Operations Research (3): Theory from Coursera

What's inside

Syllabus

Course Overview

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.

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.

Sensitivity Analysis and Dual Simplex Method

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.

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.

Convex Analysis

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.

Lagrangian Duality and the KKT condition

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.

Case Study

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.

Course Summary and Future Learning Directions

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.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Involves advanced mathematical concepts

Provides a strong foundation for those interested in deterministic optimization

Covers diverse applications, including network flow, transportation, and resource allocation

Taught by an experienced instructor with expertise in optimization

Requires a background in linear algebra and calculus

Reviews summary

Operations research theory course

Learners say this Operations Research Theory course is excellent and well-delivered. They describe the lectures as engaging and the mathematical concepts as well-explained. Students particularly value the instructor's teaching style and say they've learned a lot from this specialization. The course covers Lagrangean decomposition, duality theory, convex analysis, and network flows. Students highlight the mathematical solid presentation and say the course requires a good mathematical background. Overall, learners express that this course is of high quality and provides a solid foundation in operations research.

Clear and organized presentation of material.

"A detailed presentation of the important ideas underlying modern operations research, with a well-structured flow from the motivating problem statement to the theories and applications resolving those problems."

"Convex analysis and network flows are the surprising cases."

"By the way, the course from week 5 is a mathematical solid presentation of Statistical Learning."

Covers complex mathematical concepts in depth.

"Very thorough and challenging for Operations Research candidates!"

"Gives a very good foundation of Lagrangean decomposition and Duality theory!"

"The course is very well delivered and covers several mathematical concepts, which means it requires a good mathematical understanding and background."

Taught by an engaging and knowledgeable instructor.

"The teaching style is awesome!"

"I have learnt literally way too much."

"It is difficult for me to decide if my favourite instructor to date is andrew ng or HIM!"

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Operations Research (3): Theory with these activities:

Gather and Organize Course Materials

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Enhance organization and recall by compiling and reviewing course materials.

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Gather lecture notes, assignments, and other relevant materials.
Organize materials into a logical structure, such as by topic or date.
Review materials regularly to reinforce concepts.

📘 Read 'Introduction to Operations Research' by Frederick S. Hillier and Gerald J. Lieberman

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Establish a foundational understanding of OR concepts by reading a classic textbook in the field.

View ISE Introduction to Operations Research on Amazon

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Review chapters 1-5 to understand the basics of OR and linear programming.
Focus on chapters 6-10 for integer programming, network flow, and nonlinear programming.

Follow Tutorials on OR Techniques

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Supplement course materials by exploring online tutorials and resources to reinforce concepts.

Browse courses on Linear Programming

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Search for tutorials on specific OR topics you want to strengthen.
Follow step-by-step instructions and work through examples.

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Join a Study Group or Discussion Forum

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Collaborate with peers to clarify concepts, solve problems, and share insights.

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Join or create a study group with other students in the course.
Meet regularly to discuss course material, work on problems together, and quiz each other.

Solve OR Problems on LeetCode

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Develop problem-solving skills by working through curated OR problems on LeetCode.

Browse courses on Linear Programming

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Create a LeetCode account and set a goal to solve 10-15 OR-related problems.
Focus on problems tagged with 'linear programming', 'integer programming', or 'network flow'.
Analyze solutions provided by others to enhance your understanding.

Apply OR Techniques in Practice

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Reinforce concepts by finding a practical OR problem and applying the techniques covered in the course to develop a solution.

Browse courses on Linear Programming

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Define the business problem and the constraints involved.
Formulate an OR model to represent the problem.
Solve the OR model using appropriate software or techniques.
Analyze the solution and interpret the results.
Implement the solution in practice (optional).

Create OR-Based Visualizations

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Enhance understanding by visualizing OR concepts and applying them to real-world scenarios.

Browse courses on Linear Programming

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Choose a topic such as linear programming or integer programming.
Create visualizations using tools like Tableau or Python to illustrate concepts and solve problems.
Share your visualizations with others for feedback and discussion.

Develop an OR-Based Decision Support Tool

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Apply your knowledge by creating a practical tool that solves optimization problems in a business or industry context.

Browse courses on Linear Programming

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Identify a decision-making problem that can be solved using OR techniques.
Develop an OR model to represent the problem and solve it using appropriate methods.
Create a user-friendly tool that enables non-experts to use the OR model.

