Topics 4, 5, and 6 form Module 2 of MOOCOR. They are devoted to Simplex Algorithm. In Topic 4 the steps of the algorithm were introduced for a canonical form of LP (max problem with all variable non-negative and all constraints with "<=" signs). In topics 5 and 6 methods and techniques are discussed for cases where non-canonical LP are present. Big-M method (Topic 5) and Two-phase method (Topic 6) both address cases in which constraint signs are different than "<=". Additionally, the first half of Topic 6 is devoted to discussions of LP that are in the form of minimization or cases where variables may not be non-negative (i.e., non-positive or unrestricted). It is necessary to mention that one major difference between Module 1 and 2 video lectures is the number of times you need to pause the videos. Module 1 materials mainly contained the  materials with which most college students (in related fields) are familiar. The video lectures for those topics could be viewed with minimum number of pauses needed to understand different points raised in those topics. That is not the case for Module 2 videos (actually all videos from topics4 through 10). For example, videos of module 2 contain simplex tableaux iterations and for a participant to learn the topic, he/she needs to actually do the problems that are worked out in the videos and then compare them with steps performed in the video. Thus an iteration shown in the video in 15-20 seconds may require 15-20 minutes to complete. And there are many such iterations contained in the Module 2 videos. Finally, it needs to be reminded that in MOOCOR each topic is built based on the knowledge presented in previous topics and expectations are that participants "develop autonomous learning strategies, thus promoting their own cognitive, affective and psychomotor learning skills and knowledge" (see Instructional scaffolding). 

Learning Goals of Topic 5

  • Understanding the concepts of penalizing the objective function
  • Understanding the need and concepts of artificial variables
  • Understanding the concept of M as a very large positive value and its role in the Big-M method
  • Ability to prepare and set up the starting initial tableau for Big-M method and carrying out iterations of simplex method in Big-M method
  • Ability to identify infeasible problems from final Big-M simplex tableau
  • Ability to recognize the general form of Z-row elements as indicators of whether a solution is feasible or not

Study Guide

  • Watch Topic 5 video (35:29 minutes). Since, this topic uses concepts developed in topic 4 make sure that you are comfortable with the concepts and procedures related to simplex method applied to canonical forms. If needed, please view Topic 4 video again before watching Topic 5 video
  • Visit the Operations Research course on my Web site. On the sliding panel on the left hand side click on "Archive" and select "Solved Problems". In the solve Problems window click on "Big-M and Two-phase" to see a number of solved problems. Browse through the problems an get a feel about the type of problems that you may encounter. Try to see whether you can solve some of them without the help of any software.
  • On the same Archive tab, select "Topic Archive" and in the new window browse through past semesters of OR class and look at the Simplex Method(Big-M) topics.
  • Try to do one of the assignments in one of the Topic Archive pages. If you have a problem, post your question to the group.
  • Select one of the problems of your choice and solve it. Between Friday and Saturday post your solution to the group (only PDF files please). If you have not finished your homework, do not look at posted solutions. On Sunday, a test problem will be posted, pick up the problem and try to do it in the allotted time. Participate in the discussion that would follow a couple of days after the test.


  • Did you complete the homework correctly within the required time? If not, what were the major reasons.
  • While solving homework, did you have to redo some work or make corrections to some of the values calculated? If so, would you categorize them as careless mistakes or conceptual mistakes? Do you feel that they might be the type of mistakes other participants make? What advice you can give others to reduce the possibility of those mistakes?
  • Did you finish the test within the time identified for the test? If not, how many more minutes it took you to finish the test? Did you finish the test correctly? With passing threshold of 70% did you pass the test? What was the concepts in the test that were not discussed in video tapes, homework, or solved problems? Were they type of concepts that could be deducted from other concepts discussed in Topic 5?
  • About the course: Did you have difficulty finding and studying the materials for this course? How can it be improved?

Additional Resources 

Many resources are available on the Internet in terms of Web document pages, PDF documents and videos. Some of these links can also be found on my Operations Research Web page. Two specific sets of videos from India Institute of Technology, Madras and one set from India Institute of Technology, Kanpur are excellent resources that can help your development in operations research. They are more advanced than MOOCOR series and also covering additional topics, but for those of you who are using MOOCOR to learn operations research for the first time or as a refresher course, following those lectures is much easier. The video series are Fundamentals of Operations Research (22 lectures) and Advanced Operations Research (29 lectures) both by Professor G. Srinivasan from the Department of Management Studies at IIT-Madras. and Linear programming and Extensions (40 lectures) by Professor Prabha Sharma of the Department of Mathematics and Statistics at IIT-Kanpur. Links to those videos are also provided on my operations research pages. In any case do not forget that my YouTube channel has several videos related to this topic as well.

Professional Organizations 

INFORMS is the professional society for researchers and practitioners of OR. It has hundreds of resources on its Web site that can help introduce the field to interested people. In one of its pages under Related Societies it provides an extensive link to other societies around the world that perform similar services.

More Information  

Topic 4 | Go to | Topic 6