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Michael L Washington, PhDDeputy Director, Preparedness Modeling Unit
Industrial & Systems EngineerCenters for Disease Control and Prevention
August 2009
Evaluating the Capacity, Efficiency, and Cost of a
Mass Influenza/ Pneumococcal Vaccination
Clinic Via Simulation DIMACS/MBI US - African BioMathematics Initiative: Workshop on
Economic Epidemiology, 3 Aug 2009
Engineering Jokes
Engineers aren’t boring people, we just get excited over boring things.
Half Full or Half Empty?• To the optimist, the glass is half full. • To the pessimist, the glass is half empty. • To the engineer, the glass is twice as big
as it needs to be.
Agenda
• Measurements to evaluate model or actual clinic (including efficiency)
• Estimating the capacity of a mass vaccination clinic
• Issues with the optimized clinic
Measurements
• How do you evaluate a good and efficient clinic?
• First, let us evaluate a mock clinic and learn about a technique to improve the efficiency of a clinic.
Line Balance
8 hours or 480 minutesArrival Rate = 1 person per minute1 person per station
FYI. Does not reach a steady state for 1 to 2 hours and queuing theory does not work.
0.1 min 0.7 min 1 min 0.5 min 0.2 min
Which Set-up is Best?And what measure to use?
0.1 min 0.7 min 1 min 0.5 min 0.2 min
0.1 min 0.7 min 1 min 0.5 min 0.2 min
Station 10.8 min
Station 30.7 min
Station 21 min
0.1 min 0.7 min 1 min 0.5 min 0.2 min
Station 12.5 mins
1
2
3
Station 1 Station 2 Station 3 Station 4 Station 5
Some Measures of Performance
• Number of people served • # of people served or treated over time
(Throughput)• Average time people are waiting or in the
clinic• Average # of people in clinic or station (WIP)• Resource utilization – people and equipment• Cost• Customer satisfaction• Effort per person (i.e., $/person or CE ratio)
Measures
Measurement Pros Cons
Number of people served
Simple - count peopleFamiliar
No measure of efficiencyNo customer satisfaction
measure
Throughput Simple - people/hrFamiliar
No measure of efficiencyNo customer satisfaction
measure (a Honda plan - 36 cars/hr)
Exit rate Simple – ID bottleneckHelps with things
down the line
No measure of efficiencyCan be miss leading
Measures
Measure Pro Con
Clients time in the clinic
Measure of efficiency and customer satisfaction
Measure variabilityIf measured per stations,
measure trainingEasy way to ID bottleneck
Additional data requiredDifficult to collect per
stationNo standardsNot = throughput
Ave # of people in clinic (or station)
Measures of efficiencyIf measured per station,
can identify bottleneckCan easily measure for
the entire clinic
May have to be done electronically
Difficult to measure per station manually.
Measures
Measure Pro Con
Resource utilization
Measures efficiencyID over- or understaffing Can be calculated post-
event if the right data are collected
Does not provide information about one main goal
Cost Measure of resources needed to accomplish an objective
Compare across clinics
It takes time to consider all costs
Some consider it unimportant in an emergency (which I think is a mistake)
Measures
Measure Pro Con
Customer satisfac-tion
Being able to measure how the people you serve feel about your service is always a great idea.
Surveying clients is trick, and clients can be very fickle.
