EMS Central Communications Centre (CCC)
Staffing Analysis – Final Presentation & Deliverables
Shuang E Scott Van Bolhuis
Derek Hewitt Jenny Morrow
Problem Recap
Reduced Effectiveness and Planning Ability
Over/understaffing Unable to plan for the future
Inefficiency and Simplicity
Lacked Robustness Lacked Scalability Suboptimal Staffing Forecast
Simple Rudimentary
Solution Recap
Increased Effectiveness and Planning Ability
Implementation and Intelligence Possible solutions depending on demand and Increased Planning Ability
Created Model and Controlled for Variability and Inefficiency
Created Staffing model to account for variability
Analyzed Results in ARENA and Improved Robustness
Analyzed Large amounts of Data
CAD and Telephony Found patterns and discovered service times and demand figures
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)Pn(t) = probability that exactly n customers are in queueing system at time t, given number at time 0s = number of servers in queueing systemλn = mean arrival rate (expected number of arrivals per unit time) of new customers when n customers are in the systemЧn = mean service rate (expected number of customers completing service per unit time)
Solution Recap (cont’d)
Variable Demand
Evaluator Service Times Based on Call Type
Schedule Model Optimal Staff Required and Optimal Shifts
Performance Measurement and Analysis (ARENA)
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
Minimum Servers is a Stepwise Function
M/M/s Queueing Model Displays no
Significant Variation
Distribution of Time in System
Observations
0:002:00
4:006:00
8:0010:00
12:0014:00
16:0018:00
20:0022:00
0
5
10
15
20
25
30
StrathERCCCCC
Hour of the Day
Arriv
al R
ate
per H
our
Observations
0:002:00
4:006:00
8:0010:00
12:0014:00
16:0018:00
20:0022:00
0
5
10
15
20
25
30
OtherAir IFTAir EmergTransferNon EmergEmerg
Hours of the Day
Arriv
al R
ate
per H
our
Testing for Correlations
12:00:00 AM
01:00:00 AM
02:00:00 AM
03:00:00 AM
04:00:00 AM
05:00:00 AM
06:00:00 AM
07:00:00 AM
08:00:00 AM
09:00:00 AM
10:00:00 AM
11:00:00 AM
12:00:00 PM
01:00:00 PM
02:00:00 PM
03:00:00 PM
04:00:00 PM
05:00:00 PM
06:00:00 PM
07:00:00 PM
08:00:00 PM
09:00:00 PM
10:00:00 PM
11:00:00 PM0
5
10
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40
WednesdaySaturday
Hour of the Day
Arriv
al R
ate
per H
our
Testing for Correlations
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 240
5
10
15
20
25
30
35
40
WednesdayThursday
Hour of the Day
Arriv
al R
ate
per H
our
Testing for Correlations
Saturday Friday Thursday Wednesday Tuesday MondaySunday 0.934 -4.615 -5.734 -5.677 -4.075 -3.524Monday 3.107 -0.138 -1.844 -1.924 -0.538Tuesday -3.359 -0.948 -4.064 5.092Wednesday 4.582 2.226 0.207Thursday 4.651 2.056Friday 3.840
T-test for Significant Differences
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.
