Visualization in Operations Research

Transcription

1 Visualization in Operations esearch by Bruce L. Golden H Smith School of Business niversity of Maryland M.I.T. Operations esearch Center 50 th Anniversary Celebration April 24, 2004

2 Focus A common thread: visualization Psychologists claim that more than 80% of the information we absorb is received visually (Cabena et al., 1997) Early contacts with visualization Vehicle routing anking great sports records College selection Conclusions 1

3 A Small Transportation Problem Supply 300 Plant A Warehouse X Demand B C Y Z Goal: Determine product flows from Plants to Warehouses to minimize total cost The Traveling Salesman Problem Original problem Possible solution Goal: Sequence the buildings on a college campus for a security guard to inspect to minimize total time 2

4 My Dissertation esearch 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 3

5 Transition from Ph.D. Student to Consultant 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 niversity 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 4

6 Founding and unning a Consulting Company Assad, Ball, Bodin and Golden founded outesmart 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 outesmart until early 2004 outesmart Technologies, Inc. is currently run by Larry Levy my newspaper boy in 1978 & 1979 outesmart has major installations in the newspaper, utility, waste/ sanitation, and postal/local delivery industries Let s focus on outesmart s work in newspaper distribution 5

7 A Partial List of outesmart s Newspaper Clients Washington Times The (Toronto) Globe and Mail Dow Jones & Company Orlando Sentinel Pittsburgh Tribune-eview The Baltimore Sun The New York Times The Boston Globe The Seattle Times Chicago Tribune St. Louis Post-Dispatch The New York Post Detroit News San Diego nion Tribune The San Francisco Chronicle Orange County egister 6

8 Newspaper oute Optimization A major success story for O: optimization & visualization Two different routing problems Home delivery (arc routing) Single-copy routing (node routing) ecent 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 7

9 Home Delivery: outes within a Zip Code 8

10 HD: Sequenced Stops as Crow Flies (Streets Suppressed) 9

11 HD: Travel Paths over the Street Network 10

12 HD: Detailed Display of a Single Travel Path 11

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

14 Single-Copy outing: Sequence of Stops from the Depot 13

15 SC: Stops and the Street Network 14

16 SC: Travel Path over the Street Network 15

17 Newspaper oute Optimization: Then and Now mapping wall map with pins, sophisticated GIS technology Euclidean distances (think Mapquest) customer static: locate once daily changes: no problem locations driving driver s responsibility detailed travel path provided directions each day goal just find a feasible take full advantage of costset of routes saving and advertising possibilities 16

18 anking Outstanding Sports ecords Address several key questions What makes a great sports record? What factors separate good records from great records? What are the great sports records? ank the greatest active sports records season records (discussed here) career or multiple-year records daily or single-game records Study conducted in

19 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 18

20 Select Best Active Season Sports ecord Duration of ecord Incremental Improvement Other ecord Characteristics Years ecord Has Stood Years ecord Is Expected To Stand % Better Than Previous ecord % Better Than Contemporaries Glamour Purity DiMaggio 56 game hitting streak Maris 61 home runs uth.847 slugging average Wilson 190 runs batted in Chamberlain 50.4 scoring average Dickerson 2105 yards gained rushing Hornung 176 points scored Gretzky 215 points scored 19

21 esults of 1986 Comparison Select Best Active Season Sports ecord Duration of ecord Incremental Improvement Other ecord Characteristics Years ecord Has Stood Years ecord Is Expected To Stand % Better Than Previous ecord % Better Than Contemporaries Glamour Purity uth DiMaggio Chamberlain Wilson Gretzky Maris Hornung Dickerson

22 Babe uth s record was broken by Barry Bonds in

23 Application of Visualization to College Selection 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 22

24 Overlaps and Adjacency 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 23

25 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 Minimize n ( dij ( xi x j ) + ( yi y j ) ) k i= 1 i j d ij 2 24

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27 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 26

28 B 3 B 1 B 1 1 B 1 0 B 4 B 8 B 2 B 7 B 6 B 5 B 9 A 2 8 A 1 1 A 3 2 A 4 4 A 4 2 A 3 3 A 5 3 A 5 2 A 6 7 A 5 7 A 5 8 A 6 1 A 2 9 A 6 4 A 9 A 1 3 A 5 5 A 2 6 A 2 5 A 3 9 A 3 6 A 2 4 A 3 4 A 2 7 A 1 7 A 2 0 A 4 5 A 1 9 A 3 7 A 6 8 A 4 7 A 2 3 A 6 5 A 6 6 A 7 3 A 7 4 A 2 1 A 3 A 5 A 4 3 A 4 8 A 6 A 2 2 A 4 9 A 1 6 A 4 6 A 3 5 A 4 1 A 2 A 6 0 A 6 3 A 1 5 A 5 1 C 5 C 2 A 6 9 C 4 C 6 C 3 C 8 C 1 C 7 A 1 4 A 6 2 A 1 0 A 7 0 A 5 9 A 3 1 A 4 0 D 1 D 6 A 8 D 4 D 5 A 5 6 D 7 D 3 D 2 A 4 A 1 2 A 7 A 3 8 A 1 A 5 0 A 5 4 A 3 0 A 7 2 A 7 1 A 1 8 Sammon Map with Each School Labeled by its Group Identifier 27

29 S C A L T N S C S C G A A L G A F L F L F L P A V A P A P A N C N J V A P A N C N J T N M D V A V A N C G A D E V A V A V A D C M A P A N Y M A N J C T M A C A I N Y M A M A M A P A M E M E M E P A P A P A N Y IN M I IN M I M O IL IL W I IN M A M A M A M A C T N H V T N Y N Y M N M N C A IA O H O C A C A C A V T W I M N IA IA A Z C O O C A C A C A W A C O A Z O O W A O W A C O Sammon Map with Each School Labeled by its Geographical Location 28

30 Sammon Map with Each School Labeled by its Designation ( Public () or Private () ) 29

31 Sammon Map with Each School Labeled by its Cost 30

32 Sammon Map with Each School Labeled by its Academic Quality 31

33 A45 A65 A66 A73 C5 C2 C8 C3 C7 C1 NC VA VA VA PA NY CT MA CA I A19 GA A21 A60 DC MA A68 A5 A43 A3 MO MA NY NY (a) Identifier (b) State (c) Public or private (d) Cost NC VPI VAW&M Penn Cornell Yale Harvard Stanford Brown Emory Georgetown Tufts Wash BC NY Barnard (e) Academics (f) School name Six Panels Showing Zoomed Views of Schools that are Neighbors of Tufts niversity 32

34 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

35 Conclusions Visualization helps to sell O techniques and tools, especially in the commercial world Visualization of O solutions makes them transparent and promotes credibility Visualization (and animation) plays a positive role in many other O applications (e.g., decision trees, clustering, simulation, belief networks) Visualization plus optimization is a powerful, winning combination 34