ENG MGT 5414 – Introduction to Operations Research
Fall 2024 Schedule
The textbook adopted is: Vanderbei, Robert J. Linear Programming: Foundations and Extensions. Vol. 285. Springer Nature, 2020.
| Lecture | Day | Topics | Readings (bold) Suggested Problems (in italic) |
|
| Textbook (Chapter or Chapter. Section) |
Notes (Section) | |||
| 1 | Aug 20th | – Syllabus – Discussion of course expectations – Motivational introduction to Linear Programming |
– | 1 and 2 |
| 2 | Aug 22nd | – Linear Programming problems – Graphical solution |
1 and 2.5 1.1, 1.2, 2.2 (solve graphically), 2.5 (solve graphically) |
2 and 3 2, 15 |
| 3 | Aug 27th | – Introduction to the Simplex Method | 2.1 and 2.2 | 2 |
| 4 | Aug 29th | – Initialization of the Simplex Method – Unbounded problems |
2.3 and 2.4 2.7 (solve via Phase I/Phase II) |
6 6, 7 ,8 and 9 |
| 5 | Sept 3rd | – Degeneracy – |
3.1 – 3.3 | – |
| 6 | Sept 5th | – Bland’s Rule – Fundamental Theorem of Linear Programming – Geometry of degeneracy |
3.4 – 3.6 3.2 |
6 16, 17 |
| 7 | Sept 10th | – The Simplex Method in vector-matrix form | 6.1 – 6.3 Solve using the vector-matrix form: – Geppetto’s Problem – Portfolio Problem |
8 and 9 20 and 21 |
| 8 | Sept 12th | |||
| 9 | Sept 17th | Buffer session | ||
| Exam 1 | Sept 18th (Wednesday) | Lectures 1 – 9 | ||
| 10 | Sept 24th |
In-class solution of Exam 1 |
||
| 11 | Sept 26th | |||
| 12 | Oct 1st | – Motivational Introduction to Duality – Geppetto’s and Capybara Diet Problems | ||
| 13 | Oct 8th | – Introduction to Duality Theory – Weak Duality Theory |
5.1 – 5.3 5.6 (don’t solve it, write the dual only) |
10 25, 26, 27 and 28 |
| Oct 10th | No lecture (Fall Break) |
|||
| 14 | Oct 15th | – Strong Duality Theory – Complementary Slackness Conditions (CSC) |
5.4 and 5.5 5.3, 5.4 |
10 30 |
| 15 | Oct 17th |
– Dual of Linear Programs in general form |
5.8 5.1 |
10 29 |
| Oct 22nd | No lecture (Dr. Nicolosi at INFORMS Conference) | |||
| 16 | Oct 24th |
– The Dual Simplex Method |
5.6 and 5.7 |
|
| 17 | Oct 29th | – Economical interpretation of the Dual |
5.9 |
10 28 |
| 19 | Oct 31st | – – |
6.4 and 6.5 | – |
| 20 | Nov 5th | – Sensitivity Analysis | 7.1 (but preferably notes from blackboard) 7.1.(c) |
– |
| 21 | Nov 7th | Buffer session | ||
| 22 | Nov 12th | Buffer session |
||
| Exam 2 | Nov 13th | Lectures 10 – 21 | ||
| 23 | In-class solution of Exam 2 | |||
| 24 | – Introduction to Network Flow Problems – Networks and Graphs – Spanning Trees and Bases |
14.1 – 14.2 | – | |
| 25 | – The Primal Network Simplex Method | 14.3 | – | |
| 26 | – The Dual Network Simplex Method | 14.4 | – | |
| 27 | – The Transportation Problem – The Assignment Problem |
15.1 and 15.2 | – | |
| 28 | – The Shortest-Path Problem – Dijkstra’s Algorithm |
15.3 | – | |
| 29 | Buffer session | |||
| 30 | Nov 26th | No lectures (Thanksgiving) | ||
| 31 | Nov 28th | |||
| 32 | – Introduction to Integer Programming – Travelling Salesman Problem |
23.1 and 23.2 | – | |
| 33 | – Branch-and-Bound – Gomory Cuts |
23.5 and 23.6 | – | |
| Final Exam |
Week of Dec 9th |
Comprehensive | ||
Previous Exams
Below you can find past exams. These are for purposes of studying only, and students should not expect them to be reapplied in the future. Students are also responsible for checking what topics are going to be covered in each future exam and should understand that, from semester to semester, topics, exam duration/format and class schedules all change. For instance, in 2023 I covered Dynamic Programming, which is not included in the Fall 2024 schedule. Aspects that students can expect to be similar are the style and difficulty levels of the questions. I hope that these exams will help students prepare for their actual exams and assess their understanding of the course topics throughout the semester.