$/person Probably the bestMeasure the effort
involved in treating one person
Easy to get cost if documentation is good
May be difficult to collect cost, especially indirect cost
No standardDon’t worry about $ in
emergencies (mistake)
Results (100 Runs)Mean (min, max)
Measurement 1 2 3
Number of people served
454 (411, 510)
454 (409, 494)
192 (175, 213)
Throughput(client/hr)
57 (51, 64)
57 (51, 62)
24 (22, 27)
Exit rate 1 1 2.5
Results (100 Runs)Mean (min, max)
Measurement 1 2 3
Clients time in the clinic (min)
19 (7, 57)
19 (9, 45)
145 (122, 172)
Average # of people in the clinic (people)
26 (0, 96)
28 (2, 81)
287 (219, 342)
Resource utilization (%)
48 (40, 56)
80 (71, 88)
100 (99, 100)
Results (100 Runs)Mean (min, max)
Measurement 1 2 3
Direct Cost ($28/hr/staff)
$1,120 $672 $224
Indirect Cost ($18/hr/client)
$155,372($52,478, $523,967)
$160,795($64,059, $396,121)
$502,961($387,009,
659,256)
Total Cost $156,492($53,598, $525,089)
$161,467($64,722, $396,792)
$503,186($387,233, $659,480)
Results (100 Runs)Mean
Measurement(easiest)
1 2 3
Direct Cost/client
2.47 1.48 1.17
Indirect Cost/client
343 354 2,626
Total Cost/client
345 356 2,627
Agenda
• Measurements to evaluate model or actual clinic (including efficiency)
• Estimating the capacity of a mass vaccination clinic
• Issues with the optimized clinic
Simulation Model
• Evaluate one clinic design
• The main measure is the # of people vaccinated
• We will examine other measures in evaluating the clinic
• Try to improve the clinic design based upon the main measure
Optimizing a Clinic
• History– Anticipated vaccination 15,000 in 17 hours – Only 8,300 showed up and were vaccinated– Could they have vaccinated 15,000 with
current design and staff
• Simulation (very difficult with queuing)– Arrival rate was not consistent– Violate a big rule in queuing (service rate >
arrival rate)– Looked to optimize staff placement
Clients
• “Medicaid” – Assumed to be retired, > 65 years old
• “Special”– A sub-population of “Medicaid”– Usually the physically challenged
• “Cash” – Normal work force
Office
500 sq. ft. Office
300 sq. ft.
RN R
RN RN
R R R R R R
CASH
RNRN RNRN RNRN RNRN RNRN
R
Educational Display
Ed
Disp
lay
Work Station Vaccine PrepStaff Break
Area
Pneumonia Shot
Special Needs
C C
10%
20%
90%
10%
70%
10%90%
EnterExit
C C
C
Special Need
Cash
Regular Medicare
C = CopierRN = ShotsR = Registration
Staff Sits Patient Stands or Sits
Key
Staff
• Special Copy• Special Flu Form• Special Flu Vac• Pnu Form
Yellow = RNWhite = Support staffContractor/Volunteer not included (EMT, security, runners, etc)
• Pnu Vac• Medicaid Copy• Medicaid Flu Form• Reg Flu Vac• Cashier
InputsService Time at Each Station
Station # of Staff a
Type of Staff Distribution b
(SD)(minutes)
Source n
Special Flu Copy 1 AP Beta 0.40 (0.813) EO -
Special Flu Registration 2 AP Gamma 2.63 (0.930) TS 102
Special Flu Vaccination 2 RN Lognormal 1.13 (0.590) TS 158
Pnu Registration 2 AP
Medicare Client Lognormal 1.01 (0.416) TS c
Special Client Gamma 2.18 (3.140) TS c
Pnu Vaccination 4 RN
Medicare Client Lognormal 1.18 (0.561) TS c
Special Client Lognormal 1.13 (0.590) TS c
Medicare Copy 4 AP Beta 0.40 (0.813) EO -
Medicare Registration 18 AP Lognormal 1.01 (0.416) TS 402
Medicare/Cash Flu Vaccination 20 RN Lognormal 1.18 (0.561) TS 895
Cashier 3 AP Beta 0.43 (0.084) EO -
Facility Costs
• Printing• Vaccine• Copiers • T-Shirts• Signs/Banners• Food• Advertising
• Tables/Chair Rental• Rent• Supplies• Medical Billing• Sharps Removal• Refrigerator Rental
Some Cost
• Salary– Nurses– Support Staff
• Usage – Every client usedVaccine, printing, copies, supplies, etc…
InputsSupplies Type Distribution Minimum ($) Maximum ($)
Influenza Vaccine a Uniform 9.71 19.94
Pneumococcal Vaccine a Uniform 14.24 24.19
Copying/Printing Cost b 0.10
General Supplies b Varies form $0.20 to $0.25 per station
Staff Type Distribution Salary (SD) - $/hr
Registered Nurses c Lognormal 23.1 (4.5)
Administrative Personnel c Lognormal 13.3 (3)
Clients Type Distribution Salary (SD) - $/hr
Special d Lognormal 21.5 (79.5)
Medicare d Lognormal 21.5 (79.5)
Cash c Lognormal 18.1 (15)
Why worry about Client salary?
