Welcome to the Course Page of
AS/SC/AK/MATH  3170 6.0 A
Operations Research I

2006-2007 Full Year

Department of Mathematics and Statistics
York University
4700 Keele Street
Toronto, Ontario  M3J 1P3

Course Organization:

Course Information
Course Schedule
Exams  Information
Links & Other Resources


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.
May 03: Please click  here  to see  your final exam mark and unofficial letter grade
  for the course. Also, please note that your official grade will be sent to you
  by the Registrar's Office upon the approval by the Senate.
April 05: As it was announced earlier, the Final Examination will take place on
  Thursday, April 12 from 9:00 A.M. to 12:00 P.M. in ACE  004.
  The exam will be comprehensive, covering the entire year's work
  according to the  Course Schedule, but with an emphasis on more recent
  material from the second term. Please note that there will be NO questions
  on the material covered in class from Chapter 18 of the text-book.
April 04: Please click to check your grades for the term-tests. If you find any discrepancy,
  please send me an e-mail and see me before the final examination with your
  test papers.
April 02: Assignment #10 questions (not to be handed in, for practice only):
  Chapter 8: Review Problem #4.
  Chapter 9: Section 9.2 #12, #20, #21, #23 and #25; Section 9.3 #2,  #7
  and #9; Section 9.4 #1 and #3.
  Please click to view  solutions  to Assignment #10 questions.
March 29: Please note that Assignment #9 papers were returned at the end of the class
  today, Test #3 papers will be returned in the review class on Tuesday,
  April 03.
March 20: I am making available  solutions  to Assignment #9.
March 15: Please note that we will write Test #3 during the lecture period on Thursday,
  March 22. On the test you will be responsible for all the material covered in class
  from Sections 7.1-7.3, 7.5, 7.6, 8.1-8.3, 8.4 (CPM only) and 8.6 of the text-book.
March 12: Please note that Assignment #8 papers will be returned at the end of the class
  on Tuesday, March 13.
March 11: As it was announced in the class on Thursday, I am posting Assignment #9
  questions (Due Tuesday, March 19 in class):
  Chapter 8: Section 8.2 #2, #4 and #9, Section 8.3 #2,  #4 and #16,
  Section 8.4 #2,  #5, #14 and #15, Section 8.6 #2.
March 05: Please note that the exam schedule has been published to the Registrar's web site.
  The course web page has been updated to show exam date, time and venue.
  However, it is your responsibility to check with official York web site in case
  of last minute changes.
March 03: I am making available  solutions  to Assignment #8.
February 06: Assignment #8 (Due Tuesday, February 20 in class):
  Chapter 7: Section 7.1 #1 and #5, Section 7.2 #1 (for 7.1 #1 only) and
  #3 (for 7.1 #5 only), Section 7.3  (for 7.1 #1 and #5 only), Section 7.5 #1
  and #6, Section 7.6 #3, Review Problem #5.
January 29: Please note that Test #2 and Assignment #7 papers will be returned in the class
  on Tuesday, January 30.
January 16: I am making available  solutions  to Assignment #7.
January 12: We will write Test #2 during the lecture period on Thursday, January 18.
  On the test you will be responsible for all the material covered in class from
  Sections 4.2-4.12, 4.14, 4.16, 4.17, 5.1 and 5.2 of the text-book.
  Please note that since January 23 is Religious Observance Day (Basant
  Panchami), we cannot move the test date to that date.
  Please also note Tutorials for Winter term will begin on Tuesday, January 16.
  Tutorial Leader for this term is Ka-Ho Lee, time: 11:30-12:20 P.M., room: N501 R.
  Further tutorial sessions will be held on the following dates: January 30, February 6
  and 27, March 6, 13, 27 and April 3 (the dates are subject to any changes
