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.
![National Taiwan University](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-university-assets.s3.amazonaws.com/1d/af896d9aaed8926efc02bdcbd37a64/Emblem72.png?auto=format%2Ccompress&dpr=1&w=28&h=28)
![National Taiwan University](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/http://coursera-university-assets.s3.amazonaws.com/ca/1fae86849a421d8aadc224ad843ae0/logo_s.png?auto=format%2Ccompress&dpr=1&h=45)
Operations Research (3): Theory
Taught in English
Some content may not be translated
8,359 already enrolled
(68 reviews)
Recommended experience
What you'll 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'll gain
Details to know
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/31ebcba3851b87d1d8609abf15d0ff7e.png?auto=format%2Ccompress&dpr=1&w=24&h=24)
Add to your LinkedIn profile
8 quizzes
See how employees at top companies are mastering in-demand skills
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/74c8747e8210831049cf88dd4eefe26c.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=320)
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/de1a6556fbe605411e8c1c2ca4ba45f1.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=259)
Earn a career certificate
Add this credential to your LinkedIn profile, resume, or CV
Share it on social media and in your performance review
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/de1a6556fbe605411e8c1c2ca4ba45f1.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=333)
There are 8 modules in this course
In the first lecture, after introducing the course and the importance of mathematical properties, we study the matrix way to run the simplex method. Being more familiar with matrices will help us understand further lectures.
What's included
5 videos1 reading1 quiz
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.
What's included
14 videos1 quiz
In the past two weeks, we study the simplex method and the duality. On top of them, the dual simplex method is discussed in this lecture. We apply it to one important issue in sensitivity analysis: evaluating a linear programming model with a new constraint. A linear programming model with a new variable is also discussed.
What's included
8 videos1 quiz
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.
What's included
11 videos1 quiz
As the last lesson of this course, we introduce a case of NEC Taiwan, which provides IT and network solutions including cloud computing, AI, IoT etc. Since maintaining all its service hubs is too costly, they plan to rearrange the locations of the hubs and reallocate the number of employees in each hub. An algorithm is included to solve the facility location problem faced by NEC Taiwan.
What's included
13 videos1 quiz
In this week, we study nonlinear programs with constraints. We introduce two major tools, Lagrangian relaxation and the KKT condition, for solving constrained nonlinear programs. We also see how linear programming duality is a special case of Lagrangian duality.
What's included
15 videos1 quiz
In this week, we introduce two well-known models constructed by applying the mathematical properties we have introduced. First, we formulate a simple linear regression problem as a nonlinear program and derive the closed-form regression formula. Second, we introduce support-vector machine, one of the most famous classification model, from the perspective of duality.
What's included
14 videos1 quiz
In the final week, we review the topics we have introduced and give some concluding remarks. We also provide some learning directions for advanced studies.
What's included
3 videos1 quiz
Instructor
![孔令傑 (Ling-Chieh Kung)](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera-instructor-photos.s3.amazonaws.com/b2/f19ff0a32011e7ab7087c8181ea8c1/____.jpg?auto=format%2Ccompress&dpr=1&w=75&h=75&fit=crop)
Offered by
Recommended if you're interested in Algorithms
École normale supérieure
National Taiwan University
National Taiwan University
The University of Melbourne
Why people choose Coursera for their career
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Felipe_Moitta.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Jennifer_John.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Larry_Tao_Wang_1.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
![](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/growth_testimonials/passionate_learner/Chaitanya_Anand.png?auto=format%2Ccompress&dpr=1&w=64&h=64&fit=crop)
Learner reviews
Showing 3 of 68
68 reviews
- 5 stars
98.55%
- 4 stars
1.44%
- 3 stars
0%
- 2 stars
0%
- 1 star
0%
New to Algorithms? Start here.
![Placeholder](https://d3njjcbhbojbot.cloudfront.net/api/utilities/v1/imageproxy/https://coursera_assets.s3.amazonaws.com/images/7a1c0e2e779c1ff27cae62480adfe003.png?auto=format%2Ccompress&dpr=2&blur=200&px=8&max-w=120)
Open new doors with Coursera Plus
Unlimited access to 7,000+ world-class courses, hands-on projects, and job-ready certificate programs - all included in your subscription
Advance your career with an online degree
Earn a degree from world-class universities - 100% online
Join over 3,400 global companies that choose Coursera for Business
Upskill your employees to excel in the digital economy
Frequently asked questions
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:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
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.
When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
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.