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)
Pn(t) = probability that exactly n customers are in queueing system at time t, given number at time 0
s = number of servers in queueing system
λn = mean arrival rate (expected number of arrivals per unit time) of new customers when n customers are in the system
Чn = 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
Arrival Rate per Hour
30
25
20
15
Strath
10
ERCC
5
CCC
0
Hour of the Day
Observations
25
20
Other
15
Air IFT
Air Emerg
10
Transfer
5
Non Emerg
Hours of the Day
22:00
20:00
18:00
16:00
14:00
12:00
10:00
8:00
6:00
4:00
2:00
0
0:00
Arrival Rate per Hour
30
Emerg
Hour of the Day
11:00:00 PM
10:00:00 PM
9:00:00 PM
8:00:00 PM
7:00:00 PM
6:00:00 PM
5:00:00 PM
4:00:00 PM
3:00:00 PM
2:00:00 PM
1:00:00 PM
12:00:00 PM
11:00:00 AM
10:00:00 AM
9:00:00 AM
8:00:00 AM
7:00:00 AM
6:00:00 AM
5:00:00 AM
4:00:00 AM
3:00:00 AM
2:00:00 AM
1:00:00 AM
12:00:00 AM
Arrival Rate per Hour
Testing for Correlations
40
35
30
25
20
15
Wednesday
10
Saturday
5
0
Testing for Correlations
40
Arrival Rate per Hour
35
30
25
20
Wednesday
Thursday
15
10
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
Testing for Correlations
T-test for Significant Differences
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Friday
Thursday Wednesday Tuesday
Monday
0.934
-4.615
-5.734
-5.677
-4.075
-3.524
3.107
-0.138
-1.844
-1.924
-0.538
-3.359
-0.948
-4.064
5.092
4.582
2.226
0.207
4.651
2.056
3.840
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
Hang Up
More detailed version in appendices and written report
Call back
Evaluators
Emergency Arrival
Queue
Evaluators
Pre Alert
Pro QA
Evaluators
IFT Arrival
Evaluators
Coordination
Scheduling
Helicopter
Notified
Air Arrival
Evaluators
Contact With
Ground
Coordination
Paramedics
Notified
Station Capacity
Building a Model
Deciding Inputs
Minimal
Achieve Desired Result
Defining Output
Usefulness
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
Weekend days
follow the
same pattern,
with less
demand
Model Assumes
2 Different Days,
Weekdays and
Weekend
Min servers isDays
a
Weekdays follow
the same
pattern
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
Step 2
Step 3
• 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
• Go to the “Scheduling Model” tab and press solve
• 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
15 min break 30 min break 15 min break
525460
12 5:30:00 AM 8:15:00 AM 11:15:00 AM 2:30:00 PM
966492
12 6:30:00 PM 9:15:00 PM 12:15:00 AM 3:30:00 AM
308384
12 9:00:00 PM 11:45:00 PM 2:45:00 AM 6:00:00 AM
584997
10.5 10:30:00 AM 1:00:00 PM 3:30:00 PM 6:30:00 PM
733703
10.5 9:00:00 PM 11:30:00 PM 2:00:00 AM 5:00:00 AM
206250
8.25 7:30:00 AM 9:15:00 AM 11:30:00 AM 1:45:00 PM
275492
8.25 8:30:00 AM 10:15:00 AM 12:30:00 PM 2:45:00 PM
529698
8.25 10:30:00 AM 12:15:00 PM 2:30:00 PM 4:45:00 PM
516983
8.25 9:00:00 PM 10:45:00 PM 1:00:00 AM 3:15:00 AM
757914
6.25 7:30:00 AM 8:45:00 AM 10:30:00 AM 12:15:00 PM
654707
6.25 12:00:00 PM 1:15:00 PM 3:00:00 PM 4:45:00 PM
737753
4.25 7:30:00 AM 9:30:00 AM
167357
4.25 2:30:00 PM 4:30:00 PM
589771
4.25 4:30:00 PM 6:30:00 PM
607777
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
Queueing
Toolpak
• Runs and optimizes
schedule model
• 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
Process 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 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)