This is an introductory textbook on optimization—that is, on mathematical programming—intended for undergraduates and graduate students in management or in engineering. The principal coverage includes linear programming, nonlinear programming, integer programming, and heuristic programming; and the emphasis is on model building using Microsoft^® Office Excel^® and Solver.

The emphasis on model building (rather than algorithms) is one of the features that make this book distinctive. Most textbooks devote more space to algorithmic details than to formulation principles. These days, however, it is not necessary to know a great deal about algorithms in order to apply optimization tools, especially when relying on the spreadsheet as a solution platform.

The emphasis on spreadsheets is another feature that makes this book distinctive. Few textbooks devoted to optimization pay much attention to spreadsheet implementation of optimization principles, and many books that emphasize model building ignore spreadsheets entirely. Thus, someone looking for a spreadsheet-based treatment would otherwise have to use a textbook that was designed for some other purpose, such as a survey of management science topics, rather than one devoted to optimization.

WHY MODEL BUILDING?

The model building emphasis derives from an attempt to be realistic about what management and engineering students need most when learning about optimization. At an introductory level, the most practical and motivating theme is the wide applicability of optimization tools. To apply optimization effectively, the student needs more than a brief exposure to a series of numerical examples, which is the way that most mathematical programming books treat applications. With a systematic modeling emphasis, the student can begin to see the basic structures that appear in optimization models and, as a result, develop an appreciation for potential applications well beyond the examples in the text.

Formulating optimization models is both an art and a science, and this book pays attention to both. The art can be refined with practice, especially supervised practice, just the way a student would learn sculpture or painting. The science is reflected in the structure that organizes the topics in this book. For example, there are several distinct problem types that lend themselves to linear programming formulations, and it makes sense to study these types systematically. In that spirit, the book builds a library of templates against which new problems can be compared. Analogous structures are developed for the presentation of other topics as well.

WHY SPREADSHEETS?

Now that optimization tools have been made available with spreadsheets (i.e., with Excel), every spreadsheet user is potentially a practitioner of optimization techniques. No longer do practitioners of optimization constitute an elite, highly trained group of quantitative specialists who are well versed in computer software. Now, anyone who builds a spreadsheet model can call on optimization techniques and can do so without any need to learn about specialized software. The basic optimization tool, in the form of Excel’s Standard Solver, is now as readily available as the spell-checker. So why not raise modeling ability up to the level of software access? Let’s not pretend that most users of optimization tools will be inclined to shop around for algebraic modeling languages and industrial-strength “solvers” if they want to produce numbers. More likely, they will be drawn to Excel.

Students using this book can take advantage of even more powerful software packages (Analytic Solver Platform and OpenSolver) by using the material in the online appendices. For the instructor who wants students to be working on one of these platforms, the book provides sufficient information to get started and to learn the user interface.

WHAT’S SPECIAL?

Mathematical programming techniques have been invented and applied for more than half a century, so by now they represent a relatively mature area of applied mathematics. There is not much new that can be said in an introductory textbook regarding the underlying concepts. The innovations in this book can instead be found in the delivery and elaboration of certain topics, making them accessible and understandable to the novice. The most distinctive of these features are as follows:

• The major topics are not illustrated merely with a series of numerical examples. Instead, the chapters introduce a classification for the problem types. An early example is the organization of basic linear programming models in Chapter 2 along the lines of allocation, covering, and blending models. This classification strategy, which extends throughout the book, helps the student to see beyond the particular examples to the breadth of possible applications.
• Network models are a special case of linear programming models. If they are singled out for special treatment at all in optimization books, they are defined by a strict requirement for mass balance. Here, in Chapter 3, network models are presented in a broader framework, which allows for a more general form of mass balance, thereby extending the reader’s capability for recognizing and analyzing network problems.
• Interest has been growing in data envelopment analysis (DEA), a special kind of linear programming application. Although some books illustrate DEA with a single example, this book provides a systematic introduction to the topic by providing a patient, comprehensive treatment in Chapter 5.
• Analysis of an optimization problem does not end when the computer displays the numbers in an optimal solution. Finding a solution must be followed with a meaningful interpretation of the results, especially if the optimization model was built to serve a client. An important framework for interpreting linear programming solutions is the identification of patterns, which is discussed in detail in Chapter 4.
• The topic of heuristic programming has developed somewhat outside the field of optimization. Although various specialized heuristic approaches have been developed, generic software has seldom been available. Now, however, the advent of the evolutionary solver brings heuristic programming alongside linear and nonlinear programming as a generic software tool for pursuing optimal decisions. The evolutionary solver is covered in Chapter 9.

