Throughout MOOCOR, one issue is constantly highlighted: we are interested in
not only how the procedures are performed but also the concepts that those
procedures are built upon them. If we trained ourselves to build our knowledge
based on those concepts we would not need to memorize details of algorithms and
special cases associated with one. For example, if one conceptually know how to
find the solution to a linear system of equations by progressively creating
smaller problems based on original problem, say by substitution, then the only
remaining thing is to practice and through practice develop efficient ways to
solve different problems.
This approach would also help developing a keen sense of knowing when there
are mistakes or inconsistencies in the solution approach. Thus instead of trying
to finish a work that due to mistakes would lead to incorrect answers, one can
evaluate each completed step before going forward.
In Topics 1 and 2 we will restrict ourselves to problems of two dimensions so
we can plot them and visually inspect some important concepts related to
optimization. As we extend to multi variable problems where no visual inspection
is possible, same concepts are useful in our understanding of the features of
the problem. For example, the intersection of two line in a two dimensional
problem is the solution for a linear system of equations represented by those
two lines, while the intersection of three planes in three dimension and
intersection of n hyper planes in n dimension in the solution of linear system
of equations in 3 and n dimensions respectively.
Learning Goals of Topic 1
The ability to plot lines in two dimensional Cartesian coordinate system
Understanding and having the ability to identify solutions of linear
equations and inequalities
The ability to identify solutions to a system of linear inequalities
Understanding the features of feasible region and its extreme points in
terms feasible and infeasible extreme points and their significance in
overall scheme of optimization
Understanding the concept of an objective function and its role in a
linear programming (LP) model
Recognizing the general models of LP
Watch Topic 1 video (26:53 minutes). Somewhere around minute 9:00 a
reference is made to another video on my channel (Line
Plot), pause Topic 1 video and on a new window watch the other
video. Upon completion return to the Topic 1 video and resume watching.
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 "Graphical
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 plot the feasible region without the help of any
software. Use graph papers and try to be as accurate as you can.
On the same Archive tab, select "Topic Archive"
and in the new window browse through past semesters of OR class and see
whether you can find topics that are related. You should be looking for
topics that come under "Plotting feasible region" and visit some of them.
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 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 1?
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 are 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. Professional software such as
MATHEMATICA, ... have such capabilities. 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. You can see an example of this, related to Topic 1 materials
Finite mathematics utility: linear programming grapher page
which allows users to enter their LP and plot the feasible region and more. 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.