The Internal Revenue Service

Post-Of-Duty Location Modeling

System - Final Report

Paul D. Domich, Karla L. Hoffman, Richard H. F. Jackson

Marjorie A. McClain

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Applied Mathematics

Gaithersburg, MD 20899

July 1986

Issued February 1987

Sponsored by

Research Division

lal Revenue Service

100 ington, DC 20224

V%

NO.$b-34$l W

NBSIR 86-3482

THE INTERNAL REVENUE SERVICE

POST-OF-DUTY LOCATION MODELING

SYSTEM - FINAL REPORT

Paul D. Domich, Karla L. Hoffman, Richard H. F. Jackson

Marjorie A. McClain

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Applied Mathematics

Gaithersburg, MD 20899

July 1986

Issued February 1987

Sponsored by

The Research Division

Internal Revenue Service

Washington, DC 20224

U.S. DEPARTMENT OF COMMERCE, Malcolm Baidrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

ABSTRACT

This report documents a project undertaken by the National Bureau of

Standards to develop a mathematical model which identifies optimal locations

of Internal Revenue Service Posts-of -Duty . The mathematical model used for

this problem is the uncapacitated, fixed charge, location-allocation model

which minimizes travel and facility costs, given a specified level of

activity. The report includes a discussion of the location problem and the

mathematical model developed. Data sources identified and used are also

described. Brief descriptions of the mathematical techniques used and the

interactive, user-friendly computer system built to solve the problem are also

provided. The system is microcomputer -based and uses menus and graphically

displayed maps of tax districts for interactive inputs and solution outputs

.

Keywords: facility location, uncapacitated, location-allocation, plant

location, warehouse location, fixed- charge , personal computer, microcomputer,

interactive graphics, greedy algorithm, heuristic algorithm.

ii

ACKNOWLEDGMENT

There have been many who have participated in the successful completion

of this project to whom we owe a great debt of gratitude. From the National

Bureau of Standards, there is Ralph Schofer, whose experience in

transportation modeling was invaluable. Thanks are also due to Dmitri Krass,

who worked out the details of the graph coloring algorithm to display the

final solution, to Dave Tate for his work on the solver routines, and to

Howard Hung who helped in the model formulation. At the Internal Revenue

Service, a huge debt is owed to Ellie Convery, whose guidance at all levels of

project design and implementation made it possible to complete it

successfully. Jim Iocozzia's untiring work behind the scenes ensured, as much

as humanly possible, the receipt of data and documents on time and accurately.

John Hiniker, John Angle, and John Kam also provided assistance, guidance, and

answers when sorely needed.

iii
TABLE OF CONTENTS

1 . Introduction 1

2 . The Physical and Mathematical Models ................................ 4

2.1 Quantification of Levels of Activity. ........................... 4

2 . 2 Data Aggregation ................................................ 5 2 . 3 Distance Measurements 5 2 . 4 Geographical Difficulty 6

2 . 5 Costs of Traveling Between Zip Codes ............................ 6 2 . 6 The Physical Model 6 2 . 7 The Mathematical Model 7 2 . 8 Assumptions ..................................................... 9 2 . 9 Flow of Solution Procedure Use .................................. 10

3 . Data Description 13

3 . 1 Data on Activity Within a Zip Code .............................. 13

3 . 2 Zip Code Pair Data .............................................. 16

3.3 Post-of-Duty Site Data. ......................................... 16

3.4 General Cost Data. 18

4. Solution Algorithm Overview. ........................................ 19

5 . Overview of the Location Modeling System. ........................... 21

6 . Conclusions and Future Work. 23

Bibliography. 24

Appendix A: Transportation Variable Development. 25

Appendix B: Sample of Printed Output 27

IV
1. INTRODUCTION

The Internal Revenue Service (IRS) maintains field offices, called Posts - of-Duty (POD's), within each tax district. Staff at these offices are drawn

from the Taxpayer Service, Examination, Collection, and Criminal Investigation

Divisions. These POD's are located within the tax district to minimize travel

and facility costs while maintaining a high degree of accessibility to the

taxpayers. In order to keep costs at a minimum, the IRS would like its Postsof-Duty close to its centers of activity. Thus whenever economic and

demographic shifts within a state cause corresponding shifts in the location

of tax activities, the POD's responsible for such activities might also need

to be moved. Although general guidelines are set forth in an Internal Revenue

manual, each district develops its own specific guidelines and methodology for

selecting new POD locations or eliminating existing ones.

In view of the potential benefits to be realized by both the taxpayers

and the IRS, the National Office of the IRS contracted with the National

Bureau of Standards (NBS) to produce a mathematical model which finds optimal

locations of Posts-of-Duty based on minimizing costs to the IRS and to the

public. The work statement for this project required that the following

factors be considered in this modeling effort:

a) the volume and complexity of the workload expected or already known to

be in effect at the Posts-of-Duty;

b) the accessibility of the office (bearing in mind terrain and distance

factors)

;

c) demographic considerations such as density, growth and migration of

the population; and

d) the costs including staffing, availability of staff and the

availability of Federal space in buildings where Posts-of-Duty could

be located.

The decision problem addressed here is that of determining the minimum

number of Posts-of-Duty needed to satisfy the current workload in a district

and to locate them physically in the district so as to minimize travel and

facility costs. More specifically, the problem can be stated as follows.

GIVEN

- a set of existing and potential POD locations,

- a specific level of activity in the district,

LOCATE

- POD's so as to minimize facility costs and travel costs (to IRS

staff and to taxpayers)

.

A mathematical model for the problem of determining the optimal number of

POD's in a tax district is known as a "facility location problem." When

formulated as such a problem, the model is easy to describe, but may have

thousands of variables making it impossible to solve to proven optimality on a microcomputer. We used this basic model, but built a system around a solution

technique that determines "near" optimal locations of a prespecified number of

POD's in very reasonable times on a microcomputer. Using Lagrangian

relaxation techniques, we then provide a measure of how far from optimality

the solution can be. This quick response time allows the model to be solved

1
repeatedly, altering the allowable number of POD sites each time, thereby

determining an optimal number of POD's as originally desired.

From discussions with IRS District Office staff, we found that, in most

cases, this system will be used to relocate a small number (less than five) of

POD's in a district where there are also a relatively small number of

potential locations for the new offices (usually not more than ten) . Various

configurations and their costs can thus be determined in the manner described

above, by running the model under different input conditions. If one wished

to consider reconfigurations where more of the locations would be altered,

that too is possible. The computation time increases significantly, however.

This paper is one of a series of reports documenting the Internal Revenue

Service Post-of-Duty Location Modeling System. The reports in the series are

as follows.

1)

The Internal Revenue Service Post-of-Dutv Location Modeling System:

Final Report

This report describes the Post-of-Duty location problem and its

mathematical model. It discusses the types of data which are considered in

calculating costs, describes the methods used to solve the location problem,

and gives a brief introduction to the computer implementation of the model.

