UMAP Journal 36.2 2015 ICM Contest.pdf

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TheUMAPJournal Publisher COMAP, Inc. Executive Publisher Solomon A. Garfunkel ILAP Editor Chris Arney Dept. of Math’l Sciences U.S. Military Academy West Point, NY 10996 david.arney@usma.edu On Jargon Editor Yves Nievergelt Dept. of Mathematics Eastern Washington Univ. Cheney, WA 99004 ynievergelt@ewu.edu Reviews Editor James M. Cargal 20 Higdon Ct. Fort Walton Beach, FL 32547 jmcargal@gmail.com Chief Operating Ofﬁcer Laurie W. Arag´on Production Manager George Ward Copy Editor Cara Pacifico Distribution John Tomicek Vol. 36, No. 2 Editor Paul J. Campbell Beloit College 700 College St. Beloit, WI 53511–5595 campbell@beloit.edu Associate Editors Don Adolphson Aaron Archer Chris Arney Ron Barnes Arthur Benjamin Robert Bosch James M. Cargal Murray K. Clayton Lisette De Pillis James P. Fink Solomon A. Garfunkel William B. Gearhart William C. Giauque Richard Haberman Jon Jacobsen Walter Meyer Yves Nievergelt Michael O’Leary Catherine A. Roberts John S. Robertson Philip D. Strafﬁn J.T. Sutcliffe Brigham Young Univ. Google Research U.S. Military Academy U. of Houston—Downtn Harvey Mudd College Oberlin College Troy U.— Montgomery U. of Wisc.—Madison Harvey Mudd College Gettysburg College COMAP, Inc. Calif. State U., Fullerton Brigham Young Univ. Southern Methodist U. Harvey Mudd College Adelphi University Eastern Washington U. Towson University College of the Holy Cross Georgia Military College Beloit College St. Mark’s School, Dallas

2015 Vol. 36, No. 2 Table of Contents Publisher’s Editorial On His Shoulders ICM Modeling Forum Results of the 2015 Interdisciplinary Contest in Modeling Sol Garfunkel ....................................................................... 93 Chris Arney, Amanda Beecher, and Amy Krakowka Richmond..................................................... 95 Organizational Churn: A Roll of the Dice? Canyao Liu, Jiaming Song, and Chuan Yu ..............................113 Judges’ Commentary: Managing Human Capital in Organizations Chris Arney, Kathryn Coronges, Tina Hartley, Rod Sturdivant, and Robert Ulman........................................137 Particle Swarm Optimization for Sustainable Development in Zambia Guy Blanc, Henry Bristol, and Jenny Wang.............................151 Kristin Arney and Jessica Libertini.........................................171 Judges’ Commentary: Is it Sustainable? On Jargon Policy Modeling Chris Arney and Kathryn Coronges.......................................189

Publisher’s Editorial 93 Publisher’s Editorial On His Shoulders Solomon A. Garfunkel Executive Director COMAP, Inc. 175 Middlesex Tpke., Suite 3B Bedford, MA 01730 s.garfunkel@comap.com In Memoriam: Lynn A. Steen (1941–2015) Lynn Arthur Steen passed away this June. It is impossible to overstate his importance to U.S. mathematics education. He was truly a giant, and we are in fact taller because we have had his shoulders to stand on. Quite simply, he was the best expositor that mathematicseducationhas ever known. And he cared deeplyabout our teaching all students to the best of their ability. As no one else, he was able to communicate to a broad public as well as to the mathematics and education community. He was our voice and our conscience. Lynn had a close relationship to COMAP as a member of our initial board of trustees and as the editor of For All Practical Purposes. I doubt that we would still be on the scene had it not been for his efforts on our behalf. We often differed on strategy, but never on policy. He held a fundamental belief that mathematics education was not about the education of mathematicians, but about showing all students the power and application of our subject. Through his thoughts and his words, he put the Mathematical Associaton of America and the Mathematical Sciences Education Board on the national and the world stage. We won’t see his like again. The UMAP Journal 36 (2) (2015) 93–94. cCopyright 2015 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proﬁt or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.

