Welcome to the Course Page of SC/MATH 4170 6.00 A Operations Research II 20142015 Full Year 

Department of Mathematics and Statistics 

This
area will contain announcements and solutions to tests. Announcements made in
class will be posted here in reverse chronological order and will not be
repeated in class. Please take a minute to read the announcements carefully, as
they often get updated. You may need to Reload/Refresh this page.
April 17: 
According to your requests, I am making available solutions to the selected 

problems from Sections 11.9 and 11.10 of the textbook. 
April 13: 
Please note that the Final
Examination for the
course will take place on 

Sunday, April
19, 2015 from 14:00 to 17:00 in ACE 012. The exam will 

cover the entire material covered in class from Sections 11.1, 11.2, 11.3, 

11.4, 11.5, 11.6, 11.7,
11.8, 11.9, 11.10, 11.11, 11.12 and 11.13 of the 

textbook but with an emphasis on the more recent material covered after 

the Midterm Test #2. If less common formulas are
needed on the exam, 

then those will be provided on the exam paper. 

There will be several questions, some with a few parts.
Marks for each 

question will be indicated. You have to show all your
work and should 

explain your solutions where
appropriate. Unofficial final grades for the 

course will hopefully be posted to the course web page at
the beginning 

of May, 2015. 
April 10: 
Homework problems for
Sections 11.1111.13 and review problems: 

Section 11.11: #1, 2, 4; 

Section 11.12: #1, 2; 

Section 11.13: #1, 2, 3, 4; 

Chapter 11 Review Problems:
#3(a), 6, 8, 9, 14, 15, 18, 21 (pages 705706). 
April 03: 
As it was announced in the class yesterday, the student
course evaluations are 

available at the URL link:
http://courseevaluations.yorku.ca until Friday, 

April 17, 2015.
It is the time for you to be the judge. Please go online and 

complete the course
evaluation. Thank you! 
March 27: 
Homework problems for
Sections 11.911.10: 

Section 11.9: #1, 3, 5, 6,
8, 10, 16; 

Section 11.10: #1, 2, 5, 8. 

Review Problems for Chapter
11: #8, 9, 14, 15, 18,21 (pages 705706). 
March 21: 
As it was announced in the class on Thursday, we will
write Midterm Test #2 

during the lecture period
from 19:00 to 20:20 on Thursday, March 26. 

On the test you will be
responsible for all the material covered in class 

from
Sections 11.1, 11.2, 11.3, 11.4, 11.5, 11.6, 11.7 and 11.8 of the textbook. 

Please note that the classes will end on Friday, April
17. You may click here 

to see a new course schedule. 
March 16: 
Please note that the classes will resume shortly. Click the link below for the details: 


March 03: 
Last night, in a very large membership meeting, all
three units of CUPE 3903 voted 

not to send the employer's final offer to a
formal ratification vote. Overall, the vote was 

70% against sending the offer
to ratification vote. The union executive then decided 

to call the strike, given
that it had a strike mandate in hand from earlier in February. 

That means that, as of Tuesday March 03 at 12:01am, CUPE
3903 is on strike. 

The University’s Senate Executive decided on February 27, 2015 that all academic 

activities, including classes are cancelled until the strike is
settled. Unfortunately, 

at this point there is no way to know how long the
strike might last. In the meantime, 

even though it is difficult, I strongly recommend that you take this opportunity to review 

course material covered up to now, catch up with readings if you've fallen behind, and 

even read ahead, and continue to work on your assignments.
Although due dates are 

frozen, course work will be due when we return to classes.
Keeping up with work will 

make the transition back to classes a little less shocking. 

Please distribute this message to your class mates. Thank you. 
February 28: 
Please note that the Department
of Mathematics and Statistics will be hosting 

Science@50 anniversary event on Tuesday afternoon. The
event will include 

several short and informal lectures about cool Math in
Simpsons cartoon, 

followed by pizza and a career panel (a discussion with
our alumni about 

possible career paths
in Math). The students who are interested to attend 

this event should register at this website: 



You can also find all information about the event at this
website. 
February 14: 
As it was announced in the
class on Thursday, we will write the 

Medterm Test during the lecture period from 19:00 to 20:20 on 

Thursday, March 05. On
the test you will be responsible for all 

the
material covered in class from Sections
11.1, 11.2, 11.3, 11.4, 

11.5, 11.6, 11.7 and 11.8 of the textbook. 