Career center

Learners who complete Operations Research (3): Theory will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians use mathematical techniques to solve problems in a variety of fields, including science, engineering, and business. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate mathematical models. This course provides a strong foundation in the mathematical techniques that are essential for success in the mathematics field.

See salaries and explore the career path for Mathematician

Operations Research Analyst

Operations research analysts use mathematical and analytical techniques to solve problems in a variety of industries, including manufacturing, transportation, logistics, and healthcare. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate solutions to problems such as optimizing production schedules, routing vehicles, and managing inventory levels. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the operations research field.

See salaries and explore the career path for Operations Research Analyst

Data Scientist

Data scientists use mathematical and statistical techniques to analyze data and extract insights that can be used to make better decisions. They use techniques such as linear programming, integer programming, and machine learning to develop and evaluate models that can predict future events or identify trends. This course provides a strong foundation in the mathematical and statistical techniques that are essential for success in the data science field.

See salaries and explore the career path for Data Scientist

Actuary

Actuaries analyze the financial consequences of risk and uncertainty. They use mathematical and statistical models to assess the probability and impact of future events, such as death, disability, or property damage. Actuaries play a vital role in the insurance industry, helping insurers to develop products and set prices that are fair to both the insurer and the policyholder. This course provides a strong foundation in the mathematical and statistical principles that are essential for success in the actuarial field. Topics covered in this course include probability, statistics, linear programming, and optimization.

See salaries and explore the career path for Actuary

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They use techniques such as linear programming, integer programming, and machine learning to develop and evaluate statistical models. This course provides a strong foundation in the mathematical and statistical techniques that are essential for success in the statistics field.

See salaries and explore the career path for Statistician

Quantitative Trader

Quantitative traders use mathematical and statistical models to trade financial instruments. They use techniques such as linear programming, integer programming, and machine learning to develop and evaluate trading strategies. This course provides a strong foundation in the mathematical and statistical techniques that are essential for success in the quantitative trading field.

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Management Consultant

Management consultants use mathematical and analytical techniques to solve problems and improve performance in organizations. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate solutions to problems such as optimizing production schedules, routing vehicles, and managing inventory levels. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the management consulting field.

See salaries and explore the career path for Management Consultant

Business Analyst

Business analysts use mathematical and analytical techniques to analyze business problems and identify solutions. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate solutions to problems such as optimizing production schedules, routing vehicles, and managing inventory levels. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the business analysis field.

See salaries and explore the career path for Business Analyst

Financial Analyst

Financial analysts use mathematical and statistical models to analyze financial data and make investment recommendations. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate investment strategies. This course provides a strong foundation in the mathematical and statistical techniques that are essential for success in the financial analysis field.

See salaries and explore the career path for Financial Analyst

Risk Manager

Risk managers use mathematical and analytical techniques to identify and manage risks. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate risk management strategies. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the risk management field.

See salaries and explore the career path for Risk Manager

Economist

Economists use mathematical and statistical techniques to analyze economic data and make predictions about the economy. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate economic models. This course provides a strong foundation in the mathematical and statistical techniques that are essential for success in the economics field.

See salaries and explore the career path for Economist

Industrial Engineer

Industrial engineers use mathematical and analytical techniques to improve the efficiency and effectiveness of industrial processes. They use techniques such as linear programming, integer programming, and simulation to develop and evaluate solutions to problems such as optimizing production schedules, routing vehicles, and managing inventory levels. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the industrial engineering field.

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Operations Manager

Operations managers plan, direct, and coordinate the activities of an organization's operations. They use mathematical and analytical techniques to solve problems and improve performance. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the operations management field.

See salaries and explore the career path for Operations Manager

Software Engineer

Software engineers design, develop, and maintain software systems. They use mathematical and analytical techniques to solve problems and develop efficient and reliable software. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the software engineering field.

See salaries and explore the career path for Software Engineer

Systems Analyst

Systems analysts design, develop, and implement computer systems. They use mathematical and analytical techniques to solve problems and develop efficient and reliable systems. This course provides a strong foundation in the mathematical and analytical techniques that are essential for success in the systems analysis field.

See salaries and explore the career path for Systems Analyst