Integer & Nonlinear Programming and Network Flow

# taught by Cliff Ragsdale

Aim of Course:

Many business problems involve flows through a network - transportation, stages of an industrial process, routing of data.  Students taking this online course, "Integer & Nonlinear Programming and Network Flow" will 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 will also learn how to solve Integer Programming (IP) problems (constrained optimization problems except with one or more decision variable constrained to be an integer: e.g. a firm setting up a wi-fi hotspot could use 2 routers or 3 routers, but not 2.5 routers), and Nonlinear Programming (NLP) problems (where the objective function and constraints are not linear functions of the decision variables.  Students will use spreadsheet-based software to specify and implement models.

After you complete this course, you will be 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
• Describe the scenario in which an integer programming method is used
• Specify an integer programming model
• Appropriately use rounding and stopping rules, and branch & bound
• Solve the integer programming problem with software
• Accommodate multiple goals in the analysis
• Specify a nonlinear programming model
This course may be taken individually (one-off) or as part of a certificate program.
Course Program:

## WEEK 1: Network Flow Problems

• Characteristics (nodes, arcs, decision variables)
• The objective function & constraints

## 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
• 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

HOMEWORK:

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

# Integer & Nonlinear Programming and Network Flow

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.

Level:
Intermediate

Organization of the Course:

This course takes place online at the Institute for 4 weeks. During each course week, you participate at times of your own choosing - there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirement:

Options for Credit and Recognition:
Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:
1. No credit - You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
2. Certificate - You may be enrolled in PASS (Programs in Analytics and Statistical Studies) that requires demonstration of proficiency in the subject, in which case your work will be assessed for a grade.
3. CEUs and/or proof of completion - You may require a "Record of Course Completion," along with professional development credit in the form of Continuing Education Units (CEU's).  For those successfully completing the course,  CEU's and a record of course completion will be issued by The Institute, upon request.
4. Other options - Statistics.com Specializations, INFORMS CAP recognition, and academic (college) credit are available for some Statistics.com courses

Specialization:
Specializations are an easy way for you to demonstrate mastery of a specific skill in statistics and analytics. This course is part of the Optimization Specialization which discusses linear programming, nonlinear programming, network flow, decision analysis, queuing, simulation.  Take any three of the four Statistics.com courses on this topic (this course, plus the courses listed to the right under "related courses," not including conferences).  For savings, use the promo code "optimize-specialization" and register for all three courses at once for  \$1197 (\$399 per course, not combinable with other tuition savings).  If you register for all four, you'll still receive the discounted rate.

College credit:
Integer & Nonlinear Programming and Network Flow has been evaluated by the American Council on Education (ACE) and is recommended for the graduate degree category, 3 semester hours in operation research or quantitative methods. Note: The decision to accept specific credit recommendations is up to each institution. More info here.

INFORMS CAP:
This course is also recognized by the Institute for Operations Research and the Management Sciences (INFORMS) as helpful preparation for the Certified Analytics Professional (CAP®) exam, and can help CAP® analysts accrue Professional Development Units to maintain their certification .
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 Introduction to Optimization and Risk Simulation and Queueing.

Software:
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 Statistics.com.   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.
Instructor(s):

Dates:

September 20, 2019 to October 18, 2019 September 18, 2020 to October 16, 2020

# Integer & Nonlinear Programming and Network Flow

Instructor(s):

Dates:
September 20, 2019 to October 18, 2019 September 18, 2020 to October 16, 2020

Course Fee: \$589

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