HAVE A HAPPY READING WEEK! 
February 08: 
Homework problems for
Sections 11.711.8: 

Section 11.7: #2, 3, 4, 5; 

Section 11.8: #2, 3, 4, 5,
6, 8. 
January 31: 
Homework problems for
Sections 11.511.6: 

Section 11.5: #1, 2, 4; 

Section 11.6: #1, 3, 4, 6,
7, 8. 
January 23: 
Homework problems for
Sections 11.311.4: 

Section 11.3: #4, 6, 9, 10,
11, 12, 13, 14, 15, 17, 18, 19, 21, 22, 23; 

Section 11.4: #1, 2, 3, 4,
6, 7, 13, 14, 16, 17; 

Review Problems for Chapter
11: #2 (page 705). 
January 12: 
Homework problems for
Sections 11.111.2: 

Section 11.1: #1, 8, 9; 

Section 11.2: #1, 2, 3, 5,
9, 10, 12. 
January 04: 
Please click here to see your December Exam grade. 

HAVE A NICE WINTER! 
December 09: 
According to your requests, I am making available solutions to the selected 

problems from Sections 13.1, 13.2, 13.4 and 13.5 of the textbook. 
December 05: 
As it was promised in the class yesterday, I am making
available Lecture 

Notes on
Simulation. 
December 04: 
As it was announced earlier, we will write the Midterm Examination on 

Wednesday, December 10 from 19:00 to 22:00 in TEL 1005. The exam 

will be comprehensive, covering all the
material covered in class according 

to the Course
Schedule but with some emphasis on
the more resent material 

that we have covered after
the midterm test. Please note that there
will be 

several questions on the exam,
some with few parts. Marks for
each question 

will be indicated.
You have to show all your work to justify your answers 

and should explain your solutions where
appropriate. 
November 30: 
As it was asked in the
class on Thursday, I am making available solutions


to the Homework Problems on
Cooperative nPerson Games. 
November 28: 
Homework problems for
Sections 13.413.5: 

Section 13.4: #1, 2, 3, 9,
12, 14; 

Section 13.5: #1, 2, 3, 4,
9. 

Also, solve problem #2 and problem
#5 from page 799 of the textbook. 
November 19: 
As it was promised in the
last class, I am making available Additional 

Notes on Decision Making. 
November 15: 
Extra homework problem for
Section 14.7: 

Prove that the vector of
Shapley values vector is always an imputation. 

Homework problems for
Sections 13.113.2: 

Section 13.1: #1, 4; 

Section 13.2: #1, 2, 3, 7,
10, 13, 16. 
November 05: 
Please note that the graded
Midterm Test papers will be
returned in 

the class tomorrow. 

I am making available Notes by Prof. Neal Madras on “Definitions for 

Cooperative nPerson Game Theory”. Also, an interesting article about 

game theory: The Arithmetics of Mutual Help by M.A. Nowak, R.M. May 

and K. Sigmund (Scientific American, June 1995). (Not
required for exam.) 
October 21: 
According to your requests,
I am making available solutions to the


selected problems from Sections
14.2 and 14.3 of the textbook. 
October 18: 
As it was announced in the
class on Thursday, we will write Midterm
Test #1 

during the lecture period from 19:00 to 20:20 on
Thursday, October 23. 

On the test you will be responsible for all the material covered in class 

from Sections 14.1, 14.2, 14.3 and 14.4 of the
textbook. 

Homework problems for
Sections 14.514.7: 

Section 14.7: #1, 2, 3, 7,
8, 10, 11; 

Please note that in the answer
for Problem #11 the vector of Shapley values 

(in
thousands of dollars) is: (305/3, 335/3, 266/3). 

