Welcome to the Course Page of
MATH  3170 6.00 A

Operations Research I

SU 2011

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 the tests and assignments. 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.
August 20: 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.
July 29: I am making available  solutions  to Assignment #6 questions.
  As it was announced in the class on Wednesday, the Final Examination
  will take place on Tuesday, August 02 from 19:00 to 22:00 in CLH J.
  The exam will be comprehensive, covering the entire course material
  according to the Course Schedule, but with an emphasis on more recent
  material covered on the second half of the course. Unofficial final grades for
  the course will (hopefully) be posted to the course web page by August 20.
July 22: Assignment #6 (Due on Thursday, July 28, 16:00):
  Section 8.4 #2,  #5, #14 and #15, Chapter 8 Review Problem #4,
  Section 9.2 #12, #20, #21, #23 and #25; Section 9.3 #2,  #7 and #9;
  Section 9.4 #1 and #3.
July 20: Please note that the graded Test #2 papers will hopefully be returned in the
  class on Wednesday, July 27. I am making avaialable  the scanned copy of
  solutions  to the test questions.
July 17: I am making available  solutions  to Assignment #5 questions.
July 14: As it was announced in the class yesterday, we will write Test #2 during the
  lecture period from 18:00 to 19:15 on Monday, July 18. On the test you will
  be responsible for all the material covered in class from Sections 4.6-4.12,
  4.14, 4.16, 5.1-5.2, 7.1-7.3, 7.5-7.6 and 8.1-8.3 of the textbook.
  Assignment #5 (will not be collected for grading):
  Section 7.1 #1 and #5, Section 7.2 #1 (for 7.1 Problem 1 only) and
  #3 (for 7.1 Problem 5 only), Section 7.3  (for 7.1 Problems 1 and 5 only),
  Section 7.5 #1 and #6, Section 7.6 #3, Chapter 7 Review Problem #5,
  Section 8.2 #2, #4 and #9, Section 8.3 #2,  #4 and #16.
July 12: Please note that Course Evaluations are available on-line at the URL link
  http://courseevaluations.yorku.ca  until Friday, July 29. It is the time for you
  to be the judge. Please go on-line and complete the course evaluation.
July 11: I am making available  solutions  to Assignment #4 questions. Please note that
  the graded Assignment papers will be returned in the class on Monday, July 18.
June 29: As it was announced in the class yesterday, Monday class for July 4th
  has been cancelled.
June 24: Assignment #4 (Due on Wednesday, July 06, in the class):
  Section 4.11 #2 and #4, Section 4.12 #2 and #5, Section 4.14 #4,
  Section 4.16 #6 and #7, Review Problem #19, Section 5.1 #2 and #5(*),
  Section 5.2 #4 and #6.
  (*) For 5.1 #5, each Radio 2 requires 1 (not 2) Laborer-2 hour.
June 17: I am making available  solutions  to Assignment #3 questions. Also, please note
  that Monday, June 20 is the last day to appeal your grade for Test #1.
June 15: As it was announced in the class on Monday, there will be MAKE UP CLASS
  on Friday, June 24 from 11:30 to 14:30 in CB 129.
June 10: Please note that the graded Test #1 papers will hopefully be returned in the class
  on Wednesday, June 15. I am making avaialable  solutions  to the test questions
  and the scanned copy of  page 3  of the test paper in PDF format.
June 09: Assignment #3 (will not be collected for grading):
  Section 4.5 #3 and #5, Section 4.6 #1 and #4, Section 4.7 #2 and #9,
  Section 4.8 #4 and #6, Section 4.10 #4.
June 08: Please note that the graded Assignment #2 papers will be returned in the
  class on Wednesday, June 08.
June 01: As it was announced in the class today, we will write Test #1 during the
  lecture period from 18:00 to 19:15 on Monday, June 06. 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 4.1-4.5 of the textbook.
  I am making available  solutions  to Assignment #2 questions.
May 26: Assignment #2 (Due on Wednesday, June 01, in the class):
  Chapter 3: Section 3.7 #1, Section 3.8 #10, Section 3.9 #12, Section 3.10
  #9, Section 3.11 #9; Chapter 4: Section 4.1 #1, Section 4.4 #1, #4 and #7.
  Hints: 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).
May 24: Please note that the graded Assignment #1 papers will be returned in the class on
  Wednesday, May 25. I am making available  solutions  to the assinment questions.
May 17: As it was announced in the class yesterday, you may download free trial versions
  of  LINDO and LINGO packages at the following URLs, respectively:
  Please be sure to download and use the Classic LINDO package.
May 16: Please note that Tutorials for the course will be done in MathLab, S525 Ross
  Building, which is open throughout the term: Monday-Thursday from 16:20
  to 17:50, also Mondays 10.30-12:00 P.M. and Thursdays 13:30-15:00.
  On Mondays and Wednesdays from 16:20 to 17:50 please approach with your
  questions to Yurong Cao, who is responsible for the course in MathLab.
  For more information on the MathLab please check the web page at:
May 09: Assignment #1 (Due on Monday, May 16, in the 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, Section 3.6 #4.
 May 02: Welcome back!
  To view and/or print  PDF  files you need to download the Acrobat Reader 