Beyond these specific innovations, as this book goes to print, there is no optimization textbook exclusively devoted to model building rather than algorithms that relies on the spreadsheet platform. The reliance on spreadsheets and on a model building emphasis is the most effective way to bring optimization capability to the many users of Excel.

WHAT’S NEW?

The Third Edition largely follows the topic coverage of the previous edition, with one important change. In the new edition, the presentation is organized around the use of Excel’s Solver. More advanced software, such as Analytic Solver Platform or OpenSolver, might be preferred by some instructors, so the Third Edition provides support for both of these in online appendices. However, students need access to no software other than Excel in order to follow the coverage in the book’s nine chapters.

The set of homework exercises has been expanded in the Third Edition. Each chapter now contains about ten homework exercises, most of which appeared in the previous edition. In addition, a supplementary set of homework exercises can be found online for instructors who are looking for a broader set of exercises or for students who want additional practice.

THE AUDIENCE

This book is aimed at management students and secondarily to engineering students. In business curricula, a course focused on optimization is viable in two situations. If there is no required introduction to management science at all, then the treatment of management science at the elective level is probably best done with specialized courses on deterministic and probabilistic models. This book is an ideal text for a first course dedicated to deterministic models. If instead there is a required introduction to management science, chances are that the coverage of optimization glides by so quickly that even the motivated student is left wanting more detail, more concepts, and more practice. This book is also well suited to a second-level course that delves specifically into mathematical programming applications.

In engineering curricula, it is still typical to find a full course on optimization, usually as the first course on (deterministic) modeling. Even in this setting, though, traditional textbooks tend to leave it to the student to seek out spreadsheet approaches to the topic, while covering the theory and perhaps encouraging students to write code for algorithms. This book can capture the energies of students by covering what they would be spending most of their time doing in the real world—building and solving optimization problems on spreadsheets.

This book has been developed around the syllabi of two courses at Dartmouth College that have been delivered for several years. One course is a second-year elective for MBA students who have had a brief, previous exposure to optimization during a required core course that surveyed other analytic topics. A second course is a required course for engineering management students in a graduate program at the interface between business and engineering. These students have had no formal exposure to spreadsheet modeling, although some may previously have taken a survey course in operations research. Thus, the book has proven to be appropriate for students who are about to study optimization with only a brief or nonexistent exposure to the subject.

ACKNOWLEDGMENTS

As I wrote in the preface to the first edition, I can trace the roots of this book to my collaboration with Steve Powell. Using spreadsheets to teach optimization is part of a broader activity in which Steve has been an active and inspiring leader, and I continue to benefit from his colleagueship. Several people contributed to the review process with constructive feedback and suggestions. For their help in this respect, I want to acknowledge Tim Anderson (Portland State University), David T. Bourgeois (Southern New Hampshire University), Jeffrey Camm (University of Cincinnati), Ivan G. Guardiola (Missouri University of Science & Technology), Rich Metters (Texas A&M University), Jamie Peter Monat (Worcester Polytechnic Institute), Khosrow Moshirvaziri (California State University, Long Beach), Susan A. Slotnick (Cleveland State University), and Mohit Tawarmalani (Purdue University).

The Third Edition makes only minor changes in the coverage of the previous edition, the main exception being the reliance on Excel’s Solver. To make this software emphasis possible, it was critical to have an updated package for sensitivity analysis, and this was accomplished in a timely and professional manner by Bob Burnham. In addition, there were many details to manage in preparing a new manuscript, and I was helped by several people willing to pay attention to details in order to improve the final product. I particularly want to thank Bill MacKinnon, Alex Zunega, and Geneva Trotter for their efforts.

Once again, I offer sincere thanks to my current editor, Susanne Steitz-Filler, for her support in planning and realizing the publication of a new edition. With her help and guidance, I am hopeful that the pleasures of optimization modeling will be experienced by yet another generation of students.