36.2 (2015) 94 The UMAP Journal About the Author Solomon Garfunkel is the founder and Executive Director of COMAP and Executive Publisher of this Journal. He served on the mathematics faculties of Cornell University and the University of Connecticut at Storrs, but he has dedicated the last 35 years to research and development efforts in mathematics education. He was project director for the Undergraduate Mathematics and Its Applications (UMAP) and the High School Mathematics and Its Applications (HiMAP) Projects funded by NSF, and directed three telecourse projects, including AgainstAllOdds:InsideStatisticsandInSimplestTerms:CollegeAlgebra,forthe Annenberg/CPB Project. He has been the Executive Director of COMAP, Inc. since its inception in 1980. Dr. Garfunkel was the project director and host for the video series For All Practical Purposes: Introduction to Contemporary Mathematics. He was the Co-Principal Investigator on the ARISE Project, and Co-Principal Investi- gator of the CourseMap, ResourceMap, and WorkMap projects. In 2003, Dr. Garfunkel was Chair of the National Academy of Sciences and Math- ematical Sciences Education Board Committee on the Preparation of High School Teachers. Editor’s Note The views and opinions expressed in this issue by authors employed by the U.S. Department of Defense are theirs alone and not necessarily those of the Department of Defense or of any agency of the U.S. government.

Results of the 2015 ICM 95 ICM Modeling Forum Results of the 2015 Interdisciplinary Contest in Modeling Chris Arney, ICM Director Dept. of Mathematical Sciences U.S. Military Academy West Point, NY 10996 david.arney@usma.edu Amanda Beecher, Head Judge School of Theoretical and Applied Sciences Ramapo College of New Jersey Mahwah, NJ 07430 abeecher@ramapo.edu Amy Krakowka Richmond, Head Judge Department of Geography and Environmental Engineering United States Military Academy West Point, NY 10996 amy.krakowka@usma.edu Introduction A total of 2,137 teams from seven countries (China, France, Germany, Indonesia, Singapore, United Kingdom, United States) spent a weekend workingonanappliedmodelingprobleminthe17thInterdisciplinaryCon- test in Modeling (ICM) R. This year’s contest began on Thursday, Febru- ary 5, and ended on Monday, February 9, 2015. During that time, teams of up to three undergraduate or high school students researched, modeled, analyzed, solved, wrote, and submitted solutions to an open-ended inter- disciplinary modeling problem. After the weekend of challenging and pro- ductive work, the solution papers were sent to COMAP for judging. Nine of the papers were judged to be Outstanding by the expert panel of judges. The UMAP Journal 36 (2) (2015) 95–111. cCopyright 2015 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proﬁt or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.

96 The UMAP Journal 36.2 (2015) Two of those papers appear in this issue, together with commentaries by the judges. Centeringitseducationalphilosophyonmathematicalmodeling,COMAP supports the use of mathematical tools to explore real-world problems. It serves society by developing students as problem solvers in order to be- come better informed and prepared as citizens, contributors, consumers, workers, and community leaders. The ICM is an example of COMAP’s efforts in working towards these goals. All members of the 2,137 competing teams are to be congratulated for theirexcellentworkanddedicationtointerdisciplinarymodelingandprob- lem solving. Two Contest Problems Thisyear’scontestfeatured, fortheﬁrsttime, twoICMproblemsinstead of one, giving teams more choice, providing variety, and likely contribut- ing to twice as many teams participating as in 2014. One problem involved network science, and the other involved environmental science. Both prob- lemswerechallengingintheirdemandforteamstoutilizeaspectsofscience, mathematics, and analysis in their modeling and problem solving. Network Problem The network problem involved modeling human capital issues (espe- cially “churn”) in a hypothetical organization of 370 employees, with the intent of aiding managers and decision makers to build successful systems for recruiting, hiring, training, and evaluating employees. Having teams analyze the network-related issues of human capital is a relevant issue in improving performance and proﬁts of organizations. Environmental Problem The environmental problem involved developing a model to measure sustainabilityinordertoevaluatethe20-yearsustainabledevelopmentplan for one country (of the team’s choice) on the United Nations’ Least Devel- oped Countries list. Teams searched for pertinent data and grappled with how economic development must consider ecosystem health and social equitability. Teams came up with creative and geographically relevant so- lutions, which were presented in the teams’ 20-page reports. Having teams analyzethereal-worldproblemofsustainabilityisrelevanttosociety’sneed to develop successful long-term projects to improve living conditions for future generations.