NBS Contact: Richard H. F. Jackson

2)

The Internal Revenue Service Post-of-Dutv Location Modeling System:

User's Manual

This report is a user's guide for the Post-of-Duty location computer

system. It gives hardware and software requirements, instructions for

installing the system, descriptions of data files, and detailed instructions

for operating the system. NBS Contact: Marjorie A. McClain

3)

The Internal Revenue Service Post-of-Dutv Location Modeling System:

Programmer's Manual for FORTRAN Driver

The Post-of-Duty location program is written in two sections of code, one

in FORTRAN and the other in PASCAL. This report describes the FORTRAN driver

which handles graphics displays and controls input and output for the solution

procedure. The report includes an alphabetical list of the FORTRAN routines,

describing the purpose, the calling sequence and the variables of each

routine. NBS Contact: Marjorie A. McClain

4)

The Internal Revenue Service Post-of-Dutv Location Modeling System:

Programmer's Manual for PASCAL Solver

This report describes the second part of the Post-of-Duty location

program, the PASCAL solver. It discusses the algorithms and data structures

used to solve a location problem. NBS Contact: Paul D. Domich

The remainder of this report consists of four sections and two

appendices. Section 2 provides some background material about the problem

2
under consideration, describes the process of converting from the physical

problem to a mathematical representation, describes the precise mathematical

representation subsequently developed, states the assumptions made, and ends

with a graphical depiction of the flow of the solution procedure. Section 3 contains a full description of the data used in the POD location system, and

Section 4 contains an overview of the mathematical procedures used at each

stage of the solution procedure. Section 5 is an overview of the complete

system developed to solve the problem. It includes brief discussions of the

two principal parts of that system: the graphically based input/output

procedures in the driver and the mathematically based solution procedures in

the solver. Conclusions regarding this effort are given in Section 6.

Appendix A describes a process for computing weights that could be used to

modify straight-line distances used in the model to reflect more accurately

local travel impedances. Lastly, Appendix B contains sample output.

3
2. THE PHYSICAL AND MATHEMATICAL MODELS

The purpose of this section is to describe the mathematical model

developed for the IRS Post -of- Duty problem. In order to do this

satisfactorily, it is first necessary to discuss very briefly some of the data

used in the model. The intention here is only to provide sufficient detail

regarding the data so as to achieve a full understanding of the model, not to

describe the data completely. More complete descriptions of the data are given in Section 3

.

The first step in providing an accurate mathematical model of the IRS

Post-of-Duty location problem is to describe in more detail what is meant by

"level of activity" in the simple problem statement given in the preceeding

section. This means essentially that, of all the data bases maintained by, or available to, the IRS, the most appropriate for use in representing activity

level in this modeling effort must be identified. The next problem to be

resolved is to what level this workload data must be aggregated, since there

is typically more detail in the data bases than is needed. Also, as prescribed by the statement of work, the model must account for geographic

accessibility of the POD’s. Lastly, distances between zip codes and

corresponding traveling costs must also be computed. Each of these issues is

discussed in this section.

2.1 Quantification of Levels of Activity

This POD location model is driven by existing workload within a District.

Therefore, the choice of workload measure is critical to our modeling success. A variety of possible measures of workload were postulated, and it was determined that many of them could be used in this model. Almost all of them

are available from the IRS Individual Master File (IMF) and the Business

Master File (BMF) . We examined these data bases for applicability to each of

the four main IRS District Office functions: Examination, Collection,

Taxpayer Service, and Criminal Investigation. For the Examination activity,

possibilities for workload measure include:

a) the number of returns with Discriminant Function (DIF) scores above a certain specified number, within a specified taxpayer income class, or

b) the number of returns in the top X percent (specified by the user or National Office) of DIF scores, by income class, or

c) the number of audits by return class.

For the IRS Collection function, the possibilities include:

a) the number of taxpayer delinquent accounts by return type and

amount , or

b) the number of taxpayer delinquency investigations by return type,

c) the data collected for DIIP/DIAP (Delinquent Investigation Inventory

Profile/Delinquent Account Inventory Profile) reports.

Similarly for the Criminal Investigation Division, we could use

a) the number of open cases, by return class, or

b) the number of closed cases, by return class.

4
Finally, for Taxpayer Service, the model could use the number of taxpayer

notices sent (first, second, third, and fourth), by return class, and the

number of computer- generated error notices sent.

A more complete description of the decisions made regarding the data and

the precise data used in this modeling effort is given in Section 3.

2.2 Data Aggregation

As mentioned above, another decision that must be made regarding the data

is the level of aggregation. The IMF and BMF data are completely

disaggregated to the individual taxpayer record. For the Jacksonville,

Florida Tax District, for example, there are more than nine million such

records. Both processing considerations and taxpayer security interests

dictate aggregation of this data. It was determined that aggregation to the

zip code level was both feasible and advisable. Each record on the IMF and

BMF contains a zip code, but does not contain any of the other usual

information by which an aggregation can be done; e.g., SMSA, census tract, BEA

zones. Thus, the decision was made that the data would be aggregated to the

five -digit zip code level. This means that the workload data described above

for each of the IRS functions was summed for each category to provide totals

for each zip code. (Note that zip code data cannot be aggregated to the fourdigit zip code level and that three-digit aggregation was deemed too gross to

produce meaningful travel and income -level differences.)

2.3 Distance Measurements

The decision to aggregate introduced another problem, that of how to

measure distances between zip codes. Since the model will be minimizing

travel costs and travel costs are based on distances traveled, it is necessary

to have some convenient method for measuring distances between (aggregated)

data points, or zip code regions. We needed to associate a specific and

unique point with each zip code to be used in distance calculations.

For this, the location of the main Post Office in each zip code region

was first considered, but that proved to be difficult information to obtain

and update. (The U.S. Postal Service does not keep these coordinates in a machine -readable form.) Also considered was computing a point in the interior

of each zip code, which represents, in some sense, the center. Since at least

two commercial vendors maintain machine -readable coordinates of zip code

regions, this data could be used to compute various measures of the center of

a zip code.

After an evaluation of the alternatives, it was found that no mathematical technique can guarantee that the computed point will lie

completely within the boundary of a zip code region. E.g., crescent- shaped

and doughnut -shaped regions will result in exterior "centers." For these

regions, the centers must be moved inside the boundaries by hand. This was not done in the prototype system developed for the Jacksonville District,

since the vendor from whom the boundary data files will be purchased also

supplies files of "modified" centroids which are guaranteed to lie within the

correct boundaries. Having the coordinates of these modified centroids allows

the model to compute Euclidean distances between zip code regions quickly. In

5
the interests of brevity, modified centroids will simply be called centroids

in the remainder of this report.

2.4

Geographical Difficulty

The cost of traveling between zip code regions is based on the Euclidean

distance, but it is not correct to assume that costs are independent of the

location of the zip code regions. For example, traveling in the mountains on back roads is more time consuming than in the plains on interstate highways,

and this should be reflected in a higher traveling cost for such regions.

This is incorporated into the mathematical model by providing weights used to

multiply distances between zip code pairs which are more difficult to travel.

These weighted distances can be used in regions where mountain ranges exist,

bodies of water impede, downtown traffic slows progress, or where direct line

distances do not accurately reflect true roadway distances. They could also

be used to incorporate other penalties like parking costs that are not

explicitly a part of the model.

We have not been able to identify any machine -readable data source that

can provide this information to the model for every region in the continental

United States. Therefore, if a user wishes to change these values from their

default settings, he must calculate the weights outside the model. The actual

resetting of the weights can be done interactively inside the system, however.

Furthermore, in Appendix A, we discuss a process by which the calculation of

the weights can be made more rigorous.

2.5

Costs of Traveling Between Zip Codes

There are basically three types of costs that are used in the model:

travel cost, operating cost, and the cost of opening or closing a POD. Travel

cost is determined as a dollar-per-mile cost, and is provided to the model in one of the basic input files. Operating cost is based on square feet of

office space required by a POD and the rental cost per square foot of that

space. Each potential and existing POD site has associated with it a dollarper-square-foot cost. The cost of opening or closing a POD is determined by

the District Office staff and is included as part of the input data.

(Opening/closing costs might include items such as cost of relocating

employees, cost of hiring new employees, and the cost of training new

employees.) Each of these is used in the model to determine the cost of a possible POD configuration.

