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New this week (Dec. 1)
This is week 14.
The final exam will be comprehensive. It will be on Friday, December 12th from 9-11 am in room 360 JMHH.
Both classes this week will be regular classes. Project presentations will take
place next Monday, 8 Dec., from 6 pm to 9pm +. I'll order pizza and soft finks.
Since there are 12 projects, we'll have to be strict about timing: up to 15 minutes per project.
Prepare one double-sided page to be distirbuted to the class.
Send it to me by email no later than 5 pm, and I'll print it.
If I don't get anything from you by 5 pm, I'll assume you'll print it yourself.
Please prepare professional presentations, using for instance pdf or ppt.
Concentrate on the essential: the problem, the model, your chosen solution method.
Leave the details for the final reports.
The reports will be due on the last day of the exam period.
If you are not ready by then, you'll automatically get an incomplete, and your grade will be postponed until January.
New this week (Nov. 24)
This is week 13.
No class this week, instead there is a "catch-up" exam for those who got 70 or less in the midterm. On Tuesday 25 Nov., 3-4:30, 270 JMHH.
Here is
homework 6, due Monday 8 December.
Happy Thanksgiving!
New this week (Nov. 17)
This is week 12.
Please download
(1) the file on primal affine scaling.
(2) the file on NLP(1),
(3) the file on NLP(2),
(4) the file on the KKT conditions, and
(5) the enlarged KKT picture.
We will look at NLP(2) before NLP(1).
You should also look at this
summary.
New this week (Nov. 10)
This is week 11.
Don't forget that there will be a quiz at the beginning of class this Thursday 11/13/2008. It will be based on everything, up to and including transportation and assignment.
You must let us know in advance by email if you cannot make it to class on that day.
Homework 5 will be due on Thursday 20 November.
We will look today (11/11) at
(1) cuts (p. 23-38 and 47-51)
and Gomory cuts ,
(2) the dual simplex method (see section 6.11, p. 329-334),
(3) BB and variables with upper bounds in LINDO.
On Thursday we will look at interior point methods for solving LPs in polynomial time. While Karmarkar's method is guaranteed to converge in polynomial time, it is rather difficult to understand. We will rather look at the affine scaling algorithm, another interior point method, even though it is not polynomial. It works well in practice.
Look at the gams code implementing
affine scaling, and at the Wikipedia article on
it.
To help you get some practice with
logical constraints, here is a folder full of examples. Have fun!
New this week (Nov. 3, election week!)
This is week 10.
Updated answer to midterm
problem 3.
Updated answer to midterm
problem 2.
Don't forget that there will be a quiz at the beginning of class next Thursday 11/13/2008.
You must let us know in advance by email if you cannot make it to class on that day.
A farmer is carrying a bushel of corn and is accompanied by a goose
and a wolf. He came to a river.... you know the story! Except that in France, one talks about a cabbage, a goat and a wolf...
Download, study and run the corresponding gams
model from the GAMS Model Library.
How many times does the farmer have to cross the river?
There are several errors in the slides of Sarper for Chapter 9, so please download this
file instead.
The following summary may also help you model constraints with 0-1 variables.
New this week (Oct. 27)
Good news, it seems the email account is working again...
This is week 9.
The following
file 1 and
file 2 may help you review duality in linear programming.
Here is an
example with an infinite duality gap.
The following gams files may be useful, in particular they illustrate the use of mpswrite.
Transportation problems: try to run the following gams program, this is the listing, and this is the log file.
In gams under windows you automatically obtain the log file.
In unix, it is not automatically saved, but you can get it by running your
program in batch mode,
using the command "gamsbatch mymodel" instead of "gams mymodel".
In batch mode, you can even turn your computer off, and the run continues
in the background on the unix machine. This is useful in particular for long runs.
An example of a transportation problem and questions about it: the
problem and the
answers.
New this week (Oct. 20)
Please stop sending email messages to the yahoo account, it has been suspended by yahoo for "suspicious activity".
I will let you know (by email) when it is restored. Right now it still receives your messages but I cannot reply.
Thanks for letting me know that there was a confusion between the two variables in the LINDO output, as well as a
typo in the answer to Problem 2. Oh! well...
Here are the answer to the asparagus problem,
with the typo corrected, and the answer to the incomplete LINDO
output.
The answer to Problem 3 is here.
Please read the following short note and try to figure out what it is doing (the student who wrote it wrote it in a very terse way! notice also that the dual should be a max if the primal is a min!)
Homework 4 will be due on Thursday 6 November.
Next week Jian and I will exchange days for the office hours. I will have mine on Monday, on the 6th floor of JMHH (the OPIM conference room will not be available on that day).
I suggest that if you have a few minutes to spare, you go to the following
webpage. It shows a number of real uses of OR in practice.
In addition it is really well done!
___________________________________________________________
To help you practice, here is the text of the
quiz (without answers)
and
quiz (with answers).
Remember that the midterm will be in class on Thursday 23 October, 3-4:30.
Closed book, but you can bring a sheet with all you want to have handy during the exam.
Don't forget to take a small calculator, a ruler, and an eraser. We will provide paper.
Finally, tomorrow, Wednesday, I will have expanded office hours, 3-5 and then after 6
(but no later than 7!) for those who really cannot make it between 3 and 5. In the OPIM suite, room 541.
Bring your questions.
New this week (Oct. 6)
SLIDES
Please download the following two
files, we will look at them in class on Thursday.
HOMEWORK
Here is the third
homework, due Tuesday 21 October.
Don't forget that last week, you were supposed to read the "portfolio selection" part in Financial applications!
As part of HW3, you are asked to solve the corresponding model in LINDO,
append your printout, then interpret the sensitivity analysis part in the context of this problem.