Results of the 2015 ICM 97 Next Year: A Third Kind of Problem, Too Next year we will continue the network science theme for one of the problems and environmental issues for another. However, we will also add a third interdisciplinary problem—a policy mod- eling problem. The On Jargon column in this issue describes the nature of such problems. Teams preparing for the 2016 contest should consider reviewing • interdisciplinarytopicsintheareasofnetworkscienceandsocialnetwork analysis; • human-environment interactions in the areas of environmental science, climatology, food security, and geography; and • the concept of policy modeling, as described in the On Jargon column. A Brief History of the ICM The range of topics over the 18 problems given over the 17 years of the ICM (provided in Table 1) manifests interdisciplinarity, with problems in- volving themes from chemistry, physics, biology, engineering, information science, medicine, business, environmental science, and network science. Theproblemsalsoshowabalanceofpublic(government)andprivate(busi- ness) issues. Participating teams and topics in the ﬁrst 16 years of the ICM. Table 1. Year Number of teams 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2015 40 70 83 106 146 143 164 224 273 380 374 356 735 1,329 957 1,028 641 1,496 Topic Controlling the spread of ground pollution Controlling elephant populations Controlling zebra mussel populations Preserving the habitat of the scrub lizard Designing an airport screening system Designing information technology security for a campus Harvesting and managing exhaustible resources Modeling HIV/AIDS infections and ﬁnances Designing a viable kidney exchange network Measuring utility in health care networks Balancing a water-based ecosystem affected by ﬁsh farming Controlling ocean debris Measuring the impact of electric vehicles Identifying criminals in a conspiracy network Modeling Earth’s health Using networks to measure inﬂuence and impact Measuring churn and human capital in an organization Planning sustainability for low-development countries

98 The UMAP Journal 36.2 (2015) Results and winning papers from the ﬁrst 16 contests were published in special issues of The UMAP Journal (1999–2014). In addition to this special issue of The UMAP Journal, COMAP offers a supplementary 2015 MCM-ICM CD-ROM containing the press releases for the two contests, the results, the problems, unabridged versions of all the Outstanding papers, and judges’ commentaries. Information about ordering is available at (800) 772–6627 or http://www.comap.com/product/?idx=1466 Finally, we note the availability of the volume The Interdisciplinary Con- test in Modeling: Culturing Interdisciplinary Problem Solving, edited by Chris Arney and Paul J. Campbell, which appeared in late 2014. Information about ordering it is at (800) 772–6627 or http://www.comap.com/product/?idx=1441 (CD) http://www.comap.com/product/?idx=1440 (print) Problem Statement: Managing Human Capital in Organizations Building an organization ﬁlled with good, talented, well-trained people is one of the keys to success. But to do this, an organization needs to do more than recruit and hire the best candidates—it also needs to retain good people, keep them properly trained and placed in proper positions, and eventually target new hires to replace those leaving the organization. Individuals play unique roles within their organizations, both formally and informally. Thus, when individuals depart from an organization, they leave important informational and functional components missing that need to be ﬁlled. This is true for sports teams, commercial companies, schools and universities, governments, and almost any formal group or organization of people. Human resource (HR) specialists help senior leadership manage per- sonnel by improving retention and motivation, coordinating training, and building good teams. In particular, leaders seek to create an effective or- ganizational structure, where people are assigned to positions appropriate to their talents and experience, and where efﬁcient communication sys- tems are in place to facilitate development of innovative ideas and quality products (commodities or services). These talent management and team building aspects of HR management are remaking many modern organi- zations. Managingthe ﬂuid networkof humancapital within an organizationre- quiresunderstandingpersonnelloyaltiestothecompanyandtosubgroups; building trust in the workplace; and managing the formation, dissolution, and retention of formal and informal ties between people. When people

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