Modeling & Simulation What can they offer?

March 28, 2012Ottawa, ON

Waiting Time Management Strategies for Scheduled Health Care Services: A Workshop for Researchers, Managers and Decision-makers

The Operations Research Toolkit

Strategic

Tactical

Operational

Long Range Demand

Forecasting

Long Range Demand

Forecasting

Long Range Supply Forecasting

Long Range Supply Forecasting

Capacity Planning & Allocation

Capacity Planning & Allocation

Patient Scheduling Models

Patient Scheduling Models HHR SchedulingHHR Scheduling Resource

SchedulingResource

Scheduling

Managing Demand Variability

Managing Demand Variability

Managing Supply Variability

Managing Supply Variability

Analysis of PathwaysAnalysis of Pathways

PatientsPatients PeoplePeople ResourcesResources

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Operations Research Tools

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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

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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

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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

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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

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Simulation Approach

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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

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 1 2 3 4 5

=

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A stochastic model may be used rather

than a simulation

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.

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Results

Low volumeMedium Volume

High VolumeExtreme Volume

Scenario 1 2 3 4 5 6 7 8

(arrivals/week) 0.25 0.25 1 1 3 3 5 5

(surgery/week) 0.75 0.50 1.25 1 3 2.75 5 4.75

Prob(empty) 0.6693 0.5481 0.2282 0.1304 0.0423 0.0158 0.0252 0.0087

Prob(bumping) 0.0078 0.0963 0.0353 0.1304 0.0423 0.0978 0.0252 0.0583

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Validation – Comparing DES/Queue

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Excel-based “OR Tool”

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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

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Operations Research Tools

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Thank you!

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