2.6

The Physical Model

Since we assume that aggregation of workload factors to five digit zip

code levels is adequate, the model can be structured physically around the

locations and boundaries of these five digit zip codes. The model then

becomes what is commonly known as a network model , and the physical

realization of the zip codes, shown in Figure 1, can be converted from zip

code boundaries in the "real world" to zip code nodes in a network. These

nodes are connected by arcs associated with distances between zip code

6
centroids. In this initial, simplified mathematical representation of the zip

code network, the distance from node i to node j is denoted d. .

.

Figure 1 : Conversion of Physical Problem to Mathematical Representation.

With such a mathematical representation, the problem of locating POD's in

the network and allocating zip code activity to POD locations can be

formulated in a mathematically succinct way. For small problems, this

representation can aid in the hand calculation of a solution. For example,

for the problem in Figure 1 with 5 nodes and 10 arcs , there would be 10

possible choices for locating two POD's. If one were also given the cost of

opening/closing POD's, the cost of traveling between POD's, and the workloads

at each node (which translate to a number of trips) , one could solve this

problem simply by calculating the cost of each possible choice and choosing

that which is minimal. However, more realistic situations include districts

having thousands of nodes and up to 50 potential or current Posts -of- Duty to

be located/relocated. As the size of the problem increases, the complexity

increases exponentially. Clearly, complete enumeration of such problems is

impossible on a microcomputer.

Hence, a solution procedure must be developed that will capitalize on the

special structure of the problem and solve it quickly and efficiently. There

are many ways this can be done, but before these can be discussed, it is

necessary to be more specific about the detailed structure of the proposed

mathematical model. This mathematical structure is given next.

2.7 The Mathematical Model

The specific statement of the mathematical model of the IRS Post-of-Duty

location problem is given on the next page:

7
minimize 2 u.x. . + 2 v.(l - x..) + 2 2

j

e J

J jeJ ^ j e J iel

(T. .+ S. .)x.

.

ij ij 1J

subject to

where

IJ

u.

J V.

pa

q

tpq

w.ip

S. . 1J

2 x. .= 1 , i € I

;

je j ^

2

2

iel

j J;

= set of all zip code numbers in the district;

=> subset of I containing zip code numbers of all current and

potential POD sites; = 1 if zip code iel is assigned to POD j

e J , 0 otherwise;

= cost of opening a POD at zip j e J ($) , if not already opened; = cost of closing a POD at zip j e J ($) , if already in existence;

= cost of round-trip travel from zip code iel to POD jeJ, or

2cg. . d. . f .

;

6

iJ ij i

= cost of travel ($/mi.); = a weight representing relative difficulty of travel between zip

code iel and POD j e J

;

= distance from zip code iel to POD j e J (mi.); = weighted number of trips generated by zip code iel, or

P 2 2 2

p-i q=1

a B t w. q p pq ip 9

= number of IRS activities considered by model; = weight used in balancing IRS dollars and taxpayer dollars; = on/off switch for IRS workload class p, =1 if use this class in

problem, = 0 if not used;

= number of trips per workload unit for IRS workload class p made by

traveller type q (trip factor); = workload in zip code iel for IRS workload class peP; = office space cost for assigning zip code iel to POD j e J , or hr . s .

;

J J

8
h = office space required for each IMF return (sq. ft.);

r^ = number of IMF returns filed in zip code j e J

;

Sj = rental cost for office space in POD je J ($/sq. ft./yr.); and

k = total number of POD's desired in the solution; and

M = number of zip codes in the set I

This model is referred to in the literature of Operations Research as an uncapacitated, fixed-charged location-allocation model (see Francis and White

(1974), and Wagner (1975)). The objective function is a measure of the cost

of opening/closing Posts-of -Duty plus office space costs and the costs

incurred by IRS personnel and taxpayers for traveling between POD's and

taxpayer locations. The constraints are the feasibility conditions. The

first constraint assures that each zip code region is assigned to one and only

one Post-of-Duty for coverage. The second one requires that the number of

Posts-of-Duty be some preset value, k. The third constraint assures that zip

codes are assigned only to potential or current POD zip codes which have been

chosen to be Posts-of-Duty in the solution. For the Jacksonville District,

the broadest application (where each zip code can be a POD) of this model has

at least one million variables and two thousand constraints, not counting the

integer constraints. In that form it is too big to be solved by any existing

integer programming code

.

The goal, therefore, is to find ways to exploit the special structure of

this problem to reduce its size. For example, whenever a Post-of-Duty site is

fixed (i.e., must remain in existence), the number of variables in the problem

decreases significantly. Similarly, whenever one specifies that a zip code

site does not qualify for a POD location, the number of possible alternatives

to evaluate is reduced. Finally, whenever one invokes the rule that no zip

code can be assigned to a Post-of-Duty whose distance from it is greater than

some prespecified limit (in the Jacksonville district this maximum distance is

approximately 75 miles), the number of variables is also reduced. Each of

these reasonable modeling specifications, and others, can be used to reduce

both problem- size and problem- complexity

.

One last note should be included here reqarding the calculation of S„ , the office space cost for each zip code. Currently, this is computed by

relating number of IMF returns to square feet of office space in use. A more appropriate measure would relate square footage to workload for each of the

IRS functions . Only with such a measure can one determine how much square

footage is necessary for each of the functions: Examination, Collection,

Taxpayer Service and Criminal Investigation.

2.8 Assumptions

It is important to understand the following assumptions that are implicit

in the use of this model.

a. Travel costs, operating costs, and costs of opening or closing Postsof-Duty are the driving data for the model. Staffing costs are not

to be considered in this model since all IRS functions will be

treated according to current or projected tax activity within that

9
functional area. (E.g., specification of DIF cutoff scores, which

determine examination workload, is outside this modeling effort.)

Thus the model is not intended to be used to compute the optimal

allocation of IRS staffing funds among the IRS functions, but rather

to determine the location of offices to minimize travel costs and

facility operating costs given a specified amount of activity within

each of the major IRS functions, and to assign specific zip codes to

POD'S.

b. Aggregation of workload factors to the five digit zip code level is

adequate for the purposes of this model.

c. Travel costs to the taxpayer within this model are not necessarily

considered equal to the travel costs to the IRS.

d. Taxpayer service walk-ins will be treated in the model. Taxpayer

service phone activity will not.

e. There will be no upper or lower limits set on the staff-size of

Posts -of -Duty . The model will determine both the location and the

size of a facility.

f. Future demand projections will be supplied to the model and not

generated internally. The model will produce near- optimal locations

based on the static demand data available to it. When future

projections are required, the data will be projected externally. The

model will then solve this new static problem.

g. The model user (District Director, National Office analyst, or District Office analyst) will be asked to define reasonable ranges on

the number of POD's to be located, geographical difficulty factors,

maximum distance per trip that an agent or a taxpayer will be asked

to travel, cost per square foot of office space for existing and

potential POD sites, weights for IRS/taxpayer costs, and categories

of workload to include

.

2.9 Flow of Solution Procedure Use

In Figure 2, the method by which this solution procedure is to be used is

indicated. In order to understand the use of this procedure, consider a situation where there are 25 current, fixed POD's, 10 potential sites, and the user wants up to 5 new POD's opened. In this case, five successive runs of

the Location Modeling system would be made, with five different values of k,

the number of desired sites in the final solution. The first step in the

procedure is to perform the model simplifications noted previously that reduce

the large model to a smaller, solvable one. With this reduced static data

(any required data projection is performed outside of the model), a near- optimal POD configuration with k open POD's is computed, along with the

allocation of the remaining zip codes to these POD's. In addition, the cost

of that configuration is computed, and the solution is displayed to the user

graphically. Hard-copy output is also available, as is a bound on the maximum

difference between this near-optimal configuration and the optimal one. Empirical evidence reported in the literature (see Morris (1978)) indicates

10
FLOW OF SOLUTION PROCEDURE

Figure 2: Flow of Solution Procedure Use.