Emergency Arrival Queue
Evaluators
Evaluators
Evaluators
IFT Arrival
Pre Alert Pro QA Paramedics Notified
Evaluators Coordination Scheduling
Air Arrival Evaluators
Helicopter Notified
Contact With Ground
Coordination
Hang Up Call back
Process Flow More detailed version in appendices and written report
Station Capacity
Building a Model
Discovering Intermediate Steps
Minimize Inputs Maximize Output
Defining Output
Usefulness PracticalityDeciding Inputs
Minimal Achieve Desired Result
Finding Basic Constraints
• Optimal staffing schedule with the minimum number of call evaluators that can provide desired service level
What we Need
• No less than minimum required servers in each hour
Constraint
• Queueing Toolpak formulas• Inputs• Threshold time, service level, arrival rate, and service rate
How to Find Minimum Required Servers
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
Weekend days follow the same pattern, with less demand
Min servers is a stepwise function so small differences do not matter
Weekdays follow the same pattern
Model Assumes 2 Different Days, Weekdays and Weekend Days
Minimum Required Servers
Weekday Ground Emergency and IFT Calls
Minimum Required Servers
Weekend Ground Emergency and IFT Calls
Model Assumptions
• Different call types have different arrival and service rates and must be accounted for separately
Different Arrival and Service Rates
• Call evaluators are able to answer all different call types
Cross Training
• The minimum required servers that constrains the model is the aggregate of the minimum required servers for each call type
Aggregate Minimum Required Servers
Binary Model - MechanicsSimplified 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 OutputAdded Union Constraints
Added Start Times and Breaks into the Model to create a more useful schedule
TotalStaffing
hours per week
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 OutputWednesday
Employee Number shift length Shift Start 15 min break 30 min break 15 min break525460 12 5:30:00 AM 8:15:00 AM 11:15:00 AM 2:30:00 PM966492 12 6:30:00 PM 9:15:00 PM 12:15:00 AM 3:30:00 AM308384 12 9:00:00 PM 11:45:00 PM 2:45:00 AM 6:00:00 AM584997 10.5 10:30:00 AM 1:00:00 PM 3:30:00 PM 6:30:00 PM733703 10.5 9:00:00 PM 11:30:00 PM 2:00:00 AM 5:00:00 AM206250 8.25 7:30:00 AM 9:15:00 AM 11:30:00 AM 1:45:00 PM275492 8.25 8:30:00 AM 10:15:00 AM 12:30:00 PM 2:45:00 PM529698 8.25 10:30:00 AM 12:15:00 PM 2:30:00 PM 4:45:00 PM516983 8.25 9:00:00 PM 10:45:00 PM 1:00:00 AM 3:15:00 AM757914 6.25 7:30:00 AM 8:45:00 AM 10:30:00 AM 12:15:00 PM654707 6.25 12:00:00 PM 1:15:00 PM 3:00:00 PM 4:45:00 PM737753 4.25 7:30:00 AM 9:30:00 AM167357 4.25 2:30:00 PM 4:30:00 PM589771 4.25 4:30:00 PM 6:30:00 PM607777 4.25 6:30:00 PM 8:30:00 PM
Model – Analysis/Simulation
Arena
Results of the Simulation
Call Type Average Wait Time (s) Average Service Time (min)Emergency 0.04 1.16Non Emergency 0.09 1.34IFT 0.11 1.17Air Emergency 11.65 4.80Air IFT 9.53 1.51Other 0.03 1.37
Position Utilization Rate Average Number ScheduledCall Evaluator 8.72% 4.09Flight Coordinator 3.88% 1.27
Impact on CCC and more
• Our analysis in action• Reducing costs• Confidence in staffing schedule• Applicability to all centers
Effectiveness
Updated Deliverables
•Summarized analysis, sensitivity Tests and recommendation
•User guide for model
Written report•Provides optimal staffing schedule
subject to Demand changes•Provides results and insightsSchedule
Model and ARENA outputs
•Detailed analysis of processes and actors
•Derived from our modeling
Process flow
What you need
• Runs and optimizes schedule model
Premium Solver
• Supports embedded queueing formulas in model
Queueing Toolpak
We will help you install and use these add-ins and applications through our personal demonstration and user’s
guide.
QUESTIONS?
AppendicesProcess flow
1) 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 populatedStep 3) Call evaluator prealerts dispatcher and paramedicsStep 4) Conduct ProQA (roughly 45sec) while paramedics are getting readyStep 5) Information populates into CADStep 6) After scenario is confirmed and acuteness identified, paramedics are notifiedStep 7) Time stamp recorded
Note: Children stay on the phone for the entire durationRoughly 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 callStep 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)