About this Course

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Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Electrical Engineering, etc.
The series of courses consists of three parts, we focus on deterministic optimization techniques, which is a major part of the field of OR.
As the third part of the series, we study mathematical properties of linear programs, integer programs, and nonlinear programs. We also introduce applications of these theoretical properties: How they help us develop better ways to solve mathematical programs.

Flexible deadlines

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Shareable Certificate

Earn a Certificate upon completion

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Coursera Labs

Includes hands on learning projects.

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Advanced Level

This course is appropriate for students with experience Calculus, Linear Algebra, and Probability.

Approx. 14 hours to complete

English

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What you will learn

Understand the theoretical properties of linear programs, integer programs, and nonlinear programs.
Apply the mathematical properties to reduce the complexity of real-world problems or to solve it.

Skills you will gain

Theory
Business Analytics
Mathematical Optimization

Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Advanced Level

This course is appropriate for students with experience Calculus, Linear Algebra, and Probability.

Approx. 14 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Instructor rating

4.89/5 (20 Ratings)

孔令傑 (Ling-Chieh Kung)

副教授 (Associate Professor)

資訊管理學系 (Department of Information Management)

68,783 Learners

8 Courses

Syllabus - What you will learn from this course

Week1

Week 1

1 hour to complete

Course Overview

1 hour to complete

5 videos (Total 65 min), 1 reading, 1 quiz

Week2

Week 2

2 hours to complete

Duality

In this week, we study the theory and applications of linear programming duality. We introduce the properties possessed by primal-dual pairs, including weak duality, strong duality, complementary slackness, and how to construct a dual optimal solution given a primal optimal one. We also introduce one important application of linear programming duality: Using shadow prices to determine the most critical constraint in a linear program.

2 hours to complete

14 videos (Total 120 min)

14 videos

2-0: Opening.4m2-1: Introduction.1m2-2: Primal-dual pairs – The first example.8m2-3: Primal-dual pairs – More examples.7m2-4: Primal-dual pairs – General rule.12m2-5: Weak duality and sufficiency of optimality.7m2-6: Dual optimal solution and strong duality.11m2-7: An example for the theorems.5m2-8: Complementary slackness.12m2-9: Motivating examples for shadow prices.9m2-10: Shadow prices.9m2-11: Shadow prices and duality.12m2-12: Computers – Gurobi and Python for shadow prices.13m2-13: Closing remarks.4m

1 practice exercise

Quiz for Week 220m

Week3

Week 3

1 hour to complete

Sensitivity Analysis and Dual Simplex Method

1 hour to complete

8 videos (Total 52 min)

Week4

Week 4

2 hours to complete

Network Flow

In this lecture, we introduce network flow models, which are widely used for making decision regarding transportation, logistics, inventory, project management, etc. We first introduce the minimum cost network flow (MCNF) model and show hot it is the generalization of many famous models, including assignment, transportation, transshipment, maximum flow, and shortest path. We also prove a very special property of MCNF, total unimodularity, and how it connects linear programming and integer programming.

2 hours to complete

11 videos (Total 89 min)

11 videos

4-0: Opening.5m4-1: Introduction.5m4-2: MCNF problems.12m4-3 LP formulation for MCNF8m4-4: Total unimodularity.12m4-5: MCNF and total unimodularity.6m4-6: Transportation problems.7m4-7: Assignment and transshipment problems.7m4-8: Shortest path and maximum flow problems.12m4-9: Computers – Gurobi and Python for network flow.7m4-10: Closing remarks.3m

1 practice exercise

Quiz for Week 420m

Week5

Week 5

2 hours to complete

Convex Analysis

2 hours to complete

13 videos (Total 125 min)

13 videos

5-0: Opening.4m5-1: Motivating examples.7m5-2: Convex sets and functions.12m5-3: Global optimality and extreme point.11m5-4: Convex programming.13m5-5: Convexity of twice differentiable functions.6m5-6: Example – EOQ12m5-7: Second-order derivatives.8m5-8: Positive semi-definiteness.13m5-9: Analytically solving multi-variate NLPs.6m5-10: Example – Two-product pricing.10m5-11: Computers – Implementation of gradient descent.13m5-12: Closing remarks.3m

1 practice exercise

Quiz for Week 520m

Week6

Week 6

2 hours to complete

Lagrangian Duality and the KKT condition

2 hours to complete

15 videos (Total 120 min)

15 videos

6-0: Opening.5m6-1: Motivation.8m6-2: Lagrange relaxation.7m6-3: An example of Lagrange relaxation.4m6-4: Weak duality of Lagrange relaxation.6m6-5: The KKT condition.9m6-6: Visualizing the KKT condition.11m6-7: Example 1 of applying the KKT condition.10m6-8: Example 2 of applying the KKT condition.14m6-9: The KKT condition in general.4m6-10: More about Lagrange duality.3m6-11: Convexity and strong duality of Lagrange relaxation.9m6-12: An example of Lagrange duality.9m6-13: Lagrange duality vs. LP duality.10m6-14: Closing remarks.4m

1 practice exercise

Quiz for Week 620m

Week7

Week 7

2 hours to complete

Case Study

2 hours to complete

14 videos (Total 90 min)

14 videos

7-0: Opening.6m7-1: Introduction.3m7-2: Simple linear regression.6m7-3: Solving the simple linear regression problem.8m7-4: Remarks and other regression models.8m7-5: Support vector machine.8m7-6: Formulating the SVM model.9m7-7: Simplifying the objective function.4m7-8: SVM for imperfect separation.6m7-9: Dualization for the SVM problem (1).7m7-10: Dualization for the SVM problem (2).5m7-11: Convexity of the dual program.5m7-12: Final remarks.3m7-13: Closing remarks.5m

1 practice exercise

Quiz for Week 720m

Week8

Week 8

1 hour to complete

Course Summary and Future Learning Directions

1 hour to complete

3 videos (Total 29 min)

Reviews

5.0

14 reviews

5 stars
97.87%
4 stars
2.12%

TOP REVIEWS FROM OPERATIONS RESEARCH (3): THEORY

by SWApr 17, 2022

This is a good course. It provides necessary theoretical foundations.

by ANJul 21, 2022

Very thorough and challenging for Operations Research candidates! Gives a very good foundation of Lagrangean decomposition and Duality theory!

by OGOct 30, 2021

Excellent intro into the vast world of optimization and operations research. Please make one on stochastic processes and programming next!

View all reviews

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
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The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I purchase the Certificate?
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What is the refund policy?
You will be eligible for a full refund until two weeks after your payment date, or (for courses that have just launched) until two weeks after the first session of the course begins, whichever is later. You cannot receive a refund once you’ve earned a Course Certificate, even if you complete the course within the two-week refund period. See our full refund policy.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

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Operations Research (3): Theory