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Integer and Nonlinear Programming and Network Flow

Integer and Nonlinear Programming and Network Flow

This course will teach you a number of advanced topics in optimization: how to formulate and solve network flow problems; how to model and solve optimization problems; how to deal with multiple objectives in optimization problems, and techniques for handling optimization problems.


Many business problems involve flows through a network – transportation, stages of an industrial process, routing of data. Students taking this course learn to specify and implement optimization models that solve network problems (what is the shortest path through a network, what is the least cost way to route material through a network with multiple supply nodes and multiple demand nodes). Students also learn how to solve Integer Programming (IP) problems and Nonlinear Programming (NLP) problems. Spreadsheet-based software is used to specify and implement models.

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

Learning Outcomes

Students who complete this class are able to:

  • Describe the characteristics of a network flow problem
  • Specify an objective function and constraints for a network problem, and model it with software
  • Solve the integer programming problem with software
  • Appropriately use rounding and stopping rules, and branch & bound
  • Describe the scenario in which an integer programming method is used
  • Specify an integer programming model
  • Accommodate multiple goals in the analysis
  • Specify a nonlinear programming model

Who Should Take This Course

Business analysts with responsibility for specifying, creating, deploying or interpreting quantitative decision models.  Users of optimization software who need to attain a more solid grounding in network optimization, integer programming, non-convex optimization, and multi-criteria optimization.

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

Network Flow Problems

  • Characteristics (nodes, arcs, decision variables)
  • The objective function & constraints
  • Modeling in a spreadsheet

Week 2

Integer Linear Programming

  • Integrality condition, relaxation
  • Rounding
  • Stopping rules
  • Binary variables
  • Implementing/solving the model
  • Branch & bound

Week 3

Multiple Goals

  • Soft/hard constraints
  • Defining the objective
  • Analysis/solution
  • Tradeoffs & goal revision
  • Multiple objective linear programming (MOLP)
  • Minimax

Week 4

Nonlinear Programming (NLP)

  • Generalized reduced gradient (GRG) overview
  • Local vs. Global optimality
  • Economic Order Quantity (EOQ) problem
  • Location problem
  • Evolutionary Optimization

Class Dates


09/08/2023 to 10/06/2023


09/13/2024 to 10/11/2024


09/12/2025 to 10/10/2025


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.
  • Skill: Intermediate
  • Credit Options: ACE, CAP, CEU
Karolis Urbonas
Susan Kamp
Stephen McAllister
Amir Aminimanizani
Elena Rose
Leonardo Nagata
Richard Jackson

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Integer and Nonlinear Programming and Network Flow

Additional Information


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

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 our courses, Introduction to Optimization and Risk Simulation and Queueing. 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 operation research,  computer programming, statistics, or computer information systems. 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

Integer and Nonlinear Programming and Network Flow