11
that very often the solution obtained by this procedure is optimal. The

results of Morris indicate that if the bounding procedure is used and allowed

to run to termination, 96% of the time it will terminate with the optimal

solution (Morris, (1978)). In any case, the solution is guaranteed to be no worse than the bounds provided.

This solution process stops once the user has obtained runs for all

values of the input data of interest. A major assumption governing the use of

this procedure is that each of the model runs can be performed quickly. This

has turned out to be true. For example, one of the test runs with 23 current,

16 potential, and three new sites to be chosen, required less than 5 minutes

on an IBM PC -XT to find a solution, which in fact was optimal.

The computer programs could be easily modified to produce solutions for a range of values of k automatically, thereby simplifying this iterative

process. However, this would be done at the expense of increased solution

times for single values of k.

Now that the model of the POD location problem has been given, we are ready to describe in complete detail the data used by it. This is given in

the next section.

12
3. DATA DESCRIPTION

Critical to the success of any quantitative analysis effort is both the

ability to model adequately the system under question, and the ability to

acquire the data which this representation requires. This section will

discuss the data acquisition issues related to modeling the IRS Post-of Duty

Study as a "facility location problem".

When we first began this effort, we were asked to consider the following

factors which affect the location of offices: 1) the workload currently

existing or projected to exist in various regions, 2) the accessibility of the

office (considering terrain and transportation patterns) , 3) the likely shifts

in population and tax activity, and 4) the costs, including opening and/or

closing costs, availability of staff, and variable' space costs.

We had a variety of meetings with IRS National Office and Field Personnel

to determine which of this information was quantifiable and what might be the

best ways of acquiring data. Not surprisingly, some data were much easier to

acquire than others. For simplicity of exposition, we will categorize the data

by whether they are: a) descriptive of activity within a zip code, b)

descriptive of how zip code pairs relate, or c) general cost data which are not unique to specific zip codes.

3.1 Data on Activity Within a Zip Code

Data which pertain to activities within a zip code are workload data. It was determined that much of the information concerning the workload of a specific zip code could be ascertained from the IRS Individual and Business

Master Files.

For examination workload , the Individual and Business Master Files

contain information on the returns which had been audited and, for certain

types of returns, the DIF score of every return. From this information, one could define workload as

:

1) number of taxpayers with DIF score above national cutoff levels in zip

code i and tax class j

,

2) number of taxpayers with DIF scores above some inventory level in zip

code i and tax class j

,

3) number of taxpayers audited within tax class j and zip code i.

Each of these data items were collected for each zip code and tax class

within a district. When discussing the use of this data as representative of

"examination workload", both IRS field-office and national-office personnel

agreed that DIF score information adequately represented workload for return

classes with scores.

For the collection workload , the problem is more complicated. Fieldpersonnel believe that the zip code DIIP/DIAP (Delinquent Investigation

Inventory Profile/Delinquent Account Inventory Profile) reports would provide

a good measure of workload. However, these data are not yet collected into

machine -readable summary reports by zip code. (There are only District

summaries at this time.) For this reason, the study group chose to use both

the number of Individual Master File Taxpayer Delinquency Investigations

13
(TDI's) and Taxpayer Delinquent Accounts (TDA's) issued within a zip code.

Field-office collection personnel believe that these data serve only as a weak

substitute for the true measure of collection workload. We understand that

DIIP/DIAP monthly workload summary reports are currently being instituted on a trial basis. When these data become more widely available, we recommend that

they be substituted for the TDI and TDA data currently in use.

For the taxpayer- service function , surrogate data must be used, since

currently counts do not exist of the number of people arriving at IRS offices

for taxpayer assistance. What is needed is not the number of people who

arrive, but the number of people residing within each zip code in a district

who come to an IRS office for taxpayer assistance. Although this would be the

"perfect" measure of taxpayer service workload, we do not believe it

worthwhile to create a data-collection effort to acquire these data. Instead, we chose to use as a substitute the number of TDA and TDI first notices and

the number of math error notices which originated in each zip code. (Second,

third and fourth notices were ignored for fear of too much double counting.)

These data can easily be retrieved from counts of the Individual and Business

Master Files. Although these data are only a surrogate for the true data,

they are believed to be a relatively good measure.

For criminal investigation , the number of criminal investigation cases were tallied by zip code. The total number of criminal investigation cases,

in even the largest of Districts (e.g. Jacksonville), is very small relative

to the amount of workload in other IRS functions . Due to this small workload

count, we suspect that eliminating this data from the model will not affect

the final locations of zip codes. The Criminal Investigation Function will

not be adversely affected by this omission since many of these criminal

investigations are performed jointly with local, state and federal law

enforcement officials, and Criminal Investigation personnel can use offices

provided by these agencies. Currently, the Criminal Investigation data is

being collected and used in the modeling effort. We will investigate -- using

sensitivity analysis -- the degree to which this data affects the overall

results of the model.

Once these workload counts have been collected, we need to be able to

relate the amount of workload within a zip code to the number of trips

required to handle each of these instances of workload. For example, suppose

we have determined that there are 25 examination returns with high DIF score

in zip code 11111 for class 1. We must then be able to translate these 25

returns into the number of trips the taxpayer and/or an IRS employee takes to

complete these audits. We have received data from Jacksonville indicating the

conversion factors necessary to convert workload counts into trips for each

audit class and each IRS function. Table 1 provides this data.

14
TABLE 1

TRIP FACTORS FOR JACKSONVILLE DISTRICT

Examination*

% handled by

IRS

% handled by Trips per

Taxpayer 100 cases-IRS

Trips per

100 cases -Taxpayer

Class 1 10.9 89.1 95

Class 2 18.4 81.6 88

Class 3 6.7 93.3 47

Class 4 12.0 88.0 72

Class 5 10.0 90.0 69

Class 6 51.1 48.9 100

Class 7 34.4 65.6 142

Class 8 40.2 59.8 176

Class 9 66.3 33.7 203

Class 10 26.7 73.3 113

Class 11 33.0 67.0 156

Class 12 61.3 38.7 212

105

165

140

185

195

230

120

148

190

123

123

138

* These data are used in the following way. If there are 100 cases in Class

1, they will generate a total of 104 trips because:

1) 100 x .109 x .95 = 10.4 trips,

2) 100 x .891 x 1.05= 93.6 trips, and

3) 10.4 + 93.6 = 104.

Collection

For each 100 cases

,

taxpayers

:

the following trips will be generated for IRS and

Trips/100 cases

Case type IRS Taxpayers Total

TDI 300 75

TDA 200 30

375

230

Taxpayer Service

Trips per 100 notices = .0247.

Criminal Investigation

Trips per C.I. Case = 120.

15
3.2 Zip Code Pair Data

For each zip code-POD pair, a measure of the geographic difficulty of

traveling between the zip code regions, and the distance between regions, is

needed. As described above, a modified centroid is used as the specific

location to be used with each zip code in distance calculations. The Euclidean

distance between two centroids is then used to represent the average distance

a taxpayer/IRS employee traveled.

We have incorporated geographic difficulty into the mathematical model by

allowing the user to specify weights with which to multiply distances between

zip code pairs which are more difficult to travel. For more on this see Section 2.4 and Appendix A.

Other data which must be described is data relating to each current or potential POD site.