Review Problems for Chapter
14: #6. 
October 14: 
Please note that you may download free trial versions of LINDO and 

LINGO packages at the following URLs, respectively: 

http://www.lindo.com/index.php?option=com_content&view=article&id=1&Itemid=9 

http://www.lindo.com/index.php?option=com_content&view=article&id=2&Itemid=10 

Please be sure to download and use the Classic LINDO
package. 
October 06: 
Please check the web site
below for funding and awards: 

http://gradstudies.yorku.ca/currentstudents/studentfinances/fundingawards/ 

Also, I am making available
the URL for the newly created Facebook page of 

the Department of
Mathematics and Statistics: 


October 04: 
Homework problems for
Section 14.314.4: 

Section 14.3: #1(a), (b), (c), (d); 2; 3; 4; 5(a),(b); 

Section 14.4: #1, 2, 3, 5. 
September 23: 
Please make note that we are going to have an information session on York's 

Actuarial Science program on Thursday, September 25 at
4:00 PM in CLH D. 

Also, right after the session (at 5:00 PM) a group of
upper administration from 

Sun Life Financial will speak about the profession, the
hiring process in general 

as well as about the set of skills Sun Life is
seeking when recruiting. The students 

will have a rare opportunity to address their questions
directly to professional 

actuaries that are involved in hiring. Beverages and
snacks are to be provided. 
September 21: 
Homework problems for
Section 14.2: 

# 1, 3, 4, 5, 6; 9, 10, 11. 
September 14: 
Homework problems for
Section 14.1: 

# 1, 2, 3, 4. 

As it was asked in the
class, please also show that a TwoPerson ZeroSum 

Game, with a payoff matrix
of 3x3 cannot have exactly five saddle points. 
September 11: 
Welcome! 
To view and/or print
PDF files you need to download the Acrobat Reader 
Course: 
Term
and Session: 
Fall/Winter
20142015 
MATH
4170 
Section: 
A 

Lectures: 
Thursday
19:0021:50, BC 215 
Instructor: 
Name: 
Dr.
Iulduz Raguimov 

Office: 
S512
Ross 

Phone: 
4167362100,
Ext. 66092 or 4167365250 

Office
Hours: 
MF
12:0013:00 and T 16:0017:00, also by appointment 

Email: 

Grading: 
Two
midterm tests: 
20%
each 

Two
endofterm exams: 
30%
each 
Course Description: This course is integrated with the graduate courses GS/MATH 6900 3.00 F “Operations Research I” and GS/MATH 6901 3.00 W “Operations Research II”. The course deals with deterministic and probabilistic models based on optimization. The following topics will be discussed: 1) game theory (how to find the best strategies in a confrontation between two or more players with differing interests); 2) decision theory (how to act to minimize loss, subject to available data); 3) simulation (how to sample from a probability distribution and how to conduct statistical experiments by computer); 4) queueing theory (how to assess what may happen in a system where the customers arrive randomly, wait in line, and then get served); 5) nonlinear programming (how to optimize a nonlinear objective function subject to equality or inequality constraints). Time permitting, some additional topics (such as inventory theory or reliability) will also be discussed. For a more detailed list of topics with references to the textbook, please see Course Schedule.
Textbook: 
Operations Research: Applications and Algorithms, Fourth Edition 
by
Wayne L. Winston 


Books/Cole, Thomson, 2004. ISBN
0534423582 
Optional
aid: 
Student Solutions Manual for
Operations Research, Fourth Edition 

by Wayne L. Winston 

Books/Cole, Thomson, 2004. ISBN
0534423604 
Suggested
supplementary 
(a)
Nonlinear
Programming: Theory and Algorithms, Third
Edition 
reading
for graduate students: 
by
Mokhtar S. Bazarra, Hanif D. Sherali, and
C.M. Shetty 

John Wiley & Sons, 2006; 

(b) Probabilistic Models in Operations Research, by S. Guiasu 

Nova
Science Publishers, Inc., New York, 2009; 

(c) Operations Research. An Introduction, Ninth Edition 

by Hamdy A. Taha 

Pearson Education, Inc., New
Jersey, 2011; 

(d)
Introduction to Operations Research,
by F.S. Hillier and G.J. Lieberman 

(HoldenDay); 

(e)
Nonantagonistic Games, by Yu. B.
Germeier 

D.
Reidel Publishing Company, Boston, 1986. 


Course
Prerequisites: 
Multivariable
Calculus (SC/MATH 2010 3.00 or SC/MATH 2015 3.00 

or
MATH 2310 3.00), Elementary Probability (SC/MATH 2030 3.00) and 

Operations
Research I (SC/MATH 3170 6.00). 
Course
Credit 
AS/MATH
4570 6.00. 
Exclusion: 

Important
Dates: 
September
08: Classes
commence. 
September
22: The
last date to enrol in the course without my permission. 

