EMS Central Communications Centre (CCC)

Staffing Analysis – Final Presentation & Deliverables

Shuang E Scott Van Bolhuis Derek Hewitt Jenny Morrow

Problem Recap

Suboptimal Staffing Forecast Simple Rudimentary Inefficiency and Simplicity Lacked Robustness Lacked Scalability Reduced Effectiveness and Planning Ability Over/understaffing Unable to plan for the future

Solution Recap

Analyzed Large amounts of Data CAD and Telephony Found patterns and discovered service times and demand figures Created Model and Controlled for Variability and Inefficiency Created Staffing model to account for variability Analyzed Results in ARENA and Improved Robustness Increased Effectiveness and Planning Ability Implementation and Intelligence Possible solutions depending on demand and Increased Planning Ability

Solution Recap

Queue length

= number of customers waiting for service (=state of system minus number of customers being served)

N(t)

= number of customers in queueing system at time t (t>=0)

P n (t) s

= probability that exactly n customers are in queueing system at time t, given number at time 0 = number of servers in queueing system

λ n Ч n

= mean arrival rate (expected number of arrivals per unit time) of new customers when n customers are in the system = mean service rate (expected number of customers completing service per unit time)

Solution Recap

(cont’d) Performance Measurement and Analysis (ARENA)

Variable Demand

Schedule Model

Optimal Staff Required and Optimal Shifts Evaluator Service Times Based on Call Type

Planning Ability

Observations-Call Demand

Demand may increase over time, however, the percentage of weekly demand in each hour should remain about the same The model uses the percentage of weekly demand per hour to find hourly demand given expected weekly demand

Distribution of Service time

Service Rates Log Normal M/M/s Queueing Model Displays no Significant Variation Minimum Servers is a Stepwise Function

Distribution of Time in System

Observations

30 25 20 15 10 5 0

Hour of the Day

Strath ERCC CCC

Observations

30 25 20 15 10 5 0

Hours of the Day

Other Air IFT Air Emerg Transfer Non Emerg Emerg

Testing for Correlations

15 10 5 0 40 35 30 25 20

Hour of the Day

Wednesday Saturday

Testing for Correlations

20 15 10 40 35 30 25 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour of the Day

Wednesday Thursday

Testing for Correlations

T-test for Significant Differences Sunday Monday Tuesday Wednesday Thursday Friday Saturday

0.934

3.107

Friday

-4.615

-0.138

-3.359

4.582

4.651

3.840

-0.948

2.226

2.056

Thursday

-5.734

-1.844

-4.064

0.207

Wednesday

-5.677

-1.924

5.092

Tuesday

-4.075

-0.538

Monday

-3.524

If value <-2 or >2, the two corresponding days have significantly different arrival patterns.

The red cells indicates the days that have similar arrival patterns.

Process Flow

More detailed version in appendices and written report

Call back Hang Up Evaluators Emergency Arrival Queue Evaluators Pre Alert Pro QA Paramedics Notified Evaluators IFT Arrival Evaluators Coordination Scheduling Air Arrival Evaluators Helicopter Notified Contact With Ground Coordination

Station Capacity

Building a Model

Minimal Deciding Inputs Achieve Desired Result Usefulness Defining Output Practicality Discovering Intermediate Steps Minimize Inputs Maximize Output

Finding Basic Constraints

What we Need • Optimal staffing schedule with the minimum number of call evaluators that can provide desired service level Constraint • No less than minimum required servers in each hour How to Find Minimum Required Servers • Queueing Toolpak formulas • Inputs • Threshold time, service level, arrival rate, and service rate

Determining Threshold and Service Level Sensitivity Analysis

• Found min number of servers required under different threshold and service levels

Minimum Required Work Stations

• Conducted analysis for a peak hour in the week, so selected results determined the min required work stations

Determining Threshold and Service Level

Model Assumptions

Weekdays follow the same Weekend days

Model Assumes

with less demand

Weekdays and Weekend Days

stepwise function so small differences do not matter

Minimum Required Servers

Weekday Ground Emergency and IFT Calls

Minimum Required Servers

Weekend Ground Emergency and IFT Calls

Model Assumptions

Different Arrival and Service Rates • Different call types have different arrival and service rates and must be accounted for separately Cross Training • Call evaluators are able to answer all different call types Aggregate Minimum Required Servers • The minimum required servers that constrains the model is the aggregate of the minimum required servers for each call type

Binary Model - Mechanics

Simplified model without union constraints

Binary Model Constraints

Shift start times must be reasonable Shift lengths must follow union guidelines Breaks must be accounted for Days must be connected since shifts wrap into the next day

Creating Useful Output

Added Union Constraints

Total Staffing hours per week

Added Start Times and Breaks into the Model to create a more useful schedule

How to Operate the Model

Step 1 • The first tab “Staff Optimizer 3000” contains 3 input cells, these are expected weekly demand for each call type • Those input cells properly constrain the model Step 2 • Go to the “Scheduling Model” tab and press solve Step 3 • Go to the “Week’s Schedule” tab to find the output • Filter out the 0s in the column labeled “Number of Shifts”