3.3 Post-of-Duty Site Data

For each POD zip code region, we need to know the cost of opening a Postof-Duty (if it is does not currently exist), the cost of closing an existing

Post-of -Duty , and the operating costs associated with maintaining a Post-ofDuty in that zip code. Operating costs are defined to be the costs of leasing

space in a building for the purpose of housing the personnel assigned to this

POD site. We believe that this cost should be relative to the number of

people assigned to that zip code. Therefore, square footage cost of space is

used in the model.

The opening/closing costs for the Jacksonville district are provided in

Table 2 below, as well as the cost of square footage for each potential and

current POD zip code region. Note that the data on square footage costs

cannot be uniform throughout a zip code. The Facilities Management personnel

within IRS were asked to provide costs based on the most likely locations for an office within that zip code region. In discussions with field office

personnel, they indicated that this type of information is relatively wellknown and easy to acquire. Note also that since travel costs and rental costs

are calculated on an annual basis, the one-time costs of opening/closing a POD

must be amortized across some fixed number of years.

16
TABLE 2

OPENING, CLOSING, AND RENTAL COSTS FOR JACKSONVILLE DISTRICT

POD TYPE OPENING COST* CLOSING COST* OFFICE RENTAL COST/SO. FT

32018 CURRENT 0.00 1.00 9.54

32202 CURRENT 0.00 1.00 8.93

32301 CURRENT 0.00 1.00 13.25

32401 CURRENT 0.00 1.00 8.99

32501 CURRENT 0.00 1.00 10.35

32601 CURRENT 0.00 1.00 8.53

32670 CURRENT 0.00 1.00 8.30

32771 POTENTIAL 1.00 0.00 10.00

32801 CURRENT 0.00 1.00 13.84

32901 CURRENT 0.00 1.00 8.23

33130 CURRENT 0.00 1.00 11.36

33169 CURRENT 0.00 1.00 13.25

33173 CURRENT 0.00 1.00 0.00

33174 POTENTIAL 1.00 0.00 13.00

33301 CURRENT 0.00 1.00 11.19

33401 CURRENT 0.00 1.00 0.00

33432 POTENTIAL 1.00 0.00 16.00

33450 CURRENT 0.00 1.00 10.13

33583 CURRENT 0.00 1.00 10.68

33602 CURRENT 0.00 1.00 11.95

33616 POTENTIAL 5.00 0.00 0.00

33702 FIXED 0.00 1.00 10.06

33801 CURRENT 0.00 1.00 6.10

33907 CURRENT 0.00 1.00 10.89

* These are fictitious, since actual costs of opening and closing were unavailable at the time these runs were made.

17
Finally, data regarding situations unique to specific districts might

also be collected. Examples include offices which must remain open, areas which cannot be considered for POD locations, any unusual transportation costs

(e.g., high parking fees, severe traffic problems), and any rules specific to

the district (e.g., Revenue Officers never travel more than 60 miles,

taxpayers are never asked to travel more than 45 miles for an audit)

.

The only other data which this modeling effort requires is data which is

global in nature; that is, data not unique to a specific zip code region.

3.3 General Cost Data

The facility location model requires the specification of a functional

relationship between workload and personnel. This function together with a square footage per person requirement determines the staff assigned to a specific zip code and the accompanying square footage required for the POD

site. This data is not only needed by the model to represent adequately the

costs of operating a POD site, but is also useful for presenting the results.

It is far more informative to provide information regarding staffing needs

within a POD site than to state only where each of the POD's is to be located.

Finally, one needs the cost per mile to be associated with traveling to or from a POD site for both an IRS agent and a taxpayer. This data should be

provided in terms of a cost-per-mile figure. The tables provided as part of

the sample output in Appendix B contain the existing realization of these data

for the Jacksonville District Office. The next section gives an overview of

the algorithms developed to solve the POD location problem using the data

described above

.

18
4. SOLUTION ALGORITHM OVERVIEW

Two approaches to the computer solution of the mathematical POD location

problem can be categorized by whether the problem is to be solved on a mainframe computer or on a microcomputer. In the former case, using good

reduction and reformulation techniques yielding less than 50 zero -one variables, the problem can be solved to optimality. If, on the other hand,

the problem size cannot be reduced sufficiently, "heuristic" approaches can be

used together with other integer programming techniques to yield "good"

solutions with estimates of how far from optimality they could be. A major

advantage of using the heuristic approach is that facility location problems

such as those considered by IRS can typically be solved in seconds on a mainframe computer, which correspondingly means that they can be solved in a few minutes on a microcomputer.

The latter is an option which has associated with it a number of other

advantages, including ease-of-use, portability, and interactive, graphically

based input of problem parameters and output of solution configuration. It is

for these reasons that the decision was made to use a heuristic approach to

solving the problem and capitalize on the use of a microcomputer, thereby

avoiding the communications problems of building a mainframe procedure that

would be resident on a central computer and available on a time -sharing basis

by dial-up for each District Office.

The method for finding a "good" solution to -the facility location problem

involves two well-known and dependable heuristic procedures. The first is a Greedy heuristic (see, for example, Cornuejols, et al. , (1977)) and the

other is the Interchange heuristic (see, for example, Teitz and Bart (1968)).

To display the solution found by this method, a coloring of the zip code areas on the map is required. The graph coloring algorithm used is the Sequential

Least-first Interchange Algorithm (see Matula et al. , (1972)), which

determines a coloring of the map so that no two adjacent zip code areas share

the same color. These three procedures are briefly outlined below.

Assume that the desired number of POD's in the final solution is

different from the number of currently existing POD locations . The Greedy

heuristic in its simplest form will add/delete POD sites from the current POD

configuration sequentially, so to minimize the total cost given the set of POD

sites already selected. This procedure is called "greedy" since it will only

examine the cost of a single addition/deletion at each step, and does not

consider the addition, deletion, or exchange of two or more POD sites jointly.

For the facility location problem, a Greedy procedure will terminate with a good, but not necessarily best, set of POD locations of the prescribed number.

Once the target number of facilities has been allocated by the greedy

procedure, the interchange procedure tries to determine a better solution with

the same number of open POD sites. The procedure iteratively locates pairs of

POD sites, one which is currently selected and one not, such that if the two are interchanged in the current configuration, the overall cost will be

reduced. When no such pair exists, the routine terminates with the last

configuration

.

The Greedy heuristic and the interchange heuristic described above are well-known (see Cornuejols, et al. (1977) and Erlenkotter (1978)) to produce

19
good solutions to the facility location problem. A drawback of these

procedures is that it is difficult to determine when the generated solution is

in fact the optimal integral solution to the described problem. However, it

is possible to investigate the optimality of a solution by generating lower

bounds on the optimal integer objective function value. One such bound can be

obtained by solving the linear programming (LP) relaxation of the original

problem, i.e., the original problem without the integrality constraints.

In general, the LP formulation of the facility location problem has a large number of constraints in the problem description and it, too, can be

difficult to solve. Lagrangian relaxation techniques can be used to produce

the optimal LP objective function value in an efficient iterative manner, and

provide at each step a lower bound on the optimal solution to the original

facility location problem. The relaxation we used is one which removes the

restriction that a zip code is serviced by only one POD and adds a penalty to

the objective function for violations of these constraints. Further, by

rounding the possibly fractional real -valued solution produced by this method, an improved integral solution may be found as a. by-product. The interested

reader may refer to the many articles in this subject (e.g., Cornuejols, et

al. (1977)).