October
14: The
last date to enrol in the course with my permission. 


October
29November 02:
CoCurricular Days (no classes). 
December
05: Fall
classes end. 


January
05: Classes
resume. 

February
06: The
last date to drop the course without receiving a final grade. 
February
1420: Reading
Week (no classes). 


April
17: Classes
end. 
April
19May 03: Examination
period. 
(tentative, subject to any changes announced in class)
Thursdays: 
Sections: 
Events: 
Sept 11 
Introduction, 14.1 
Classes
begin on Thursday, September 11. 
Sept 18 
14.114.2 
September
22 is the last day to enrol without my permission. 
Sept 25 
14.214.3 

Oct 02 
14.3 

Oct 09 
14.4 

Oct 16 
14.514.6 

Oct 23 
Test #1, 14.7 
Test
#1 will take place on Thursday, October 23. 
Oct 30 
No classes 
CoCurricular
Days. 
Nov 06 
13.1 

Nov 13 
13.2 

Nov 20 
13.413.5 

Nov 27 
21.121.3 

Dec 04 
21.4, 21.5, Review 
Fall
classes end on Friday, December 05. 
Dec 05 
Fall classes end 
Last
day to submit fall term work. 
Dec 0922 
Fall Term Exam 
TBA. 
Jan 08 
11.1, 11.2 
Winter
classes begin on Monday, January 05. 
Jan 15 
11.2, 11.3 

Jan 22 
11.4, 11.5 

Jan 29 
11.6 

Feb 05 
11.7 

Feb 12 
11.8 

Feb 19 
No classes 
Reading
Week. 
Feb 26 
11.9 

March 05, … 


March 26 
Test #2, 11.10 
Test
#2 will take place on Thursday, March 26. 
April 02 
11.10, 11.11 