  announced in class).
January 09: I am making available  solutions  to Assignment #6.
  Assignment #7 (Due Tuesday, January 16 in class):
  Chapter 5: Section 5.1 #2 and #5(*), Section 5.2 #4 and #6.
  (*) For 5.1 #5, each Radio 2 requires 1 (not 2) hour of Laborer 2.
January 02: Please note that Assignment #5 papers will be returned at the end of the class
  on Thursday, January 04.
December 06: Assignment #6 (Due Thursday, January 04 in class):
  Chapter 4: Section 4.10 #4, Section 4.14 #4, Section 4.16 #6 and #7,
  Section 4.17 #4, Review Problem #19.
November 28: I am making available  solutions  to Assignment #5.
November 23: Please note that graded Assignment #4 papers were returned in the class today.
November 19: Assignment #5 (Due Tuesday, November 28 in class):
  Chapter 4: Section 4.8 #4 and #6, Section 4.11 #2 and #4, Section 4.12 #2 and #5.
November 15: I am making available  solutions  to Assignment #4.
November 07: Assignment #4 (Due Tuesday, November 14 in class):
  Chapter 4: Section 4.5 #3 and #5, Section 4.6 #1 and #4,
  Section 4.7 #2 and #9.
  Please also note that Assignment #3 papers will be returned at the end
  of the class on Thursday, November 09.
November 06: Please note that Test #1 papers will be returned in the class on Tuesday,
  November 07.  I am making available  solutions  to the test questions.
November 03: I am making available  solutions  to Assignment #3.
October 26: Assignment #3 (Due Thursday, November 02, in class):
  Chapter 4: Section 4.1 #1, Section 4.4 #1, #4 and #7.
October 19: We will write Test #1 during the lecture period on Thursday, October 26.
  On the test you will be responsible for all the material covered in class from
  Sections 1.1-1.5, 3.1-3.6, 3.8-3.11 and 4.1-4.2 of the text-book.
October 18: Please note that Assignment #2 papers will be returned at the end of the class on
  Tuesday, October 24. I am making available  solutions  to the assignment questions.
October 10: Please note that Assignment #1 papers will be returned at the end of the class on
  Thursday, October 12. Also, please note that office hour for Friday, October 13
  has been cancelled.
October 09: Assignment #2 (Due Tuesday, October 17, in class):
  Chapter 3: Section 3.6 #4, Section 3.7 #1, Section 3.8 #10,
  Section 3.9 #12, Section 3.10 #9, Section 3.11 #9.
  Hints: For 3.6.4, cash not used in Year 1 cannot be used in Year 2.
  For 3.9.12, due to the way the products are obtained as outputs of different
  processes, not all the product produced must/can be sold.
  For 3.10.9, since there is an inventory cost, some workers may not produce
  exactly 500 mixers.
  For 3.11.9, assume each debt has a 6-month term (i.e. debt plus interest must
  be repaid in cash in exactly 6 months).
  Please note that Tutorials for the course will begin on Wednesday, October 10.
  Tutorials Leader for Fall term is Jian Li, room: N501 Ross, time: 2:30-3:30 P.M.
  There will be eight tutorials in Fall term and eight tutorials in Winter term.
October 04: I am making available  solutions  to Assignment #1.
  Please note that the software manuals for LINDO you may find on 2-hour reserve at
  the desk in Steacie library. You may find there also the software manuals for EXCEL
  but you should rarely need these because EXCEL itself has substantial on-line help files.
  To access these files, you will require a personal "ACADLABS" account; to obtain such
  an account, follow the instructions available at the Computing Commons or at this
  website, ACADLABS accounts.
September 25: Assignment #1 (Due Tuesday, October 03, in class):
  Chapter 3: Section 3.1 #3, Section 3.2 #4 and #6, Section 3.3 #3 and #9,
  Section 3.4 #3, Section 3.5 #6.
 September 09: Welcome back!
  To view and/or print  PDF  files you need to download the Acrobat Reader 