To display in color the final assignment of zip code areas to POD

locations determined above, it is necessary to ensure that no two adjacent POD

service areas, i.e., two areas sharing a common border, are colored with the same color. This is a map coloring problem, where the regions involved are groups of customers aggregated by their assigned POD facility. The problem is

to choose colors for the regions V. of a graph G, such that CL is not equal

to CL if and are adjacent regions, and in such a fashion that a "small"

number of colors are used. Since all of the zip code maps can be represented

as planar graphs (i.e., graphs that can be drawn on a sheet of paper so that

no two edges cross), theoretically all can be colored using only four colors.

In practice, to find a four-coloring is a very difficult problem, so a fiveor six-coloring is used. For a description of the coloring algorithm, see Matula, et al.

,

"Graph Coloring Algorithms," (1972). The procedure used is

called the Sequential Least-first Interchange heuristic (SLI)

.

20
5. OVERVIEW OF THE LOCATION MODELING SYSTEM

The model and solution techniques described earlier in this report have

been implemented in a microcomputer-based software system. It is a highly

interactive, menu-driven system, that uses function keys to allow the user to

move through the solution process. It was developed on an IBM PC-XT with a math coprocessor, a ten-megabyte hard disk and a color monitor, but has been

run on a similarly configured compatible. The graphical displays are accomplished by way of zip code maps drawn on the screen from latitude

longitude data points that describe each zip code in the tax district. Zip

code data files and IRS data files containing workload and other information

are required by the system, and must be obtained by the user. The package

performs the following functions.

1) Displaying Workload

The user may choose the type of workload to be displayed, such as the

number of returns examined or the number of criminal investigation cases

.

A state zip code map is then drawn, with each zip code shaded according to the

workload it generates.

2) Displaying Initial POD Sites

A state zip code map is drawn showing where POD's are currently located

and also where new POD's could potentially be located. The user may make

modifications interactively to this information to specify POD's which may not

be or must be in the set of POD's determined by the solution procedure.

3) Solving for Optimal POD Locations

Using the initial POD information specified by the user, the solution

procedure calculates the cost of assigning each zip code to each current or potential POD. The cost includes travel costs associated with the workload of

each zip code, office rental costs, and costs of opening new POD's or closing

old POD's. The user may set parameters indicating what types of workload

(such as taxpayer service or criminal investigation) should be included in the

travel cost calculations. Also, weights may be assigned to pairs of zip codes

and POD sites to scale travel costs. The user must specify the number of

POD's desired in the solution. The solution procedure then determines the set

of POD's which will result in the least total cost for the district.

4) Displaying Optimal POD Locations

A state zip code map is drawn showing where the new POD's determined by

the solution procedure are located. Also, a report file is generated which

summarizes the problem specification and the solution. The report includes a list of which zip codes are to be assigned to which POD's.

5) Controlling Display of Maps

On any of the state zip code maps mentioned above, the user may zoom in on a small region, back up to a larger region, or find the five-digit zip code

number of an area on the map.

21
There are four stages to solving a POD location-allocation problem with

the IRS POD Location Modeling system. In the first stage, problem data are input by the user. In many cases, the data files will have been previously

created and the user need only update them if necessary. In the second stage

the user will interact with the POD Location System to provide additional

local data, or modify problem parameters for a particular configuration

desired. During this preprocessing and data manipulation stage, one can also

obtain information about the data or the physical situation by using the

display properties of the system. The third stage is the one in which the

problem is actually solved using the heuristic approach mentioned above.

Finally, in the last stage, the solution is displayed and a summary report of

the solution is written. Each of these stages is discussed in more detail in

(Domich, et al , . (1986a)).

22
6. CONCLUSIONS AND FUTURE WORK

The model and system described here have been built and will be

undergoing extensive field tests in the Jacksonville District Office of the

Internal Revenue Service. Preliminary response to its use has been

gratifyingly good. We will be responding to suggestions for improvements and

modifications and will test it using data for the Pittsburgh District in the

near future

.

In this concluding section, we wish to point out that the IRS POD

Location Modeling System has potential uses other than those described in this

report. For example, it could easily be modified to solve other facility

location problems in different application areas. In fact, the solution

algorithm routines could be separated from the graphical display routines to

become part of a general facility location solution routine. In addition, the

graphical display routines could be used as a stand-alone data display

package

.

Another possible use is as a device for determining the optimal size of

Posts-of-Duty . If there were good data available on the workload that can be

handled by employees in each of the four IRS functional areas, then, once locations have been determined, optimal size could also be output.

Some of these ideas will be pursued in our future work.

23
BIBLIOGRAPHY

Cornuejols, G. , Fischer, M.L., and Nemhauser, G.L., "Location of Bank Accounts

to Optimize Float: An Analytical Study of Exact and Approximate Algorithms,"

Management Science, Vol. 23, 789-810, 1977.

Domich, P.D., Jackson, R.H.F., and McClain, M.A. , "The Internal Revenue

Service Post-of Duty Location Modeling System: User's Manual," National

Bureau of Standards Technical Report NBSIR 86-3471, Gaithersburg, MD, July,

1986a.

Domich, P.D. , Jackson, R.H.F., and McClain, M.A. , "The Internal Revenue

Service Post-of Duty Location Modeling System: Programmer's Manual for the

FORTRAN Driver," National Bureau of Standards Technical Report NBSIR 86-3473,

Gaithersburg, MD, July, 1986b.

Domich, P.D. , Jackson, R.H.F. , McClain, M.A. , and Tate, D.M. , "The Internal

Revenue Service Post-of Duty Location Modeling System: Programmer's Manual

for the PASCAL Solver," National Bureau of Standards Technical Report NBSIR

86-3472, Gaithersburg, MD, July, 1986c.

Erlenkotter, D. , "A Dual-Based Procedure for Uncapacitated Facility Location,"

Operations Research . Vol. 26, no. 6, 992-1009, 1978.

Francis, R.L.

,

and White, J.A., Facility Layout and Location . Prentice-Hall,

Englewood Cliffs, NJ , 1974.

Garfinkel, R.S. and Nemhauser, G.L., Integer Programming . John Wiley & Sons,

New York, NY, 1972.

Morris, J.G., "On the Extent to which Certain Fixed-Charge Depot Location

Problems Can Be Solved by LP," Journal of the Operational Research Society . Vol. 29, no. 1, 71-6, 1978.

Matula, D.W.

,

Marble, G. , and Isaacson, J.D., "Graph Coloring Algorithms," in

Ronald C. Read, Graph Theory and Computing . Academic Press, New York, NY,

1972.

Teitz, M.B. and Bart, P. , "Heuristic Methods for Estimating the Generalized

Vertex Median of a Weighted Graph," Operations Research . 16, 955-61, 1968.

Wagner, H.M.

,

Principles of Managment Science, Prentice-Hall, Englewood

Cliffs, NJ, 1975.

24
APPENDIX A: TRANSPORTATION VARIABLE DEVELOPMENT

In this appendix we describe, for the record, a process for modifying

straight-line distances used in the model so as to reflect more accurately

travel times between the points in question. The technique for incorporating

these modifying weights is described in Section 2.4 of this report and also in

(Domich, et al. (1986a)). However, what is not described in either place is

how one might determine the weights required by the system. That is the

subject of this appendix.

The purpose here is to develop a measure of travel impedance between

pairs of zip code centroids for use in selecting efficient locations for

POD's. Since a limited number of POD's usually will be provided within each

state boundary, each zip code centroid in a state need not have an impedance

value between itself and every other such centroid in the state: it is

necessary only to develop impedance values among pairs of centroids which

cluster around the established or projected POD's. The maximum allowable

travel distance mentioned in section 2.7 can be used to determine these

clusters

.

We recommend that a pilot test be conducted using real data from the

Jacksonville District. A prime objective of the test is to provide costeffective impedances among zip code centroids for subseqeunt use in location

studies. Many measures of impedence have been tested and explored by land-use

and transportation modelers over the years. The exercise described here

considers two of the most popular ones, and considers only off-peak (mid-day)

travel times by automobile.

