Visualization in Operations Research

by

Bruce L. GoldenRH Smith School of Business

University of Maryland

M.I.T. Operations Research Center 50th Anniversary CelebrationApril 24, 2004

Focus

A common thread: visualization

Early contacts with visualization

Vehicle routing

Ranking great sports records

College selection

Conclusions1

Psychologists claim that more than 80% of the information we absorb is received visually (Cabena et al., 1997)

A Small Transportation Problem

Plant Warehouse

2

Supply Demand

A

B

C

300

600

500

X

Y

Z

600

300

500

041

1

73

6

36

Original problem Possible solution

The Traveling Salesman Problem

Goal: Determine product flows from Plants to Warehouses to minimize total cost

Goal: Sequence the buildings on a college campus for a security guard to inspect to minimize total time

My Dissertation Research

3

Involved large-scale vehicle routing

Partially supported by the American Newspaper Publishers Association (from January 1974 to June 1975)

� Develop a computer code for specifying vehicle routes for bulk newspaper deliveries

� Determine if these computerized approaches look promising

We worked with the Worcester Telegram (WT)� Evening circulation of 92,000, approximately 600 drop points� We located the depot and drop points on a large map with pins

� We used Euclidean distances and generated routes quickly

Transition from Ph.D. Student to Consultant

4

Next, we compared our routes to existing WT routes

WT re-examined their routes and altered several

The experiment was reasonably successful and fun

Larry Bodin and I started at the University of Maryland in 1976

Arjang Assad and Mike Ball arrived in 1978

In 1978 and 1979, the four of us worked for Scientific Time Sharing Corp.

(STSC) on two projects involving vehicle routing

We worked with Donald Soults at STSC

The projects were exciting, but STSC got most of the money

Founding and Running a Consulting Company

5

Assad, Ball, Bodin and Golden founded RouteSmart in 1980

In the 1980s, we consulted with large companies on vehicle routing

Starting in 1989, we designed and sold vehicle routing software

In 1998, we sold the business to a large NY civil engineering company

We remained connected to RouteSmart until early 2004

RouteSmart Technologies, Inc. is currently run by Larry Levy – my newspaper boy in 1978 & 1979

RouteSmart has major installations in the newspaper, utility, waste/ sanitation, and postal/local delivery industries

Let’s focus on RouteSmart’s work in newspaper distribution

A Partial List of RouteSmart’s Newspaper Clients

Washington Times

The (Toronto) Globe and Mail

Dow Jones & Company

Orlando Sentinel

Pittsburgh Tribune-Review

The Baltimore Sun

The New York Times

The Boston Globe

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The Seattle Times

Chicago Tribune

St. Louis Post-Dispatch

The New York Post

Detroit News

San Diego Union Tribune

The San Francisco Chronicle

Orange County Register

Newspaper Route Optimization

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A major success story for OR: optimization & visualization

Two different routing problems

� Home delivery (arc routing)

� Single-copy routing (node routing)

Recent Developments

� The distribution task is being outsourced (PCF)

� Numerous newspapers are distributed simultaneously (e.g., Orlando Sentinel, IBD, New York Times, Wall Street Journal)

�The routing is driven by advertising

8Home Delivery: Routes within a Zip Code

9

HD: Sequenced Stops as Crow Flies (Streets Suppressed)

10HD: Travel Paths over the Street Network

11HD: Detailed Display of a Single Travel Path

12HD: Detailed Display of a Travel Path from the Depot

13Single-Copy Routing: Sequence of Stops from the Depot

14SCR: Stops and the Street Network

15SCR: Travel Path over the Street Network

Newspaper Route Optimization: Then and Now

1974 2004

mapping wall map with pins, sophisticated GIS technologyEuclidean distances (think Mapquest)

customer static: locate once daily changes: no problem locations

driving driver’s responsibility detailed travel path provideddirections each day

goal just find a feasible take full advantage of cost-set of routes saving and advertising

possibilities 16

Ranking Outstanding Sports Records

Address several key questions

� What makes a “great” sports record?

� What factors separate “good” records from “great” records?

� What are the “great” sports records?

Rank the greatest active sports records

� season records (discussed here)

� career or multiple-year records

� daily or single-game records

Study conducted in 1986

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Motivation

It’s fun to argue the merits of your favorite sports records

It’s a challenge to carry out the comparison in a rigorous and comprehensive manner

It provides a nontrivial application of the analytic hierarchy (decision-aiding) process (AHP)

The AHP is based on the concept of pairwise comparisons and a hierarchy, which is very visually informative

We focus here on season records

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Select Best Active Season Sports Record

Incremental Improvement

Other Record Characteristics

Duration of Record

Years Record Has

Stood

Years Record Is Expected To Stand

% Better Than

Previous Record

% Better Than Contemporaries

Glamour Purity

DiMaggio 56 game hitting streakMaris 61 home runsRuth .847 slugging averageWilson 190 runs batted inChamberlain 50.4 scoring averageDickerson 2105 yards gained rushingHornung 176 points scoredGretzky 215 points scored 19

