UMAPJournal38.22017ICMContest

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The

UMAP

Journal

Publisher

COMAP, Inc.

Vol. 38, No. 2

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

David R. Heesen

Distribution

John Tomicek

Editor

Paul J. Campbell

Beloit College

700 College St.

Beloit, WI 53511–5595

campbell@beloit.edu

Associate Editors

Chris Arney

Ron Barnes

Joanna A. Bieri

Robert Bosch

James M. Cargal

Lisette De Pillis

Solomon A. Garfunkel

William B. Gearhart

Richard Haberman

Jessica M. Libertini

Yves Nievergelt

Michael O’Leary

Andrew Oster

Philip D. Strafﬁn

Shaohui Wang

Krista Watts

U.S. Military

Academy

U. of Houston—Downtn

University of Redlands

Oberlin College

Fort Walton Beach, FL

Harvey Mudd College

COMAP, Inc.

Calif. State U., Fullerton

Southern Methodist U.

Virginia Military Institute

Eastern Washington U.

Towson University

Eastern Washington U.

Beloit College

Adelphi University

U.S. Military Academy

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 wit h 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 t imes 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.

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 t hat the modeler may need

to go back to earlier steps and repeatthe 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 modelingoften reduces assump-

tions to a minimum and attempts to embrace the complexity of the real

situation. Interdisciplinary 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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