Overview of Simulation Models and a Simulation Model for NHIS Field Operations and Cost Estimates
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Overview of Simulation Models and a Simulation Model for NHIS Field
Operations and Cost Estimates
Bor-Chung Chen
Office of Railroad SafetyFederal Railroad Administration/USDOT
April 7, 2011
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Simulation Modeling
An Operations Research Method
Optimization
Save Resources and/orImprove Data Quality
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Operations Research (OR) seeks the determination of the best (optimum) course
of action of a decision problem under the
restriction of limited resources
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An optimization model is a decision-making tool that recommends an answer (the goal to be optimized) based on analyses of information (constraints and decision variables). It consists of three components:
• The goal to be optimized,• Constraints, and• Decision variables
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Operations Research Models
• Deterministic Models– Linear Programming Models– Integer Programming Models– Network Flow Programming Models– Nonlinear Programming Models
• Stochastic Models– Inventory Models– Queueing Models– Queueing Networks and Decision Models– Simulation Models
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Types of OR Models• Analytical Models:
– The objective and constraints of the models can be expressed quantitatively or mathematically as functions of the decision variables.
• Simulation Models:– The relationship between input and output of
the models are not explicitly stated; the models break down the modeled system into basic or elemental modules that are then linked to one another by well-defined logical relationships.
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An M/M/c Queueing System
System
DepartingCustomers
ServiceWaiting line
Queue orFacility
ArrivingCustomers x x x x x x
1
2
c
...
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Performance Measures of Queueing Systems
Arrival rate Departure rate
Server utilization 1c
qL
sL
qW
sW
11
02
1
})1(!
)(!)({
)()!1()(
c
cnc
ccc cc
n
nc
cLq
qL
1
qW
Expected number of customers in queue
Expected number of customers in system
Expected waiting time in queue
Expected waiting time in system
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Total Cost of A Queueing System (Taha[2011])Cost ofWaiting
TotalCost
Cost ofOperation
Optimum Numberof Servers (Tellers)
Number of Servers (Tellers)
Cos
t Per
Uni
t Tim
e
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Queueing Systems vs. Field Operations
• Queueing Systems– The customers come
to the servers– The system is small
and simple– No traveling time
involved
• Field Operations (Personal Visits)– The servers
(interviewers) go to the customers (respondents)
– The system is very large and complicated
– Server traveling time
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Inbound vs. Outbound Telephone Call Centers
• Inbound– 800 Customer
Services– Help Desks
• Outbound– Telemarketing– Telephone Surveys– Charities– Politicians– Some Companies
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Outbound Telephone Dialing Systemas a Closed Queueing Network (Samuelson[1999])
ServiceFacility
Queue orWaiting Line
x x x x x xA
NA D
RN
Party Does Not Answer
Party Answers
Lines with PartiesWho Hang Up orGet Turned Away
WaitingTo Dial
1
2
c
...
S
W
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Outbound Telephone Dialing SystemDecision Variables
• Amount of time to anticipate service completions– Obtaining the new party too early, resulting in
an abandoned call and the need to start dialing again
– Cost of waiting too long, resulting in unnecessary idle time for the representatives
• Number of calls to attempt at once– Two or more answer, we will have one or more
abandoned calls– None answers, we will have idle representative
time
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Objectives
• Develop a valid method of predicting cost, response rates, and timing of new or continuing surveys for the field operations.
• The simulation modeling will be followed by the optimization of the field operations if a simulation model is feasible and valid.
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Definition of Discrete-Event Simulation
• Event Driven: Each occurrence of an event changes the state of the system
• Using a model (implemented as a computer program), rather than experimenting with a real system
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Steps of Simulation Study (Banks 1998)
• Model Conceptualization• Data Collection• Input Data Analysis• Model Translation• Verification and Validation• Experimental Design• Production Runs and Output Analysis
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Model Conceptualization
• Problem Formulation
• Objectives and Project Plan
• The modeling begins simply and the model grows until a model of appropriate complexity has been developed with the objectives in mind.
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Data Collection
• A data set for each variable from a survey is collected.
• Whenever possible, collect between 100 and 200 observations.