How to Operate the Model

Inputs

Sample Schedule Output

Wednesday Employee Number shift length Shift Start

525460

15 min break 30 min break 15 min break

12 5:30:00 AM 8:15:00 AM 11:15:00 AM 2:30:00 PM 966492 308384 584997 733703 12 6:30:00 PM 9:15:00 PM 12:15:00 AM 3:30:00 AM 12 9:00:00 PM 11:45:00 PM 10.5 10:30:00 AM 1:00:00 PM 10.5 9:00:00 PM 11:30:00 PM 2:45:00 AM 6:00:00 AM 3:30:00 PM 6:30:00 PM 2:00:00 AM 5:00:00 AM 206250 275492 529698 516983 757914 654707 737753 167357 589771 607777 8.25 7:30:00 AM 9:15:00 AM 11:30:00 AM 1:45:00 PM 8.25 8:30:00 AM 10:15:00 AM 12:30:00 PM 2:45:00 PM 8.25 10:30:00 AM 12:15:00 PM 8.25 9:00:00 PM 10:45:00 PM 2:30:00 PM 4:45:00 PM 1:00:00 AM 3:15:00 AM 6.25 7:30:00 AM 8:45:00 AM 10:30:00 AM 12:15:00 PM 6.25 12:00:00 PM 1:15:00 PM 4.25 7:30:00 AM 9:30:00 AM 3:00:00 PM 4:45:00 PM 4.25 2:30:00 PM 4:30:00 PM 4.25 4:30:00 PM 6:30:00 PM 4.25 6:30:00 PM 8:30:00 PM

Model – Analysis/Simulation

Arena

Results of the Simulation

Call Type

Emergency Non Emergency IFT Air Emergency Air IFT Other

Position

Call Evaluator Flight Coordinator

Average Wait Time (s)

0.04

0.09

0.11

11.65

9.53

0.03

Average Service Time (min)

1.16

1.34

1.17

4.80

1.51

1.37

Utilization Rate

8.72% 3.88%

Average Number Scheduled

4.09

1.27

Impact on CCC and more

Effectiveness

• Our analysis in action • Reducing costs • Confidence in staffing schedule • Applicability to all centers

Updated Deliverables

Written report • Summarized analysis, sensitivity Tests and recommendation • User guide for model Schedule Model and ARENA outputs • Provides optimal staffing schedule subject to Demand changes • Provides results and insights Process flow • Detailed analysis of processes and actors • Derived from our modeling

What you need

Premium Solver

• Runs and optimizes schedule model

Queueing Toolpak

• Supports embedded queueing formulas in model

We will help you install and use these add-ins and applications through our personal demonstration and user’s guide.

QUESTIONS?

Appendices

1)

• •

Process flow

Emergency

We describe in detail what the adjacent diagram represents for 911 calls: Step 1) Emergency incident occurs, caller calls 911 EPS (EPS primary, AHS secondary) Step 2) Call evaluator verifies location of caller, while location information from TELUS and phone companies is populated Step 3) Call evaluator prealerts dispatcher and paramedics Step 4) Conduct ProQA (roughly 45sec) while paramedics are getting ready Step 5) Information populates into CAD Step 6) After scenario is confirmed and acuteness identified, paramedics are notified Step 7) Time stamp recorded Note: Children stay on the phone for the entire duration Roughly 10% of the time the call evaluator stays on the line to conduct pre-arrival instructions

2) IFT (Inter-facility transfer)

• Step 1) Call or fax from AHS entity or other contracting company • - Fax is pre-booked days in advance, Calls are within hours or the same day • Step 2) Multiple calls can be made and modifications to facility transfer route • -IFT transfer planning is one of the most cognitively demanding positions Notes: -Dispatching for IFT is not linear and static like 911 calls, can be pushed backed and modified -Seven or more radio calls are used for each IFT (inter-facility transfer call), CCC deals with roughly 150 IFT calls per-day -One person is designated for time-stamping and another person is designated for radio receiving.

• •

3) Air Ambulance

• The flight portion of the incoming calls are also a diverse entity. Flight call evaluators have to be fluent in both inter facility transfer coordination as well as emergency because the incoming flight calls could be either. The IFT’s are pre-booked and the info waits in CAD for 3-4 days before the transfer takes place. Flight calls are also much longer than the normal emergency call and can be overly demanding.

Emergency Flight Calls: Step 1) Helicopter takes off within 30min of call Step 2) Many more calls are made to coordinate activities between ground crew, paramedics and critical care teams, multiple events must be coordinated Notes: -Time of a call may be double, triple or even longer than a regular ground 911 call -Two flight call evaluators, also take regular calls (one dispatcher) -Heavy call demand for time stamping from multiple areas ( STARS etc)