Would it not make sense to question the apparent "arbitrariness" of some of the constraints?
SUMMARY
The class
summary for Tuesday 30 September is now available.
READINGS
No reading this week, you have enough to do with class material, the first project, and HW3.
You might however find the following files useful for a deeper understanding of class material:
(*) an incomplete LINDO
output (expect to get such a question for the midterm!)
(*) another
example of how to determine
graphically the range of an objective function coefficient
within which the optimal basis is unchanged
(*) an example with detailed sensitivity analysis.
There are many questions, and you could try to answer them
first without looking at the answers. Good practice for the midterm :)
EMAIL/OFFICE HOURS
Finally don't hesitate to come to office hours (3:30 to 5, Mo. and Wed., in one of the OPIM conference rooms, 5th floor, JMHH),
or to write us email at opim910@yahoo.com if you have questions. Not just for the homework, but on any course related issue.
QUIZZZZZ
Here is the
answer to Thursday's quiz.
There will be another quiz this Thursday, and this time, it will be collected and graded. It will count as a mini homework.
New this week (Sept. 29)
This might make your life easier if you use the DOS version of LINDO and want to print (part of) the screen.
The procedure goes as follows:
when you have the DOS window open, (black background), click on the c:\ at the top left corner, click on edit,
then on mark, then mark by select-clicking the part of the screen that you want to print (that part will be white).
Click on c:\ again and click on copy. Then go to your text editor and paste your selection in a new file
that you can then print normally or send us as a text file... That is all there is to it. You could also
click on select all if that is what you want... it is easier, and you can then edit the text file :)
For Thursday's class, as well as next Tuesday's class, please download Sarper's
notes
on Chapter 5.
I would suggest that you read the slides on CH. 5 by Orlin on your own as a complement.
Note: in the homework, in general, if the question is: "what is the optimal solution," don't forget to give the optimal value as well. This is obviously important information!
Reading for the week:
this file contains a number of applications.
Read in particular the "portfolio selection" part in Financial applications, solve the corresponding model in LINDO,
and append your printout to the next homework (HW 3). Interpret the sensitivity analysis part in the context of this problem. Would it not make sense to question the apparent "arbitrariness" of some of the constraints?
New this week (Sept. 22)
Please go to "slides" and download "my" slides for week 4.
Look at
this!
Here is the second
homework, due Thursday 2 October.
Remember that you are allowed, and even encouraged, to work in groups on the homework problems.
However, you must each return your own answer, and
it must be your own!
In particular, for this homework, you must write your own model in LINDO and run it yourself.
It is NOT allowed to use any outside help or outside source in this class without referencing it.
It is all right to cooperate with your classmates as long as you do not copy someone else's work.
New this week (Sept. 15)
For your enjoyment:
click here. Be sure to move the cursor over the picture!
Now, something more serious! Office hours will be Mondays and Wednesdays,
3:30 to 5 pm, in the OPIM conference room.
The first project description can be found
here.
Finally, the reading for this week is by George Dantzig in Interfaces. The reference is
George B. Dantzig, "The Diet Problem." Interfaces 20:4 (July-August 1990) 43-47.
This time use EBSCO MegaFILE for the download.
To get the slides go there.
If you want to download the free version of the text editor NoteTabLight, click
here.
New this week (Sept. 10)
Here is the first
homework, due Thursday September 18.
Remember that you are allowed, and even encouraged, to work in groups on the homework problems.
However, you must each return your own answer, and
it must be your own!
It is NOT allowed to use any outside help or outside source in this class without referencing it.
It is all right to cooperate with your classmates as long as you do not copy someone else's work.
Be sure to read the section on projects, and to start thinking about possible topics. The groups for the final project will be mailed to you at the end of the week.
Finally, here is a short article on modeling in Math. Programming. You might want to read it and re-read it and ... many times during the semester. Modeling is an art, and practice is the best way to become a master.
New this week (Sept. 3)
The first readings for the semester are taken from the INFORMS Journal called Interfaces.
You can download them using the Penn Library journal access system (requires Pennkey).
The first reading emphasizes the usefulness of spreadsheets in Management Science/Operations Research.
Interfaces, Vol.38, No.4, July-August 2008, p. 225-227.
The second one presents an application of spreadsheet optimization for scheduling radiology residents at a teaching university hospital.
Interfaces, Vol.38, No.4, July-August 2008, p. 311-323.
These papers should be read by the end of next week.
While this course does not emphasize the use of spreadsheets, they are a useful tool, either alone or combined with a system such as GAMS.
New this week (Aug. 16)
Well, this is the first message for this semester.
The website is under construction, and in some way, it will be so until the end of the semester :)
Feel free to browse now, and during the semester, feel obliged to do so at least every second day,
as this will be the main communication channel from instructor/TA to you.
When you install the CD from the back of the textbook on your computer, you will
August 2008, 311notice that LINDO and LINGO will be installed automatically, among other things.
Be sure that you are connected to the internet at this point, as the system will look
for a possible update on the LINDO site (and chances are there is a newer version
than that on your CD). The good news is that you don't have to go to the LINDO site
to download the LINDO package on your own, this will be done automatically.
As he stated it himself,
"Linear programming is a revolutionary development giving man the ability to state general objectives and to find, by means of the simplex method, optimal policy decisions for a broad class of practical problems of great complexity."
Read the article, or this one entitled "G. B. Dantzig 1914 - 2005", in the Bulletin of the Czech Econometric Society 22 (2005), by J.Dupacova and D.P.Morton.
Operations Research: the science of better. Click on "Benefit", then "Optimize Resource". Look at the examples.