Course Information

Course: Session: SU 2011
  Section: A
  Lectures (time and venue): M/W 18:00 - 21:00, SLH A
Instructor: Name: Dr. Iulduz Raguimov
  Office: S512 Ross
  E-mail: raguimov@mathstat.yorku.ca
  Phone: 416-736-2100, Ext. 66092
  Office Hours: W 16:30-17:30
TA Name: TBA
Grading: Four Assignments: 5%
  Two Class-Tests: 25%+20%
  Final Examination: 50%

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 textbook, please see Course Schedule.


Operations Research: Applications and Algorithms, Fourth Edition

by Wayne L. Winston 
  Books/Cole, Thomson, 2004. ISBN 0-534-42358-2
Optional Aids: Student Solutions Manual for Operations Research, Fourth Edition
  by Wayne L. Winston
  Books/Cole, Thomson, 2004. ISBN 0-534-42360-4
Course Prerequisites: AP/SC/AK/MATH 1021 3.0 or AP/SC/MATH 1025 3.0 or AP/SC/MATH 2021 3.0
  or AP/SC/AK/MATH 2221 3.0, plus AP/AK/SC/CSE/COSC 1520 3.0 or
  AP/AK/SC/CSE/COSC 1540 3.0 or AP/AK/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: May 02: Classes commence
May 13: The last date to enrol in the course without my permission
May 27: The last date to enrol in the course with my permission
July 05: The last date to drop the course without receiving a final grade
  July 29: Classes end
August 02-12: Final examination, TBA.

Course Schedule

(subject to any changes announced in class)




May 2-6 Introduction, 1.1-1.5, 3.1 Classes begin on Monday, May 02. 
May 9-13 3.2-3.6  
May 16-20 3.8-3.11 Assignment #1 is due on Monday, May 16.
May 23-27  4.1-4.3 No classes on Monday, May 23.
May 30-June 3  4.4-4.7 Assignment #2 is due on Wednesday, June 01.
June 6-10  4.8-4.9, Test #1 Test #1 will take place on Monday, June 06.
June 13-17  4.10-4.12, 4.14 Assignment #3 solutions to be posted on Friday, June 17.
June 20-24  4.16, 5.1-5.2  
June 27-30 7.1-7.3  
July 4-8 7.5-7.6, 8.1 Assignment #4 is due on Wednesday, July 06.
July 11-15 8.2-8.3, 8.6  
July 18-22 8.4, 9.1, Test #2 Test #2 will take place on Monday, July 18.
July 25 -29  9.2-9.4, Review Classes end on Wednesday, July 27.
August 2-12 Final Examination TBA.

Note: The course will not cover all the sections of the textbook.


There are four bi-weekly assignments each of which will be posted to the Announcements Section of the course web page one week before a due date. Each assignment consists of six to eight questions, of which only a selection of questions will be graded. No late assignments will be accepted. 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 will be posted to the course web page after the assignments are due. 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 two 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, calculators, 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 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 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'. Once the tests are returned in class, the distribution of 'raw scores' will be announced along with their 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:
Four bi-weekly assignments: 5% of the overall grade.
Two class-tests (75 minutes each written tests held in lecture periods):  25% and 20% of the overall grade, respectively (Tentative dates for the tests: Monday, June 6 and Monday, July 18).
(3-hour exam scheduled by the Registar's Office):  50% of the overall grade, will take place during the examination period between August 02 and 12, 2011.
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. Once you have written both tests and your final exam grade is higher than your average test grade, your final exam will be counted as 55% and each test as 20% of your overall grade for the course.

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 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 term-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. 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 416-736-2100, 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 Hawaii or Las Vegas on August 5 is NOT a legitimate excuse for absence from a final examination on August 10.

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) by the end of the third week of classes. Please note that if the final exam date poses a conflict, students must complete the Examination Accommodation Form, which can be obtained from the Registrarís Office

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 oneís programme or specialization may result in serious consequences. Refer to the Senate Policy on  Academic Honesty.  Photo identification and signing-in are required at all tests and exam. 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 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
2-  Study Groups

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

© 2006-2011, All Rights Reserved, York University & Iouldouz S. Raguimov

Last updated on August 20, 2011