: A Queueing Approach , 2008, Oper. Res..

[9]  R. Fetter,et al.  Patients' waiting time and doctors' idle time in the outpatient setting. , 1966, Health services research.

[10]  Jin Qi,et al.  Mitigating Delays and Unfairness in Appointment Systems , 2017, Manag. Sci..

[11]  Valentin Zelenyuk,et al.  Performance of hospital services in Ontario: DEA with truncated regression approach , 2016 .

[12]  Emre A. Veral,et al.  OUTPATIENT SCHEDULING IN HEALTH CARE: A REVIEW OF LITERATURE , 2003 .

[13]  Michael Pinedo,et al.  Appointment scheduling with no-shows and overbooking , 2014 .

[14]  Christoph Buchheim,et al.  Robust Critical Node Selection by Benders Decomposition , 2016, INFORMS J. Comput..

[15]  T. Cox,et al.  Optimising the queuing system for an ear, nose and throat outpatient clinic , 1985 .

[16]  Jiafu Tang,et al.  Comparison of Traditional and Open-Access Appointment Scheduling for Exponentially Distributed Service Time. , 2015, Journal of healthcare engineering.

[17]  Martin L. Puterman,et al.  Dynamic multi-appointment patient scheduling for radiation therapy , 2012, European Journal of Operational Research.

[18]  Dieter Fiems,et al.  Outpatient scheduling with unpunctual patients and no-shows , 2018, Eur. J. Oper. Res..

[19]  Oualid Jouini,et al.  Appointment Scheduling with Non-Punctual Arrivals , 2009 .

[20]  Refael Hassin,et al.  Scheduling Arrivals to Queues: A Single-Server Model with No-Shows , 2008, Manag. Sci..

[21]  J. Vissers,et al.  Selecting a Suitable Appointment System in an Outpatient Setting , 1979, Medical care.

[22]  J. F. Benders.  Partitioning procedures for solving mixed-variables programming problems , 1962 .

[23]  M. Pike,et al.  Appointment Systems in Out-patients?? Clinics and the Effect of Patients?? Unpunctuality , 1964 .

[24]  Kenneth J. Klassen,et al.  Strategies for Appointment Policy Design with Patient Unpunctuality , 2014, Decis. Sci..

[25]  Lawrence W. Robinson,et al.  Scheduling doctors' appointments: optimal and empirically-based heuristic policies , 2003 .

[26]  Brian Denton,et al.  Optimization of surgery sequencing and scheduling decisions under uncertainty , 2007, Health care management science.

[27]  Kenneth J. Klassen,et al.  Appointment system design with interruptions and physician lateness , 2013 .

[28]  Emre A. Veral,et al.  Designing appointment scheduling systems for ambulatory care services , 2006, Health care management science.

[29]  James R. Wilson,et al.  Modeling patient arrivals in community clinics , 2008 .

[30]  Kenneth J. Klassen,et al.  Improving Performance in Outpatient Appointment Services with a Simulation Optimization Approach , 2009 .

[31]  Camilo Mancilla,et al.  A sample average approximation approach to stochastic appointment sequencing and scheduling , 2012 .

[32]  Amir Ahmadi-Javid,et al.  Outpatient appointment systems in healthcare: A review of optimization studies , 2017, Eur. J. Oper. Res..

[33]  Peter Williams,et al.  Optimization of scheduling patient appointments in clinics using a novel modelling technique of patient arrival , 2012, Comput. Methods Programs Biomed..

[34]  Diwakar Gupta,et al.  Revenue Management for a Primary-Care Clinic in the Presence of Patient Choice , 2008, Oper. Res..

[35]  Ramandeep S. Randhawa,et al.  Scheduling Homogeneous Impatient Customers , 2016 .

[36]  Diwakar Gupta,et al.  Appointment scheduling in health care: Challenges and opportunities , 2008 .

[37]  Nan Liu.  Optimal choice for appointment scheduling window under patient no-show behavior , 2016 .

[38]  Diwakar Gupta,et al.  A Sequential Bounding Approach for Optimal Appointment Scheduling , 2003 .

[39]  Lawrence W. Robinson,et al.  Sequencing and Scheduling Appointments with Potential Call-In Patients , 2011 .

[40]  Maurice Queyranne,et al.  Appointment Scheduling with Discrete Random Durations , 2009, Math. Oper. Res..

[41]  Paul R. Harper,et al.  Reduced outpatient waiting times with improved appointment scheduling: a simulation modelling approach , 2003, OR Spectr..

[42]  Cassius Tadeu Scarpin,et al.  Multi-objective optimization in partitioning the healthcare system of Parana State in Brazil , 2015 .