• Collect a number of samples from different time periods, such as field operations (time of day and/or day of week)
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Input Data Analysis and Modeling
• Assessing Independence• Probability Plots• Estimation of Parameters• Goodness of Fit Tests• Empirical Distributions• Simulation Support Software
– ExpertFit (A. M. Law and Associates)– Stat::Fit (Geer Mountain Software Corporation)
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Model Translation
• The conceptual model constructed is coded into a computer-recognizable form, an operational model.
• General-Purpose Software• Manufacturing-Oriented Software• Business Process Reengineering• Simulation-Based Scheduling• Field Operations? C++, FORTRAN?
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Random Number and Random Variate Generation
• Random (pseudorandom) numbers between 0 and 1 from the uniform distribution, U(0,1) or RN(0,1)
• Use Inverse Transform Method to obtain a random variable, X:
)1ln()(
)(
)(,)()Pr(
1
;0),exp(1,0
1
uuFx
xF
uFxuxFxXxx
otherwise
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Verification and Validation
• Verification concerns if the operational model is performing properly.
• Validation is the determination that the conceptual model is an accurate representation of the field operations (or the real system).
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Verification and Validation Process• It is an iterative process:
1. Add new details to the model2. Run the model3. Evaluate the results4. The results are not sufficiently accurate5. Identify other details (operations/input data)6. Go to step 1 and the cycle starts anew7. At some point, the model is determined to be
“close enough”
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Experimental Design
• For each scenario that is to be simulated, decisions need to be made concerning the length of the simulation run, the number of runs (also called replications), the manner of initialization, and controllable decision variables as required.
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Production Runs and Output Analysis
• Production runs and their subsequent output analysis are used to estimate the performance measures (cost, timing, and response rates) for the scenario that are being simulated.
• Finite-Horizon Simulations• Steady-State Simulations
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Simulation Model of Simplified NHIS Field Operations (Prototype)
• Ten FRs, 1050 cases, 105 cases per FR• Each FR covers a PSU of 60 x 60 square
miles• FRs are given 17 days starting from a Monday• All FRs start to work at 3:00 PM each day• 2004 NHIS CHI data set for input modeling• Visiting order: Traveling Salesman Problem• The model: about 1900 lines of C++ code
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Field Operation Inputs• Frequency distribution of 28 outcomes
• Interview length distributions by outcomes
• Contact/No-Contact Bernoulli distribution
• Contact time distributions
• Uniform distributions for vehicle speed
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Software Development for Field Operations Simulation Modeling
Input Modeling
Field Operations Simulation Model
Output Analysis
Costs Response Rates Timing
Field Operations Inputs
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Performance Measures
• Low Cost: Direct Labor Cost (Hours and Mileage)– Average number of personal visits per case
• High Response Rate
• Short Timing: How long it takes each month (17 days)
• It is called LHS
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Preliminary Results• 1000 independent replications with different
seeds
• Cost: $25,475– Based on $10/hr and $0.35/mile– Average number of PV = 1.74
• Response Rate: 86.04%
• Timing: 17 days
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Response Rates of 2004 NHIS Q2Region RR(%) Region RR(%)Boston 86.09 Charlotte 90.62New York 76.40 Atlanta 91.72Philadelphia 82.86 Dallas 87.23Detroit 93.46 Denver 92.04Chicago 91.21 Los Angles 87.32Kansas City 93.48Seattle 86.99 National 88.63
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Design of Experiments:Controllable Parameters
• Starting time:10:00 AM, 12:00 noon, and 3:00 PM
