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Optimization with Linear Programming

Optimization with Linear Programming

This course will teach you the use of mathematical models for managerial decision making and covers how to formulate linear programming models where multiple decisions need to be made while satisfying a number of conditions or constraints.


The essence of management is to make choices that make optimal use of scarce resources. This course covers how to apply linear programming to complex systems to make better decisions – decisions that increase revenue, decrease costs, or improve efficiency of operations. Students will explore the role of mathematical models in decision-making and how to formulate basic linear programming models where multiple decisions need to be made while simultaneously satisfying multiple conditions or constraints.

  • Introductory
  • 4 Weeks
  • Expert Instructor
  • Tuiton-Back Guarantee
  • 100% Online
  • TA Support

Learning Outcomes

After completing this course students will be able to formulate linear programming models and describe the types of decisions that lend themselves to linear programming solutions. You will learn how to use spreadsheet software to implement and solve linear programming problems. You will also cover how to use sensitivity analysis and shadow prices to gain additional insights from linear programming results.

  • Describe what types of decisions are amenable to linear programming solutions
  • Formulate a linear programming model, and represent it graphically
  • Solve the LP model with spreadsheet-based software
  • Use LP models for various decisions: make or buy, where to invest,
  • Use sensitivity analysis and shadow prices to gain additional information from the LP solution

Who Should Take This Course

Business analysts with responsibility for specifying, creating, deploying or interpreting quantitative decision models.  Users of linear programming software who need to attain a more solid grounding in the subject.

Our Instructors

Dr. Cliff Ragsdale

Dr. Cliff Ragsdale

Cliff T. Ragsdale is Bank of America Professor of Business Information Technology at Virginia Tech. His primary research interests involve applications of quantitative modeling techniques to managerial decision making problems using microcomputers. Dr. Ragsdale has served as a consultant for a variety of organizations including General Mills, The World Bank, Frontline Systems, and Dominion Energy. His research has been published in Decision Sciences, Naval Research Logistics, Operations Research Letters, Computers and Operations Research, OMEGA, Personal Financial Planning, Financial Services Review, Decision Support Systems, and a number of other scholarly journals. He is a Fellow of Decision Sciences Institute and a member of INFORMS. He has also served as the faculty advisor for the Virginia Tech student chapter of APICS and on the Board of Directors for the Southwest Chapter of APICS.

Course Syllabus

Week 1


  • The role of models in decisions
  • Sources of bias & error in human decision making
  • Good decisions vs. good outcomes

Week 2

Linear Programming Models

  • Formulating linear programming models
  • Graphical representations
  • Solving LP models in spreadsheets

Week 3

Domain Specific Illustrations

  • Make or buy
  • Investment
  • Transportation
  • Blending

Week 4

Sensitivity Analysis

  • Role of sensitivity analysis in the larger decision context
  • Shadow prices
  • Alternate solutions
  • Robust Optimization
  • Simplex Method

Class Dates


01/12/2024 to 02/09/2024
Instructors: Dr. Cliff Ragsdale
07/12/2024 to 08/09/2024
Instructors: Dr. Cliff Ragsdale


01/10/2025 to 02/07/2025
Instructors: Dr. Cliff Ragsdale
07/11/2025 to 08/08/2025
Instructors: Dr. Cliff Ragsdale


You will need to have some facility with spreadsheet operations prior to starting this course.

Karolis Urbonas
Susan Kamp
Stephen McAllister
Amir Aminimanizani
Elena Rose
Leonardo Nagata
Richard Jackson

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Optimization with Linear Programming

Additional Information


Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, and guided data modeling problems using software.

In addition to assigned readings, this course also has supplemental readings available online.

Course Text

Spreadsheet Modeling & Decision Analysis, eighth edition by Cliff Ragsdale, which can be ordered from the publisher via the previous link. This text is also used in Integer & Nonlinear Programming and Network Flow and Risk Simulation and Queueing. Note: We do not recommend using the Kindle version of this book.


The course uses Analytic Solver Platform for Education software by Frontline systems. Analytic Solver Platform for Education is an add-in for Excel that performs risk analysis, simulation, optimization, decision trees and other analytical methods. With the purchase or rental of the book, you will have a course code that will enable you to download and install the software for 140 days. If you do not have such a license, a license is also available for course registrants through Please do not install the regular public trial copy of the software on your own; when the course starts we will provide you with the complete installation instructions to obtain the appropriate copy of the software.

Options for Credit and Recognition

ACE CREDIT | College Credit
This course has been evaluated by the American Council on Education (ACE) and is recommended for the upper-division baccalaureate degree, 3 semester hours in mathematics or business management. Please note that the decision to accept specific credit recommendations is up to the academic institution accepting the credit.

Supplemental Information

Literacy, Accessibility, and Dyslexia

At, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:






  • Navidys (for colorblindness, dyslexia, and reading difficulties)
  • HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)

Register For This Course

Optimization with Linear Programming