The simplest is to develop travel impedances among zip code centroids by

computing the Euclidian distance between selected centroids, and multiplying

this crow-flight distance by a distict-wide desired circuitry factor to obtain

a better estimate of true "road" distance. To obtain time of travel, this

distance would then be divided by an assumed speed, the value of which would

be area- dependent : rural, suburban or urban. Terminal times (unparking,

parking and walk time) and intrazonal times would also be developed and

applied for the same three area categories. Some hand modification might be

necessary to reflect impediments to travel such as bridges, toll booths and

swamps

.

A slightly more sophisticated alternative should also be tested. In this

alternative, travel impedances in major urban areas would be manually

developed and combined with the aforementioned procedures for the rest of the

state. The procedure would be first to identify the larger urbanized areas.

(In Florida, these are likely to be the Jacksonville area, the Tampa/St.

Petersburg/ Clearwater/Saratoga area, and the West Palm Beach/Greater Miami

combination.) Then, zip code boundary overlays of the 1/2" to 1 mile county

maps containing these urban areas would be prepared. The best routing and

probable mid-day, off-peak speed along these routings would be estimated and

converted into interzonal travel times. Nominal terminal times would be added

and a matrix of inter-zip travel times for these urban areas would be manually

constructed. These values would be merged with other inter-zip zonal travel

times developed in the first alternative.

25
Using the location model, IRS analysts could thus evaluate the solutions

obtained from three alternatives:

1) mechanically derived impedances for the whole state;

2) alternative (1) with manually derived travel times among zip zones in

large urbanized areas, and mechanically derived impedances

in other areas of the state; and

3) Euclidean distances provided originally.

26
APPENDIX B: SAMPLE OF PRINTED OUTPUT

For the sake of completeness and instruction, output from a run of the

system on Jacksonville, Florida data is provided in this appendix. Many of

the input data values were fictitious, so the results are not realistic.

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk kkkkkkkkkkkk

kkk kkk

kkk IRS POST-OF-DUTY LOCATION SYSTEM kkk

kkk kkk

kkk REPORT OF SESSION BEGINNING: kkk

kkk 4/25/86 9: 8 kkk

kkk kkk

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

kkk kkk

*** ' PROBLEM INITIALIZATION *** kkk kkk

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

kkkkkkkkkkkkkkkkkkkkkkk INITIAL POD INFORMATION *************'**'*'*'*•*****

POD TYPE OPENING COST CLOSING COST OFFICE RENTAL COST

32018 CURRENT 0.00 1.00 9.54

32202 CURRENT 0.00 1.00 8.93

32301 CURRENT 0.00 1.00 13.25

32401 CURRENT 0.00 1.00 8.99

32501 CURRENT 0.00 1.00 10.35

32601 CURRENT 0.00 1.00 8.53

32670 CURRENT 0.00 1.00 8.30

32771 POTENTIAL 1.00 0.00 10.00

32801 CURRENT 0.00 1.00 13.84

32901 CURRENT 0.00 1.00 8.23

33130 CURRENT 0.00 1.00 11.36

33169 CURRENT 0.00 1.00 13.25

33173 CURRENT 0.00 1.00 0.00

33174 POTENTIAL 1.00 0.00 13.00

33301 CURRENT 0.00 1.00 11.19

33401 CURRENT 0.00 1.00 0.00

33432 POTENTIAL 1.00 0.00 16.00

33450 CURRENT 0.00 1.00 10.13

33583 CURRENT 0.00 1.00 10.68

33602 CURRENT 0.00 1.00 11.95

33616 POTENTIAL 5.00 0.00 0.00

33702 FIXED 0.00 1.00 10.06

33801 CURRENT 0.00 1.00 6.10

33907 CURRENT 0.00 1.00 10.89

kkkkkkkkkkkkkkkkkkkkkkkkkkkk USER OPTIONS ‘k’k’k’k'k'k'k'k'k'k'k'k'k'kkkkkkkkkkkkkkk

# ITEM POSSIBLE ACTUAL

27
1 IMF EXAMINATION 0,1 | 1 2 IMF COLLECTION 0,1 | 1

3 IMF TAXPAYER SERVICE 0,1 | 1 4 IMF CRIMINAL INVESTIGATION 0,1 | 1

5 BMF EXAMINATION 0,1 | 0

6 BMF COLLECTION 0,1 | 0

7 BMF TAXPAYER SERVICE 0,1 | 0

8 BMF CRIMINAL INVESTIGATION 0,1 | 0

9 TAXPAYER TRAVEL COST WEIGHT [0. 0-1.0] | 1.00000000

10 IRS TRAVEL COST WEIGHT [0. 0-1.0] | 1.00000000

11 MAXIMUM TRAVEL DISTANCE IN MILES j 80.00000000

1 = INCLUDED IN COST CALCULATION, 0 = NOT INCLUDED

kick-k-k-kk-k-k-k^c-k-k-kirk-k-k-k-k-k-k TRAVEL DIFFICULTY FACTORS "k’k’k'k'k'k'k'k'k'k'k'kkkkkkkkkk

ZIP CODE POD ZIP CODE FACTOR

33557 33702 3.0

33615 33702 5.0

kkkkkkkkkkkkkkkkkkkkkkkkkkkk TRIP FACTORS kkkkkkkkkkkkkkkkkkkkkkkkkkkk

IRS TRIP FACTORS

0.1040

0.1620

0.0310

0.0860

0.0690

0.5110

0.4880

0.7080

1.3460

0.3020

0.5150

1.3000

3.0000

2.0000

0.0000

1.2000

TAXPAYER TRIP FACTORS

0.9360

1.3460

1.3060

1.6280

1.7550

1.1250

0.7870

0.8850

0.6400

0.9020

0.8240

0.5340

0.7500

0.3000

0.0002

0.0000

kkkkkkkkkkkkkkkkkkkkkkkkkk OTHER PARAMETERS kkkkkkkkkkkkkkkkkkkkkkkkkk

OFFICE SPACE REQUIREMENT = 0.062 SQUARE FEET PER IMF RETURN

TRAVEL COST = $ 0.205 PER MILE

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

kkk kkk

kkk SOLUTION kkk

kkk kkk

kkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk

28
COST = $ 156166508.72 (Note: Fictitious result due to sample problem data)

ZIP CODES ASSIGNED TO POD 32018:

32005 32010 32012 32014 32015 32016 32017 32019 32020 32021

32022 32023 32028 32030 32032 32033 32036 32037 32045 32057

32069 32074 32080 32081 32088 32090 32230 32617 32624 32631

32632 32633 32634 32654 32660 32662 32663 32664 32681 32682

32690 32706 32709 32710 32720 32722 32732 32733 32734 32740

32744 32747 32759 32763 32764 32768 32777 32790 32793 32798

32814 32816 32853 32854 32855 32856 32858 32861 32959 33848

33858

ZIP CODES ASSIGNED TCi POD :32202:

32007 32009 32011 32034 32040 32043 32046 32058 32063 32068

32072 32073 32079 32082 32084 32087 32097 32201 32203 32204

32205 32206 32207 32208 32209 32210 32211 32212 32215 32216

32217 32218 32219 32220 32221 32222 32223 32224 32225 32226

32227 32229 32233 32234 32244 32250 32265 32267 32602 32616

32658

ZIP CODES ASSIGNED TC) POD :32301:

