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
Learning Goals of Topic 6
- Ability to prepare and set up the starting basic feasible solution
tableau of the simplex method, including writing the standard form, and
identifying basic and non-basic variables at the starting basic feasible
- Ability to extract the solution from a given tableau and write the
equations from it
- Ability to recognize whether a solution provided by the tableau is
optimal or not
- Understanding and having the ability to identify entering and leaving
- The ability and knowledge to perform an iteration of the simplex
- Watch Topic 4 video (29:43 minutes). Since, this topic uses concepts
developed in topics 1, 2, and 3 make sure that you are comfortable with
those concepts. If it has been a while since you watched those topics,
please view them again before watching this video.
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 "Simplex
Method" 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
- 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 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 4?
- About the course: Did you have difficulty finding and studying the materials
for this course? How can it be improved?
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. Additionally, there are major mathematics and
engineering software that perform many calculations necessary to solve LP
problems or solve them completely. Some specific software designed for
solving LP problems are also available. Some commercial software such as
also have free student/demo version that can handle problems in limited size
that are generally well beyond the sizes required in academic environments.
Finally, some of the Internet pages contain scripts and programs that will allow
soling LPs on line. In
any case do not forget that my YouTube channel has several videos related to
this topic as well.
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.
Topic 5 | Go to | Topic 7