Course Information

Course: Session: 2006-2007 Full Year
  Section: A
  Lectures: T/R 10:00 - 11:20 A.M., SLH A
Instructor: Name: Dr. Iulduz Raguimov
  Office: S512 Ross
  E-mail: raguimov@mathstat.yorku.ca
  Phone: 416-736-2100, Ext. 66092
  Office Hours: T 12:00-12:30, 1:30-2:00pm, R 12:00-1:30pm and F 3:30-4:00pm
TA's   Jian Li, Ka-Ho Lee
  Tutorials: T 11:30-12:20 P.M., N501 Ross
Grading: Between 10 and 12 Assignments 20%
  Three-Class Tests  15% each
  Final Examination 35%

Course Description:  An introductory course in Operations Research. The course deals with standard optimization techniques used in Operations Research. The main topics include: a) Linear Programming: the theory and applications of linear programming including the simplex algorithm, duality theorem, postoptimality analysis, and a discussion of the types of problems that lead to linear programming problems; b) Transportation Problems: the transportation algorithm with applications to network flows, assignment problems, shortest-route problems, and critical path scheduling; c) Integer Programming: a study of the situations leading to integer-programming problems, branch-and-bound algorithm for solving such problems; d) Dynamic Programming: an introduction to the concepts of dynamic programming with a discussion of typical problems and their solutions. The emphasis will be on practical problems representative of the field of operations research. With the help of notes and class instructions students will be introduced to the optimization solver software LINDO/LINGO and the spreadsheet. For a more detailed list of topics with references to the text-book, please see Course Schedule.


Operations Research: Applications and Algorithms, Fourth Edition

by Wayne L. Winston 
  Books/Cole, Thomson, 2004. ISBN 0-354-38058-1
Optional Aids: Student Solutions Manual for Operations Research, Fourth Edition
  by Wayne L. Winston
  Books/Cole, Thomson, 2004. ISBN 0-354-42360-4
Course Prerequisites: AS/SC/AK/MATH 1021 3.0 or AS/SC/MATH 1025 3.0 or AS/SC/MATH 2021 3.0
  or AS/SC/AK/MATH 2221 3.0, plus AK/AS/SC/CSE/COSC 1520 3.0 or
  AK/AS/SC/CSE/COSC 1540 3.0 or AK/AS/SC/CSE/COSC 1020 3.0 or 
  equivalent. Students who do not have the prerequisites must see me within the
  first two weeks of the classes.
Course Credit AK/MATH 2751 3.0, AK/MATH 3490 6.0, AK/ADMS 3351 3.0,
Exclusions: AK/SCE/COSC 3450 6.0, AK/ECON 3120 3.0.
Important Dates: September 07: Classes commence.
September 21: The last date to enrol in the course without my permission.
October 20: The last date to enrol in the course with my permission.
  December 04: Fall classes end.
  January 03: Classes resume.
February 02: The last date to drop the course without receiving a final grade.
  February 12-16: Reading Week.
  April 03: Classes end.
April 11-30: Examination period.

Course Schedule

(subject to any changes announced in class)




September 7-8 Introduction, 1.1 Classes begin Wednesday, September 07. 
September 11-15 1.2-1.5, 3.1-3.2  
September 18-22 3.3-3.5  
September 25-29  3.6, 3.8  
October 2-6  3.9-3.10  
October 9-13  3.11, 4.1-4.2  
October 16-20  4.2-4.4  
October 23-27  4.5, Test #1 Test #1 will take place on Thursday, October 26.
Oct 30 - Nov 3 4.6-4.7  
November 6-10 4.8-4.9  
November 13-17 4.10-4.11  
November 20-24 4.12, 4.14  
Nov 27 - Dec 1  4.16, 4.17 Fall classes end Thursday, November 30.
January 3-5 5.1, 5.2 Classes resume on Thursday, January 4. 
January 8-12 7.1, 7.2  
January 15-19 7.3, Test #2 Test #2 will take place on Thursday, January 18.
January 22-26 7.5, 7.6  
Jan 29 - Feb 2 8.1, 8.2  
February 5-9 8.3, 8.4  
February 12-16 No classes Reading week.
February 19-23 8.6, 9.1  
Feb 26 - Mar 2 9.2, 9.3  
March 5-9 9.3, 9.4  
March 12-16 9.4, 18.1  
March 19-23 18.1, Test #3 Test #3 will take place on Thursday, March 22.
March 26-30 18.2, 18.3  
April 3 Review The classes end Tuesday, April 3.
April 11-30 Final Examination Thursday, April 12, 2007 9:00-12:00pm. in ACE 004.