32013 32053 32059 32302 32303 32304 32305 32306 32307 32308

32309 32311 32312 32321 32322 32323 32324 32327 32330 32331

32332 32333 32334 32336 32337 32340 32343 32344 32346 32347

32350 32351 32352 32355 32356 32357 32358 32360 32361 32362

32423 32442 32460 32466

ZIP CODES ASSIGNED TO POD !32401:

32320 32328 32335 32403 32405 32407 32409 32410 32420 32421

32422 32424 32425 32426 32427 32428 32430 32431 32432 32433

32437 32438 32439 32440 32443 32444 32445 32446 32448 32449

32452 32453 32454 32455 32456 32459 32461 32462 32463 32464

32465 32537 32538 32544 32564

ZIP CODES ASSIGNED TO POD :32501:

32434 32503 32504 32505 32506 32509 32510 32511 32512 32522

32530 32531 32533 32535 32536 32541 32542 32560 32561 32563

32565 32567 32568 32569 32570 32577 32578 32579 32580

ZIP CODES ASSIGNED TO POD :32601:

32008 32031 32038 32042 32044 32047 32048 32049 32052 32054

32055 32060 32061 32062 32066 32071 32077 32083 32089 32091

32094 32096 32359 32615 32618 32619 32621 32622 32626 32628

32635 32638 32640 32643 32648 32656 32666 32667 32669 32680

32683 32685 32692 32693 32694 32696 32697 32630

ZIP CODES ASSIGNED TO POD 32670:

32039 32093 32620 32625 32627 32629 32636 32637 32639 32642

32645 32646 32647 32649 32650 32659 32661 32665 32668 32672

32673 32679 32684 32686 32691 32695 32698 32702 32731 32735

32748 32762 32785 33502 33513 33514 33521 33524 33526 33531

33536 33538 33554 33556 33585 33593 33604 33802 33849

ZIP CODES ASSIGNED TO POD 32801:

32701 32703 32705 32707 32708 32711 32713 32725 32726 32729

29
32730 32737 32741 32745 32746 32750 32751 32753 32754 32755

32756 32757 32760 32761 32765 32766 32767 32769 32771 32775

32776 32778 32780 32784 32786 32787 32789 32792 32797 32803

32804 32805 32806 32807 32808 32809 32810 32811 32812 32813

32817 32820 33503 33530 33550 33587 33601 33623 33685 33835

33863

ZIP CODES ASSIGNED TO' pod :32901:

32739 32903 32905 32922 32925 32935 32937 32950 32951 32955

32957 32958 33438

ZIP CODES ASSIGNED TOi POD :33169:

33009 33010 33012 33013 33014 33015 33016 33019 33021 33023

33024 33025 33026 33027 33028 33029 33054 33055 33056 33126

33127 33132 33137 33138 33139 33140 33141 33147 33150 33154

33160 33161 33162 33167 33168 33179 33180 33181 33331 33332

ZIP CODES ASSIGNED TCi POD :33173:

33001 33030 33031 33032 33033 33034 33035 33036 33037 33039

33051 33070 33122 33125 33128 33129 33130 33133 33134 33135

33136 33142 33143 33144 33145 33146 33155 33156 33157 33158

33165 33166 33170 33172 33174 33175 33176 33177 33178 33182

33183 33184 33185 33186 33187 33189 33190 33192 33193 33196

33925 33943

ZIP CODES ASSIGNED TO POD 33301:

33004 33020 33060 33062 33063 33067 33068 33304 33305 33306

33308 33309 33311 33312 33313 33314 33315 33316 33317 33319

33322 33323 33324 33325 33326 33328 33330 33334

ZIP CODES ASSIGNED TO POD 33401:

33403 33404 33405 33406 33407 33408 33409 33410 33411 33430

33440 33455 33458 33460 33461 33462 33463 33470 33480

ZIP CODES ASSIGNED TO POD 33432:

33011 33022 33061 33064 33065 33066 33116 33124 33151 33153

33163 33164 33194 33197 33302 33303 33307 33318 33320 33327

33335 33338 33339 33431 33433 33434 33435 33436 33437 33441

33444 33445 33446 33493

ZIP CODES ASSIGNED TO POD 33450:

32948 32949 32960 32970 32971 33402 33439 33456 33457 33472

33476 33490 33491 33492 33494 33852 33857

ZIP CODES ASSIGNED TO POD 33583:

33504 33505 33506 33507 33508 33509 33517 33522 33523 33529

33532 33533 33545 33548 33551 33555 33558 33559 33560 33561

33564 33577 33578 33580 33581 33582 33586 33588 33595 33596

33730 33734 33736 33737 33738 33739 33740 33821 33842 33864

33865 33890 33902 33920 33927 33938 33945 33946 33952 33953

ZIP CODES ASSIGNED TO POD 33602:

33511 33512 33527 33534 33539 33547 33549 33552 33553 33557

33568 33569 33570 33574 33576 33584 33592 33594 33598 33603

33605 33606 33607 33608 33609 33610 33611 33612 33614 33615

30
33616 33617 33618 33619 33620 33621

ZIP CODES ASSIGNED TO POD 33702:

33515 33516 33519 33520 33528 33535 33540 33541 33542 33543

33563 33565 33572 33589 33590 33591 33701 33703 33704 33705

33707 33709 33710 33711 33712 33713 33714

ZIP CODES ASSIGNED TCi POD :33801:

32736 33525 33537 33566 33597 33599 33803 33805 33820 33823

33825 33827 33830 33834 33837 33838 33839 33840 33841 33843

33844 33846 33847 33850 33851 33853 33854 33855 33856 33860

33866 33868 33870 33873 33877 33880

ZIP CODES ASSIGNED TC• POD 33907:

33459 33471 33901 33903 33904 33905 33908 33922 33923 33926

33928 33929 33930 33931 33933 33934 33935 33936 33937 33939

33940 33944 33950 33954 33955 33956 33957 33960

31
N BS-1 1 4A [rev, 2 -ec) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NBSIR 86-3482 FEBRUARY 1987

4. TITLE AND SUBTITLE

The Internal Revenue Service Post-of-Duty Location Modelling System - Final Report

5. AUTHOR(S)

Paul D. Domich, Karla L. Hoffman, Richard H. F. Jackson, Marjorie A. McClain

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) 7. Contract/Grant No. national bureau of standards ______________________

DEPARTMENT OF COMMERCE 8. Type of Report 8. Period Covered

WASHINGTON, D.C. 20234 j

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City . State , ZIP)

The Research Division

U. S. Internal Revenue Service

1201 E Street

Washington, DC 20224

10. SUPPLEMENTARY NOTES

I | Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

ABSTRACT (A 200-word or less factual summary of most significant information . If document includes a significant

bibliography or literature survey, mention it here)

This report documents a project undertaken by the National Bureau of Standards to

develop a mathematical model which identifies optimal locations of Internal Revenue

Service Posts-of-Duty . The mathematical model used for this problem is the uncapacitated, fixed charge, location-allocation model which minimizes travel and facility

costs, given a specified level of activity. The report includes a discussion of the

location problem and the mathematical model developed. Data sources identified and

used are also described. Brief descriptions of the mathematical techniques used and

the interactive, user-friendly computer system built to solve the problem are also

provided. The system is microcomputer-based and uses menus and graphically displayed

maps- of tax districts for interactive inputs and solution outputs.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) facility location, uncapacitated, location-allocation, plant location, warehouse

location, fixed-charge, personal computer, microcomputer, interactive graphics,

ereedv algorithm, heuristic algorithm.

13. AVAILABILITY

14. NO. OF

[~X ] Uni i mi ted PRINTED PAGES

For Official Distribution. Do Not Release to NTIS 37

[ 1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. _ 20402. 15. Price

Cx] Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $11.95

USCOMM-OC 6043-P80