1. Modeling & Simulation What can they offer? March 28, 2012 Ottawa, ON Waiting Time Management Strategies for Scheduled Health Care Services: A Workshop for Researchers, Managers and Decision-makers

2. The Operations Research Toolkit Strategic Tactical Operational Long Range Demand Forecasting Long Range Supply Forecasting Capacity Planning & Allocation Patient Scheduling Models HHR Scheduling Resource Scheduling Managing Demand Variability Managing Supply Variability Analysis of Pathways Patients People Resources 10/4/20152

3. Operations Research Tools 10/4/20153

4. Urgent Patient Queueing Model Objective: To develop a generalized model to determine how to best allocate capacity to urgent patients Scope: Any fixed capacity intervention with 2 urgency classes and a critical MAWT to meet for the high urgency class (Winnipeg, Edmonton) Modelling methodology: Stochastic Model to create closed-form Queueing formulas, tested against DES (Arena) models 10/4/20154

5. Rationale Goal: Provide more certainty around surgery dates for all patient classes Patient Scheduling variability depends upon: – OR Schedule stability Cancellations of OR time, frequency of scramble time – Surgeon variability Longer waitlists create more uncertainty of surgeon availability – Patient readiness Prehab and case management has improved this – Arrival of urgent patients that ‘bump’ elective patients when there isn’t adequate time reserved 10/4/20155

6. Literature Overview Scheduling Policies for managing Urgent/Elective  Patrick & Puterman (2008) “Dynamic Multipriority Patient Scheduling for a Diagnostic Resource CT Scans for 3 outpatient categories, MAWT of 7, 14, 28 days Markov Decision Process (MDP) that recommends that highest priority gets scheduled right away and that lower priorities are scheduled into the latest appointment available to meet MAWT. When demand > capacity, higher priority patients are rejected vs. a bumping of elective. Increased flexibility with high priority scheduling improves system  Zonderland et al. (2010) “Planning and scheduling of semi-urgent surgeries. Stochastic model created for specific location. Difficult to multi-location replicate due to mathematical approach 610/4/2015

7. Research Question What is the ‘optimal’ number of urgent surgical slots to set aside so as to meet a desired performance metric – specifically % of urgent patients that bump electives Required data: – Patient arrival rate – MAWT for urgent patients Output: – Minimum # of surgeries to reserve of MAWT window 710/4/2015

8. Simulation Approach 10/4/20158 Average arrival rate of urgent patients = 1 per week. Surgery rate = Number of urgent surgical spots reserved over the next 4 weeks for urgent patients

9. Stochastic Model Approach ‘Simple’ representation of urgent patient arrival process Ability to calculate, with relative ease & accuracy, the effect of reserving capacity for urgent patients          0 123 45               =            10/4/20159 A stochastic model may be used rather than a simulation

10. Analytical Queueing Model Derive appropriate formulae based upon an M/D/1/N queueing model Test accuracy of queuing model against DES Implement formula in Excel front-end The stochastic model may be solved analytically to determine the probability of having 0, 1, …N patients waiting. 10/4/201510

11. Results Low volume Medium Volume High Volume Extreme Volume Scenario  12345678 (arrivals/week) 0.25 113355  (surgery/week) 0.750.501.25132.7554.75 Prob(empty)0.66930.54810.22820.13040.04230.01580.02520.0087 Prob(bumping)0.00780.09630.03530.13040.04230.09780.02520.0583 10/4/201511

12. Validation – Comparing DES/Queue 10/4/201512

13. Excel-based “OR Tool” 10/4/201513

14. Next Steps Phase I - Data gathering and Implementation of logic into Concordia Scheduling Software, early 2012  Phase II - Integrate into Generalized DES Model as part of “best practices” options Phase III - Improve user interface and test at pilot clinics – gather performance feedback 10/4/201514

15. Operations Research Tools 10/4/201515

16. Thank you! 1610/4/2015