### Integer & Nonlinear Programming and Network Flow

# 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.

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
- 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

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:

About 15 hours per week, at times of your choosing.

Credit:

Students come to the Institute for a variety of reasons. As you begin the course, you will be asked to specify your category:

- You may be interested only in learning the material presented, and not be concerned with grades or a record of completion.
- 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.
- 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.

Course Text:

*Spreadsheet Modeling & Decision Analysis*,* seventh 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.

We'll buy your book for you if you register for two or more of the above courses at the same time - actually, we'll credit the value ($279) against your second course, just request a promo code here to use during registration (may not be combined with other discounts).

Note: It is important to get the *seventh *edition of the text; earlier editions do not contain correct assignments.

This book is also available on a per-chapter basis; the chapters used in this course are 5, 6, 7, and 8.

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.

# Integer & Nonlinear Programming and Network Flow

September 22, 2017 to October 20, 2017September 21, 2018 to October 19, 2018