Table Of ContentSpringer Optimization and Its Applications 175
J. MacGregor Smith
Combinatorial, Linear,
Integer and Nonlinear
Optimization Apps
COLINA Grande
Springer Optimization and Its Applications
Volume 175
Series Editors
Panos M. Pardalos , University of Florida
My T. Thai , University of Florida
Honorary Editor
Ding-Zhu Du, University of Texas at Dallas
Advisory Editors
Roman V. Belavkin, Middlesex University
John R. Birge, University of Chicago
Sergiy Butenko, Texas A&M University
Vipin Kumar, University of Minnesota
Anna Nagurney, University of Massachusetts Amherst
Jun Pei, Hefei University of Technology
Oleg Prokopyev, University of Pittsburgh
Steffen Rebennack, Karlsruhe Institute of Technology
Mauricio Resende, Amazon
Tamás Terlaky, Lehigh University
Van Vu, Yale University
Michael N. Vrahatis, University of Patras
Guoliang Xue, Arizona State University
Yinyu Ye, Stanford University
Aims and Scope
Optimizationhascontinuedtoexpandinalldirectionsatanastonishingrate.Newalgorithmic
andtheoreticaltechniquesarecontinuallydevelopingandthediffusionintootherdisciplinesis
proceeding at a rapid pace, with a spot light on machine learning, artificial intelligence, and
quantumcomputing.Ourknowledgeofallaspectsofthefieldhasgrownevenmoreprofound.
At the same time, one of the most striking trends in optimization is the constantly increasing
emphasis on the interdisciplinary nature of the field. Optimization has been a basic tool in
areas not limited to applied mathematics, engineering, medicine, economics, computer
science, operations research, and other sciences.
The series Springer Optimization and Its Applications (SOIA) aims to publish
state-of-the-art expository works (monographs, contributed volumes, textbooks, handbooks)
that focus on theory, methods, and applications of optimization. Topics covered include, but
are not limited to, nonlinear optimization, combinatorial optimization, continuous optimiza-
tion, stochastic optimization, Bayesian optimization, optimal control, discrete optimization,
multi-objective optimization, and more. New to the series portfolio include Works at the
intersection of optimization and machine learning, artificial intelligence, and quantum
computing.
Volumes from this series are indexed by Web of Science, zbMATH, Mathematical Reviews, and
SCOPUS.
More information about this series at http://www.springer.com/series/7393
J. MacGregor Smith
Combinatorial, Linear, Integer
and Nonlinear Optimization
Apps
COLINA Grande
123
J.MacGregor Smith
Department ofMechanical
andIndustrial Engineering
University of Massachusetts
Amherst, MA, USA
ISSN 1931-6828 ISSN 1931-6836 (electronic)
SpringerOptimization andIts Applications
ISBN978-3-030-75800-4 ISBN978-3-030-75801-1 (eBook)
https://doi.org/10.1007/978-3-030-75801-1
MathematicsSubjectClassification: 65K05,90C05,90C10,90C11,90C27,90C29,90C30,90C59,90C90,68W01,
68W05,68-04
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Dedicated to my loving wife Marty and our daughter Kate for always providing
me support and encouragement during the development of this volume. Also, to
the students of MIE 379, 380, and 724 and other courses who shared my
enthusiasm for developing the Apps along with their excruciating efforts to
understand the problems and code them.
Preface
Weshapeourtools,thereafterourtoolsshapeus.
—
MARSHALLMACLUHAN
Personal mobile computing has profoundly altered the workplace during the past
decade.Appsonphonesandtabletsarecommonplaceandarebecomingmoreimportant
for the workplace and everyday life. We need optimization Apps which are not just
descriptiveofasituationbutalsoprescriptive,sothatwecanmakebetterdecisions.These
are more challenging than simple descriptive Apps and more rewarding in the long run.
Our goal is for users to be creative consumers of the new technology. How can we
benefitandrealizethisprocessandhowcanweteachourstudentsattheuniversitylevel
how they can contribute to making things and making them better, no matter what
engineering, science, or business discipline theyoriginate from?
Onapersonalnote,theoriginsofmyinterestinAppscamefromreadingtheBusiness
section of the Sunday New York Times in 2010 about a programming class at Stanford
wherestudentswerelearninghowtoprogramaphoneApponAppleiPhonewhichthey
could market. I asked why can’t we develop a similar program at the University of
Massachusetts? I found out about App Inventor Classic version #1 which was just being
developed at Google.
IntheFallof2011,IstartedteachingaboutAppInventorinmyMIE379:Introductionto
Operations Research class and had the students carry out an App Inventor optimization
term project. I felt that creating an optimization App would be challenging and give our
students a unique slant on the App market.
ItwascrazyambitioussincetheAppInventorprogramminglanguagewasinitsinitial
developingstages.ThethingthatgrabbedmyattentionwastheabilityofAppInventorto
design the user interface for the phone with all the buttons, labels, text, and diagrams.
