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

Staff Allocation Models

• Risk and Safety– Safety Data– Risk/Reliability Data– Safety Data-Driven

• Workload and Activities– Inspector Activity Report Data– Demand-Driven– Required by Regulations/Law

2

Example Model (1)

• NIP (National Inspection Plan) Staff Allocation Model

• Minimize damages of railroad accidents• Regression analysis is used based on

injuries/fatalities data• Constraints on specified percentage

changes of current inspector position slots

3

Example Model (2)

• Transportation Security Administration’s Staff Allocation Model

• Three Components:– GRA Flight Data by GRA, Inc.: baggage volume,

flight & passenger distribution, and load factor– Regal Software by Regal Decision Systems: airport

configuration and screening process– Sabre Software by Sabre Airline Solutions, Inc.:

scheduling process to determine staff needed in waiting time of 10 minutes (or 5) or less.

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Example Model (3)• Positive Train Control (PTC) Staff Allocation Model• Four PTC Components:

– Dispatch Center

– Communication Systems

– Locomotive Units

– Wayside Units

• Appropriateness/Effectiveness Index Score• Maximize the total score of all inspector assignments to all

inspector activities. (To allocate the skilled inspectors to the inspection activities in reaching the most effective performance)

• Constraints

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Simulation Modeling

An Operations Research Method

Optimization

Save Resources and/orImprove Data Quality

6

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

Service

Waiting line

Queue orFacility

ArrivingCustomers x x x x x x

1

2

c

...

11

Performance Measures of Queueing Systems

Arrival rate Departure rate

Server utilization 1c

qL

sL

qW

sW

11

02

1

})1(!

)(

!

)({

)()!1(

)(

c

c

n

c

cc

c 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

13

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 17

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?24

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

uFxuxFxX

xx

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 model

2. Run the model

3. Evaluate the results

4. The results are not sufficiently accurate

5. Identify other details (operations/input data)

6. Go to step 1 and the cycle starts anew

7. 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 Q2

Region 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 All

C

NC

10:00

12:00

49.02

50.98

51.54

48.46

49.75

50.25

50.67

49.33

53.62

46.38

51.09

48.91

55.17

44.83

51.88

48.12

C

NC

12:00

15:00

52.97

47.03

50.63

49.37

51.10

48.90

51.22

48.78

50.31

49.69

51.96

48.04

54.25

45.75

51.64

48.36

C

NC

15:00

20:00

51.95

48.05

55.50

44.50

56.05

43.95

56.94

43.06

56.26

43.74

53.86

46.14

51.77

48.23

55.32

44.68

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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 Designs46

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?

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