• Number of FRs: 10 and 15– Timing: 17 days vs. 11 days– Area: 3600 vs. 2401 square miles– Cases per FR: 105 vs. 70– FR-Days: 170 vs. 165
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Selected Frequency Distributions of Contact (C)/No-Contact (NC)
% Hours Sun Mon Tue Wed Thur Fri Sat AllCNC
10:0012:00
49.0250.98
51.5448.46
49.7550.25
50.6749.33
53.6246.38
51.0948.91
55.1744.83
51.8848.12
CNC
12:0015:00
52.9747.03
50.6349.37
51.1048.90
51.2248.78
50.3149.69
51.9648.04
54.2545.75
51.6448.36
CNC
15:0020:00
51.9548.05
55.5044.50
56.0543.95
56.9443.06
56.2643.74
53.8646.14
51.7748.23
55.3244.68
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The Six Parameter Settingsfor the Experiments
S. T. FRs Days Area FR-Days Adj. Days
1 10:00 10 17 3600 170 17.00
2 12:00 10 17 3600 170 17.00
3 15:00 10 17 3600 170 17.00
4 10:00 15 11 2401 165 11.33
5 12:00 15 11 2401 165 11.33
6 15:00 15 11 2401 165 11.33
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The Estimates of the PMs of the Six Parameter Settings
Cost($) RR(%) AVs Cost($) RR(%) AVs Saved(%)
1 25,375 86.19 1.72 25,375 86.19 1.72
2 25,238 86.86 1.71 25,238 86.86 1.71
3 25,475 86.04 1.74 25,475 86.04 1.74
4 20,722 82.23 1.68 21,349 84.72 1.73 15.86
5 20,575 83.50 1.66 21,199 86.03 1.71 16.00
6 20,589 83.88 1.67 21,213 86.42 1.72 16.73
Adjusted to 170 FR-Days
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Federal Statistics in the FY 2010 Budget
• Source: http://www.copafs.org/reports/federal_statistics_in_the_fy_2010_budget.aspx
(Total direct funding in millions)
FY2008 Actual
FY2009 Estimate
FY2010 Request
Census Bureau Current Programs
$ 232.8 $ 263.6 $ 289.0
Census Bureau Periodic Programs
1,234.0 3,906.3 7,115.7
Others 1,217.7 1,330.5 1,431.0
Total 2,684.5 5,500.4 8,835.7
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Cost Estimates of the Replication with Seed 169001
Setting TotalTime
(hours)
Wages($)
TotalDistance(miles)
Mileage($)
TotalCost($)
3 1,349.37 13,494 35,012 12,254 25,748
6 1,107.52 11,075 27,101 9,486 20,561
6(adj) 1,141.08 11,411 27,922 9,773 21,184
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The Other Three Parameter Settingsfor the Experiments
S. T. FRs Days Area FR-Days Adj. Days
1 10:00 10 17 3600 170 17.00
2 12:00 10 17 3600 170 17.00
3 15:00 10 17 3600 170 17.00
7 10:00 15 17 2401 255 11.33
8 12:00 15 17 2401 255 11.33
9 15:00 15 17 2401 255 11.33
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The Estimates of the PMs of the Other Three Parameter Settings
Cost($) RR(%) AVs Cost Saved(%)
RR Gain(%)
1 25,375 86.19 1.72
2 25,238 86.86 1.71
3 25,475 86.04 1.74
7 24,545 89.93 1.78 3.27 3.74
8 24,085 89.96 1.75 4.57 3.10
9 23,926 89.98 1.75 6.08 3.94
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Optimum number of FRs
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Conclusions
• Simulation models can be used for optimizing field operations
• Smaller PSU area is more cost effective– Less time on the roads and more time knocking on the
doors– Not at the expense of the response rate– Field operations can be completed sooner
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Microsimulation of NHIS• Physical Impediments and At-Home Patterns
of Households• Interviewer Strategies• Multiple Visits of Completed Interviews• Unrelated Persons Living in the Same House• Classification of Interviewers• Multiple Surveys• Sample Designs
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What Next?
• Most Recent NHIS CHI Data
• Classification of PSUs:– Population Densities– Car Densities– Traffic Statistics
• Development of A Simulation Language for Field Operations?
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Simulation and Modeling Textbooks
• Law and Kelton: Simulation Modeling and Analysis. 3rd edition, 2000, McGraw-Hill
• Jerry Banks, Editor: Handbook of Simulation. 1998, Wiley & Sons
• Hamdy A. Taha: Operations Research: An Introduction. 9th edition, 2011, Prentice Hall
• Hillier and Lieberman: Introduction to Operations Research, 8th edition, 2005, McGraw-Hill
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Operations Research Models
• Deterministic Models– Linear Programming Models– Integer Programming Models– Network Flow Programming Models– Nonlinear Programming Models
• Stochastic Models– Inventory Models– Queueing Models– Queueing Networks and Decision Models– Simulation Models– Field Operating Models?