The materials in this book reflect the lessons learned from my classes. In addition, two
spinoff App products derived from App Inventor have been developed and we will
illustrate these new developments at the end of this volume which are Thunkable and
Kodular. These additional software developments were intended to make AI2 and its
extensions more powerful and applicable to other than educational objectives. Thus, the
future of App development based upon App Inventor is on an upward trajectory.h
0.0.1 Why this Volume
WhyareOperationsResearchandComputerSciencerelevantandimportant?Operations
Research(OR)isrelevantandimportantbecausealmostalloptimizationproblemsrequire
some theoretical and applied mathematics understanding as their foundation. The for-
mulation of optimization problems is founded through OR concepts and techniques:
Combinatorial Optimization, Linear Programming, Integer, and Nonlinear Programming
(COLIN). Computer Science (CS) is relevant and important because algorithms and
Apps/algorithms (A) underlie the solution ofall optimizationproblems. App Inventorand
AMPL are the major algorithmic vehicles studied in this course. Thus, in summary we
vii
viii Preface
Fig.0.1 COLINAgrandeoptimization(afterPSTrickswebsitetug.org)
have COLINA which means “small hilltop” in Spanish and it is Grande! Figure 0.1
illustrates a small hilltop optimization problem in the decision variables x and y.
Forwhomisthisbookwritten?University-levelstudentsandprofessors,mainlyatthe
upper division level or higher with some background in calculus, linear algebra, and
related mathematical skills. These skills are viewed as sufficient but not necessary for
developing the Apps for Optimization, i.e. OptApps or AppOpts.h
0.0.2 Plan of the Volume
How is this book organized? Basically, each chapter provides the theoretical background
andthegeneralmethodologyfortheconceptsofoptimizationaccordingtoCOLINA,then
there are example applications of the Apps with App Inventor and AMPL software.
The COLINA categories are representative of the major areas of interest in optimization
which I have come across in my teaching experience. Links to the University of Wis-
consin NEOS server which is designed to solve complexoptimization problems are used
insomeoftheAppswheremorecomputingfirepowerisrequired.AllAppsdevelopedin
the book are available for download.
Amherst, MA J. MacGregor Smith
2020 University of Massachusetts
Amherst, Massachusetts
Acknowledgements
IamindebtedtoItalodeSouzsa(classof2016)forhiscreativeinsightsonhowtolinkApp
Inventor2totheNEOSserverinWisconsin.Thishasbeeninstrumentalinextendingthe
capabilities of AI2 to larger and more complex optimization problems. I am also deeply
indebtedtoBenHuebnerandElizabethWongoftheUniversityofWisconsinDepartment
ofComputerSciencewhodesignedawaytoupdatethecommunicationswiththeNEOS
servers when the email connection was removed.
I would like to also thank Peter Kubat for being a good friend, critic, and supporter
over the years and for his encouragement about the Apps for Optimization. I would also
like to thank Hal Ableson and his colleagues at MIT for developing App Inventor and
Robert Fourer for his help with AMPL.
I would like to thank Dr. Mei-Yau Shih of the University of Massachusetts Amherst
Center for Teaching (CLT) for her enthusiastic encouragement and financial support in
the development of the Apps in my courses.
I would like to thank the following students who contributed apps to this volume (in
orderofappearanceof theirApps):ConnorTremarche,AmandaSkriloff,D.Sokol,Jared
Marvel, Ian Taylor, Avery Stroman, Ryan Barnes, Alex Barth, Anthony Broding, Sydney
Hauver, Alexander Niemeyer, Brendan Frakfort, Thomas Johnson, Andrew Metz, Bobby
Jaycox,TimKlocker,EricWright,TomRogers,AllanTang,ErinO’Neil,BekahPerlin,Lily
Thomas,ThimiPrifti,ReneArnaud,CrystalLee,AndrewGiampa,JoeWoodman,Johnny
Zhu, Milagros Malo, Rebecca Castonguay, Sean Fitzgerald, William Andrews, Prashant
Meckoni, Xi Jiang, Luyi Wang, and finally, Rahda Dutta. Rahda was also very helpful in
providing background materials and instructions. Nicole Lynch also helped out with
instructions on using AMPL.
I would also like to thank the anonymous referees who read over the book drafts and
provided valuable comments on the manuscript. I would also like to thank Donna
Chernyk of Springer for her continued support and encouragement in developing the
book.
Finally, I would like to thank all the undergraduate and graduate students of the
University of Massachusetts at Amherst who have participated in my courses on Linear,
Network, and Nonlinear Programming over the years.
ix
Contents
0.0.1 Why this Volume. .... ..... .... .... .... .... .... ..... .... vii
0.0.2 Plan of the Volume ... ..... .... .... .... .... .... ..... .... viii
1 App Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Prologue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 Wicked Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Systematic Procedures and Algorithms . . . . . . . . . . . . . . . . . . . . 4
1.4.1 Plan of the Book . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.2 App Design Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4.3 COLINA Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 Airline Tickets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.3 Mathematical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.5 App Demonstration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5.6 Evaluation (Benefits and Costs) . . . . . . . . . . . . . . . . . . . . . 11
1.6 A Brief History of Visual Programming Languages. . . . . . . . . . 12
1.6.1 Kodular Demonstration. . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7 AI2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2 Combinatorial Optimization GðV;EÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Stowe Cycle Traveling Salesman Problem (TSP) . . . . . . . . . . . . 20
2.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2.3 Mathematical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.2.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2.5 Demonstration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.2.6 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3 Warehouse Quick Pick. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.2 Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.3 Mathematical Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.4 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.5 Demonstration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.6 Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 Analytical Hierarchy Process (AHP) . . . . . . . . . . . . . . . . . . . . . . . 30
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.4.2 Marching Band AHP App. . . . . . . . . . . . . . . . . . . . . . . . . . 33
xi