Note: The course will not cover all the sections of the text-book.


There are between 10 and 12 bi-weekly assignments each of which will be posted to the Announcements Section of the course web page more than one week before a due date. Each assignment consists of 6 to 7 questions, of which only a selection of questions will be graded. No late assignments will normally be accepted, but I will drop everybody's worst assignment mark. Assignments must be individual work: plagiarism is a serious academic offence and leads to severe consequences. Refer to the Senate Policy on  Academic Honesty. Assignment solutions are posted to the course web page after the assignments are due. It is extremely important that you complete as many problems as possible. There is nothing like a bit of computation to strengthen understanding in mathematics! 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 text-book before every class. Next to the classes, working out the answers to the end-of-chapter 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 text-book. 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.

Exams Information

Lecture/Exam Rules:

Please turn off all cell phones and pagers before entering the lecture hall. For tests and exam cell phones, digital dictionaries, palms, pagers or other electronic devices are not allowed. All such devices as well as all books, papers, knapsacks, and briefcases must be left at the front of the lecture hall. Anyone caught with electronic devices will be charged with Academic Dishonesty (see the next page). The only items you may have at your seat are pens, pencils, student ID, a non-graphing, non-programmable calculator and purses.
You are responsible for all material covered in lectures.
Note: Photo identification and signing-in are required at all
tests and exam.

Final Grade:

The composition of the final grade is as follows:
Between 10 and 12 bi-weekly assignments: 20% of the overall grade.
Three Class-Tests (75 minutes each written tests held in lecture periods):  15% each (Tentative dates for the tests: Thursday, October 26 of 2006; Thursday, January 18 and Thursday, March 15 of 2007).
Final Examination
(3-hour exam scheduled by the Registar's Office):  35% of the overall grade, will take place on Thursday, April 12 of 2007 from 9:00 A.M. to 12:00 P.M. in ACE 004.
All test marks you receive should be interpreted as raw scores and not "percentages". The statistics of scores will be announced for all tests. Students have seven days from the date of the return of a test paper to appeal their marks. Cut-off for converting midterm scores into letter grades will be announced prior to the drop date.

Make-up Policy:

No permission will be given to a student to write tests in advance of their scheduled dates. No make-ups will be done for the class-tests. Missed tests 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 class-test  for medical reasons you must turn in  within one week following the test a copy of the medical report 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. A student who misses the final examination will be allowed to write a make-up 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, 416-736-2100, Ext. 55902 or 33969) in advance that the exam will be missed,
2) the student submits a copy of the medical report form provided  here after getting it filled in by his/her doctor within one week following the exam.
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 Hawaii or Las Vegas on
April 20 is NOT a legitimate excuse for absence from a final exam on April 25.

Religious Observance:

 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 in-class tests pose such a conflict, students should contact me (raguimov@mathstat.yorku.ca) within the first two 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 Registrarís Office

Academic Honesty:

Conduct that violates the ethical or legal standards of the university community or of oneís programme or specialization may result in serious consequences. Refer to the Senate Policy on  Academic Honesty.


Individual questions can be discussed by e-mail, or in person after class, or during office hours. Please send all e-mail notes as plain text within the body of the message. Do not send attachments nor HTML-formatted mail. 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 up-dated regularly to include important announcements made in class, such as the material to be covered on the tests. E-mail notes requesting such information contained on the web page will be answered the last.

Links and Other Resources

1-  York Undergraduate Math Program

Questions and comments regarding this Web page please send to raguimov@mathstat.yorku.ca

© 2006, All Rights Reserved, York University & Iouldouz S. Raguimov

Last modified  May 03, 2007