Select Best Active Season Sports Record

Incremental Improvement

Other Record Characteristics

Duration of Record

Years Record Has

Stood

Years Record Is Expected To Stand

% Better Than

Previous Record

% Better Than Contemporaries

Glamour Purity

RuthDiMaggio

ChamberlainWilson

Gretzky

MarisHornung

Dickerson 0.066

0.098

0.099

0.110

0.139

0.151

0.166

0.171

.500 .333 .167

.800 .200 .750 .250 .667 .333

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Results of 1986 Comparison

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Babe Ruth’s record was broken by Barry Bonds in 2001

Data source: The Fiske Guide to Colleges, 2000 edition� Contains information on 300 colleges� Approx. 750 pages� Loaded with statistics and ratings� For each school, its biggest overlaps are listed

Overlaps: “the colleges and universities to which its applicants are also applying in greatest numbers and which thus represent its major competitors”

Application of Visualization to College Selection

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Penn’s overlaps are Harvard, Princeton, Yale, Cornell, and Brown

Harvard’s overlaps are Princeton, Yale, Stanford, M.I.T., and Brown

If college i has college j as one of its overlap schools, we say that j is adjacent to i

Note the lack of symmetry� Harvard is adjacent to Penn, but not vice versa

Overlaps and Adjacency

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From Adjacency to a Two-Dimensional Map

Adjacency indicates a notion of similarity (not necessarily symmetric)

If college j is adjacent to college i, we draw an arc from node i to node j of length one in an associated graph

Next, compute the shortest distance between each pair of nodes

Finally, we solve a nonlinear optimization problem to build a Sammon map

24�≠=

−+−−n

ji

i ij

jijiij

d

yyxxd

k 1

22 )()((1 )Minimize

2

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Proof of Concept

Start with 300 colleges and the associated adjacency matrix

There are many groups of colleges that comprise the 300

We focus on four large groups to test the concept (100 schools)� Group A has 74 national schools� Group B has 11 southern colleges� Group C has 8 mainly Ivy League colleges� Group D has 7 California universities

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Sammon Map with Each School Labeled by its Group Identifier

A 1

A 2

A 3

A 4

A 5 A 6

A 7

A 8

A 9

A 1 0

A 1 1

A 1 2

A 1 3

A 1 4

A 1 5

A 1 6

A 1 7

A 1 8

A 1 9

A 2 0

A 2 1

A 2 2

A 2 3

A 2 4

A 2 5 A 2 6

A 2 7

A 2 8

A 2 9

A 3 0

A 3 1

A 3 2

A 3 3

A 3 4

A 3 5

A 3 6

A 3 7

A 3 8

A 3 9

A 4 0

A 4 1

A 4 2

A 4 3

A 4 4

A 4 5

A 4 6 A 4 7 A 4 8 A 4 9

A 5 0

A 5 1

A 5 2 A 5 3

A 5 4

A 5 5

A 5 6

A 5 7 A 5 8 A 5 9

A 6 0

A 6 1

A 6 2

A 6 3

A 6 4

A 6 5

A 6 6 A 6 7

A 6 8

A 6 9

A 7 0

A 7 1

A 7 2

A 7 3

A 7 4

B 1

B 2

B 3

B 4 B 5

B 6 B 7 B 8

B 9

B 1 0 B 1 1

C 1 C 2 C 3

C 4

C 5

C 6

C 7

C 8

D 1

D 2 D 3

D 4 D 5

D 6

D 7

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Sammon Map with Each School Labeled by its Geographical Location

P A

P A

M N

A Z

P A

M E

N Y

C O

C O

C T

D E

A Z

C O

G A

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D C

IA

IL

IN

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V A

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O R

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N Y

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M D

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V T

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N H

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M AIL

IN O H

O R

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P AP A

W A

IN

O R

V A N J

M A

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T N

N Y

V T

P A M E

V A

V AN C

M O

W A

M A

W A

O R

V A

W I

A LS C

S C

F L

F LG AG A

A L

F L

S CT N

R I

C T

N YM A

M A

P A

N J

C A

C A

C AC A

C AC A

C A

C A

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Sammon Map with Each School Labeled by its Designation ( Public (U) or Private (R) )

R

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UUU

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Sammon Map with Each School Labeled by its Cost

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Sammon Map with Each School Labeled by its Academic Quality

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Six Panels Showing Zoomed Views of Schools that are Neighbors ofTufts University

A19

A21

A3A43

A45

A5A5

A60

A65

A66

A68

A73

C1C2

C3C5

C7

C8

GA

DC

NYNY

NC

MAMA

MA

VA

VA

MO

VA

RINY

MAPA

CA

CT

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Emory

Georgetown

BarnardNYU

UNC

BCBC

Tufts

VPI

UVA

WashU

W&M

Brown

CornellHarvard

UPenn

Stanford

Yale

(a) Identifier

(f) School name(e) Academics

(d) Cost(c) Public or private

(b) State

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Benefits of Visualization

Adjacency (overlap) data provides “local” information only � E.g., which schools are Maryland’s overlaps ?

With visualization, “global” information is more easily conveyed� E.g., which schools are similar to Maryland ?

33

Conclusions

Visualization helps to sell OR techniques and tools, especially in the commercial world

Visualization of OR solutions makes them transparent and promotes credibility

Visualization (and animation) plays a positive role in many other OR applications (e.g., decision trees, clustering, simulation, belief networks)

Visualization plus optimization is a powerful, winning combination

34