Optimizing a Clinic
Maximize: # of people vaccinated
ST: Support staff <= 30
RNs <= 26
Staffing per station >= 1
Only RNs can vaccinate
Only support staff provide support function
Tool
• Arena 11.0 Discrete-event computer simulation
• OptQuest 11.0– Neural network– Scatter search (use infeasible values)– Tabu search (cannot use previous
values)
Original Model
Optimized Model
Arrival Intensity (%) 80 40 80 140
Max Client Vaccinated 13,138 13,039 14,817 15,096
Special Flu Vaccination 2 1 1 1
Pnu Vaccination 4 2 2 2
Medicare Registration 18 15 15 15
Medicare/ Cash Flu Vaccination 20 23 23 23
Cashier 3 4 4 4
Others* 9
Total Staff 56 54 54 54* Special Flu Copy (1), Special Flu Registration (2), Pnu Registration(2), Medicare Copy (4)
Arrival intensity is the % increase in arrival rate above the original arrival rate.
0
3,000
6,000
9,000
12,000
15,000
0 20 40 60 80 100 120 140 160Intensity of Arrival Increase (%)
Clie
nts
All Clients
Special
Medicare
Cash
All Clients (Opt)
Special (Opt)
Medicare (Opt)
Cash (Opt)
Number Vaccinated
Time in Clinic
Medicare follows path similar to Special.
Throughput rateOriginal – 770 clients/hrOptimal – 880 clients/hr
0
50
100
150
200
250
300
350
0 20 40 60 80 100 120 140 160
Intensity of Arrival Increase (%)
Min
ute
s
Special
Cash
Special (Opt)
Cash (Opt)
Time in Clinic
Maximum ThroughputOriginal – 770 clients/hrOptimal – 880 clients/hr
0
50
100
150
200
250
300
350
0 20 40 60 80 100 120 140 160
Intensity of Arrival Increase (%)
Min
ute
s
SpecialMedicareCashSpecial (Opt)Medicare (Opt)Cash (Opt)
Cost
$
$100,000
$200,000
$300,000
$400,000
$500,000
$600,000
$700,000
$800,000
$900,000
0 20 40 60 80 100 120 140 160Intensity of Arrival Increase (%)
Material
Special
Medicare
Cash
Material (Opt)
Special (Opt)
Medicare (Opt)
Cash (Opt)
Other CostOther Cost Amount
Contract staff $2,882
Copiers 600
T-Shirts 1,043
Signs/Banners 350
Food 997
Ads 1,150
Tables/chairs 391
Rent 2,000
Medical billing 5,284
Sharp removal 375
Refrigerator Rental 80
Total $15,152
CE Ratio (Opt Model)
0102030405060708090
100
0 20 40 60 80 100 120 140 160
Intensity of Arrival Increase (%)
$/p
ers
on
Va
c
All CostNon Opp Cost
Agenda
• Measurements to evaluate model or actual clinic (including efficiency)
• Estimating the capacity of a mass vaccination clinic
• Issues with the optimized clinic
Issues with Optimization
• Targeted group with:– Little processing times– Few stations to visit– Larger numbers
• Alternative objective functions and constraints could have limited this disparity at the expense of efficiency
Issues with OptimizationObj function (instead of max # vacc)
– Max revenue – focus on one group of clients (who pays the most)
– Min cost – vaccinate no one– Max profit – we are the government– Max societal benefit minus cost –
programming dependent (societal perspective)
– Min time in clinic (client’s perspective)
Issues with Optimization
ConstraintsLimit the optimization to where no one spends more than a specific amount of time in the clinic; however, this also decreases efficiency if you want to maximize the # vacc
Issues with Optimization
Result (from the optimized model)– Elderly suffer: small number and slow
Still good to separate the elderly from others
– High resource utilization if want 15,000More staff are needed and capacity (safety) issue
– Planners did a good job in designing the clinic
Modeling Resources
• We must do this– Do we have enough– How much training is need– Where are they and how to allocate
them• Clinics and hospitals• Logistics, distribution, transportation• Appropriate supplies
• What is the right design or process
Opportunities
• PE Fellowship
• EIS
• ORISE
• Other fellowship programs– Presidential Management Intern– Informatics– Many more