April 09 
11.12, 11.13 

April 16 
20.1, 20.2, 20.3, Review 

April 17 
Classes end 

Apr 1928 
Winter Term Exam 
TBA. 
Note: The course will not cover all the sections of each chapter from the Fourth Edition of the textbook.
Throughout the term, practice exercises will be posted to the Announcements section. In order to develop your understanding of the course material you must do all assigned problems. These will not be collected for grading and hence will not directly affect your grade. However, it is extremely important that you complete all assigned exercises. Do not memorize them. Rather, learn how to solve problems like them. Learning Mathematics is not a spectacular sport, it is a participatory event. There is nothing like a bit of computation to strengthen understanding in mathematics! Use the Solutions Manual only after you have tried the problem. Successful students must keep up with homework and seek help for points they do not understand as soon as possible. Do not fall behind! It is recommended to read the relevant sections of the textbook before every class. Next to the classes, working out the answers to the problems is the most important preparation for the tests and exam that will contain for the most part but not exclusively, questions very similar to those from the textbook. It is quite practical to work on your own or together in small groups. Each student should do at least three hours of independent study for every lecture hour. The amount you learn in this course and the grade you receive will be proportional to the amount of time you spend working on problems.
All internet connected and other
distractive electronic devices (cell phones, pagers, head phones, digital
dictionaries, CD players, laptops) need to be turned off during class, i.e.
during lectures, tutorials, tests and exams. All such devices as well as all
books, papers, knapsacks, and briefcases must be left at the front of a lecture
hall during tests and exams. Anyone caught with electronic devices will be
charged with Academic Dishonesty (see the next page). The only items you may
have at your seat during exams and tests are pens, pencils, eraser, calculator,
student ID and purses. Notes need to be taken manually; use of cellphone
cameras in class is not allowed. You are responsible for all material covered
in lectures.
Note: Photo identification and signingin are required at all
tests and exams.
The official grades at York
University are LETTER grades. Qualitative descriptions of these grades can be
found in the York Calendar at this link. Your test marks
will be on a numerical scale because these have to be weighted and averaged in
various ways, but THERE IS NO AUTOMATIC PREDETERMINED CORRELATION
BETWEEN NUMERICAL GRADES AND LETTER GRADES in this course. In particular, the
"numerical" grades you receive are NOT to be interpreted as
percentages; they are merely 'raw scores'. When the tests are returned in class, the distribution of 'raw scores' will be announced along
with an approximate conversion to letter grades. The median letter grade for
the course will likely fall between C and C+.
The composition of the final grade is as follows:
Two Tests (80 minutes each written tests held in lecture periods):
20% each (Tentative dates for the tests: Thursday, October 23, 2014 and
Thursday, March 26, 2015);
Final Examination Fall Term (threehour exam scheduled by the Registar's
Office): 30% of the overall grade, will take place in December 2014, during
the examination period;
Final Examination Winter Term (threehour exam scheduled by the Registar's Office): 30% of the overall grade, will take
place in April 2015, during the examination period.
Note: Students have five days from the date of the return of test
papers to appeal their marks. Some test papers (randomly selected) are
photocopied before they are handed back, so we can detect subsequent
alterations.
Makeup Policy:
No permission will be given to a student to write tests in
advance of their scheduled dates. No makeup will be done for the tests. A
missed test will be counted as zero, except under extreme circumstances in
which case the corresponding percentage of the overall grade will be
"forwarded" to the final exam. If you miss a test for medical
reasons, you must turn in within one week following the test date the Attending
Physician's Statement form provided here
after getting it filled in by your doctor. No other type of medical note
will be accepted. However, missing tests is extremely dangerous and not
recommended. As experience has shown, students who miss class tests because
of some 'mysterious illnesses' will usually average 30% on the final exam.
Student who misses the final examination will be allowed to write a makeup
exam only if both of the following conditions are met:
1) the student notifies me (raguimov@mathstat.yorku.ca)
or the Department of Mathematics and Statistics (Undergraduate Office, N502/503
Ross Building, 4167362100, Ext. 55902 or 33969) in advance that the
exam will be missed;
2) the student submits within
one week following the exam date the Attending Physician's Statement form
provided here
after getting it filled in by his/her doctor.
Students who miss the final examination and do not meet both conditions will
receive a grade of F. It is student's responsibility to fill out and submit the
Deferred Standing
Agreement form.
Note: Do not make vacation/job plan until the final exam date is
known: having a plane ticket for Banff or Hawaii on December 18 is NOT a
legitimate excuse for absence from a final exam on December 22.
Religious Observance and Accessibility:
York University is committed to respecting the religious beliefs and practices of all members of the community and making accommodations for observances of special significance to adherents. If any of the dates specified in the course schedule for inclass tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) within the first weeks of classes. Please note that if the final exam date poses a conflict, students must complete the Final Exam Accommodation form, which can be obtained from the Registrar’s Office. Please note that York University welcomes feedback on accessibility issues. Your feedback may be provided by sending email to: mathstat@yorku.ca
Academic Honesty:
Students are responsible for familiarizing themselves with University Policies and Regulations. Conduct that violates the ethical or legal standards of the university community or of one’s programme or specialization may result in serious consequences. Refer to the Senate Policy on Academic Honesty. Photo identification and signingin are required at all tests and exams. Also, some test papers (randomly selected) will be photocopied before they are returned so that subsequent alterations can be detected.
Individual questions can be discussed by email or in person after class, or during office hours. Please send all email notes as plain text within the body of the message. Do not send attachments or HTMLformatted email. No texting, please. Also, if the name of your account is an alias, I will not know who the mail is from unless you sign it; it also risks being accidentally discarded as junk mail. The course web page will be updated regularly to include important announcements made in class, such as the material to be covered on the tests. Email notes requesting such information contained on the web page will be answered the last.
Questions and comments regarding this web page please send to raguimov@mathstat.yorku.ca
© 20042015, All Rights Reserved, York University & Iouldouz S. Raguimov
Last updated April 17, 2015