The
UMAP
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COMAP, Inc.
Vol. 38, No. 2
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Chris Arney
Dept. of Math’l Sciences
U.S. Military Academy
West Point, NY 10996
david.arney@usma.edu
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Vol. 38, No. 2 2017
Table of Contents
Guest Editorial
Learning and Teaching Interdisciplinary Modeling
Chris Arney ...............................................................................93
ICM Modeling Forum
Results of the 2017 Interdisciplinary Contest in Modeling
Chris Arney, ICM Director, and Amanda Beecher,
ICM Deputy Director ............................................................... 105
Analysis and Optimization of Airport Security Check
Yikai Huo, Zhiyu You, and Kan Chang ...................................... 129
Judges’ Commentary: Optimizing Passenger Throughput
at Airport Security
Jessica Libertini ....................................................................... 149
Applying Smart Growth Principles in Boulder, Colorado
and Canberra, Australia
Rachel Perley, Anna Goetter, and Nina Brown ........................... 161
Judges’ Commentary: Sustainable Cities
Kristin Arney, Amanda Beecher, Carrie Eaton, and
Jack Picciuto .........
................................................................... 181
Migration to Mars
Sreeram Venkat, Nikhil Milind, and Nikhil Reddy ..................... 197
Judges’ Commentary: Migration to Mars
Chris Arney ............................................................................. 221
ICM–MCM: Procedures and Tips for a Great Experience
John Tomicek ........................................................................... 233
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Guest Editorial 93
Guest Editorial
Learning and Teaching
Interdisciplinary Modeling
Chris Arney, ICM Director
Dept. of Mathematical Sciences
U.S. Military Academy
West Point, NY 10996
david.arney@usma.edu
Introduction
Interdisciplinary modeling combines concepts, methods, techniques,
and elements of various disciplines (in the sciences, humanities, and arts)
to
• obtain solutions to problems;
• develop understanding of issues;
• provide recommendations to decision makers; and
• implement and build tools, algorithms, and systems.
To be effective for society, interdisciplinary modeling must provide the
capability for analysts to solve realistic and challenging problems. Good
education programs teach students both disciplinary and interdisciplinary
modeling and problem-solving methods, and provide opportunities for
students to practice and hone their modeling skills. The Interdisciplinary
Contest in Modeling (ICM)
R
experience is one way to build experience and
refine skills.
Here we look at the nature, processes, education, and resources related
to interdisciplinary modeling and problem solving, with the hope that stu-
dents can use this information to prepare for the ICM and improve their
interdisciplinary modeling skills.
1
The UMAP Journal 38 (2) (2017) 93–104.
c
Copyright 2017 by COMAP, Inc. All rights reserved.
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1
The opinions in this article are the author’s alone and do not necessarily reflect the opinion of
his colleagues, USMA, the Department of the Army, or any other US government agency.
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94 The UMAP Journal 38.2 (2016)
Interdisciplinary Problems
Real issues and modern problems can have many challenging charac-
teristics. Some of these are:
• Intransparency (lack of clarity of the situation or changing environments
and criteria)
• Multiple Goals (many stakeholders with competing criteria)
• Complexity (large numbers of items, interrelations, decision elements,
dimensions, geometries, and time scales)
• Dynamics (time considerations, constraints, and sensitivities)
• Spatial and Geometric considerations (integral or fractional dimensions)
• Political and Social Elements (human or cyber considerations)
One element to avoid or minimize in modeling is confirmation bias, which is
favoring a preconceived notion. Confirmation bias can dramatically harm
or constrain modeling and problem solving. Modelers must be aware of
and adapt their model to avoid or resist irrelevant, biased, or erroneous
information. Since data are never perfectly accurate nor completely clean,
considerable effort to reduce errors or eliminate bad data is needed. ICM
problems often require data to be considered—and sometimes obtained or
generated—by the teams. This collection, choosing, and weighing of data
is an important step in the modeling process that should not be treated
lightly by the teams.
Mathematical Modeling
Mathematical modeling is a structured process with many loops and
choices that can make it as much art as science. In performing this process,
the modeler needs to describe the phenomena in mathematical terms. The
four basic steps in the process (as described in Arney [2014, 169–170]) are:
• Step 1: Identify the Problem The problem is stated in as precise form
as possible. Sometimes, this is an easy step, other times this may be the
most difficult step of the entire process.
• Step 2: Develop a Model This is both a translation from the natural lan-
guage statement made in Step 1 to mathematical language but also the
development of relationships between the factors involved in the prob-
lem. Because real-world situations are often too complex to allow the
modeler to account for every facet of the situation, simplifying assump-
tions must be made. Data collection is often part of model construction.
Variables are defined, notation is established, and some form of mathe-
matical relationship and/or
structure is established.
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Guest Editorial 95
• Step 3: Solve the Model The model is solved so that the answer is
understood in the context of the original problem. If the model cannot
be solved, it may need to be simplified by adding more assumptions in
Step 2.
• Step 4: Verify, Interpret, and Use the Model Before using the model,
it should be tested or verified that it makes sense and works properly.
Its output should be interpreted in the context of the problem. It is
possible that the model works, but it’s too cumbersome or too expensive
to implement. The modeler returns to earlier steps to adjust as needed.
The modeling process is iterative in the sense that the modeler may need
to go back to earlier steps and repeat the processor continue to cycle through
the entire process (or part of it) several times. If the model cannot be solved
or is too cumbersome to use, the model is simplified. If the model needs
to be more powerful, or more complication or rigor needs to be added, the
process of relaxing assumptions is called refining the model. By simplifying
and refining, the modeler can adjust the realism, accuracy, precision, and
robustness of the model. By using this mathematical modeling process,
modeling students can gain confidence to approach complex and difficult
problems and even develop their own innovative approaches to solving
problems.
Interdisciplinary Modeling
Interdisciplinary modeling is a creative process that, while sometimes
based on structured processes such as mathematical modeling, usually in-
volves an innovative and complex combination of modeling and problem-
solving methods from various disciplines and schools of thought.
The traditional modeling process was based on making viable and ap-
propriate assumptions and connections to produce a framework. This
structured, Newtonian style of modeling and problem solving was often
based in mathematics, mechanics, engineering, and physical science (see
Teller [1980]).
With the advent of the computer and the availability of tremendous
amounts of data, modern interdisciplinary modeling often reducesassump-
tions to a minimum and attempts to embrace the complexity of the real
situation. Inter
disciplinary modeling combines established methodologies
with novel procedures in its processes and structures, thus allowing for
complexity and specificity in its framework. The model is then solved,
used, implemented, tested, and/or validated, to
• produce a measure,
• design an algorithm,
• solve a problem,
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