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ENME 741
Operations Research Models in Engineering

Approximate Schedule and Homeworks

FALL 2024

Note:
Linear algebra review will be done by the students independently of the lectures, materials to be given out

Lecture number format: module.lecture #


Module 1: Mostly devoted to linear programming problems, basic concepts, some more advanced modeling

Module 2: Nonlinear programming problems (integer linear, nonlinear programs, game theory)

 

-- Lectures are pre-recorded and available on ELMS (all of them are currently available)

 

Note: You can skip in the reading, anything that touches on:
1. Tableau method (we will use the Simplex method)
2. LINGO software (we will use GAMS)
3. Any specialized methods (e.g., Hungarian method) for solving certain classes of LPs

Weeks
Week starting
Lecture subjecct (recorded video)/class time discussion Homeworks
1
Aug. 27

Module 1 : Lecture 1.1
-Skim Chapter 1, read/skim Chapter 2 if need to review basic linear algebra,

-Read Chapter 3, 3.1-3.3, a lot of this will be convered in the first lectures, skim 3.4-3.12 for interesting LP applications (some will be covered later)

-LP, Duality, Sensitivity Analysis
[Note#1 (Basic Feasible Solutions and Vertices) & Note #2 (Dual Prices and Reduced Costs), Chapter 5 and Sections 6.1, 6.4-6.6,6.8-6.10



Homework #1 assigned
2
Sept. 3

Module 1 : Lecture 1.2
-Skim Chapter 1, read/skim Chapter 2 if need to review basic linear algebra,

-Read Chapter 3, 3.1-3.3, a lot of this will be convered in the first lectures, skim 3.4-3.12 for interesting LP applications (some will be covered later)

-LP, Duality, Sensitivity Analysis
[Note #1 & Note #2 , Chapter 5 and Sections 6.1, 6.4-6.6,6.8-6.10 ]


Homework #2 assigned, homework #1 due
3
Sept. 10

Module 1 : Lecture 1.3
-LP, Duality, Sensitivity Analysis
[Note #1 and Note #2, Chapter 5 and Sections 6.1, 6.4-6.6,6.8-6.10 ]

start of

-Network Models (General)
Sections 7.1, 7.5, 8.1-8.3, 8.5-8.6]

 


Homework #3 assigned, homework #2 due

4
Sept. 17

Module 1 : Lecture 1.4
-Network Models (General)
Sections 7.1, 7.5, 8.1-8.3, 8.5-8.6]


Homework #4 assigned, homework #3 due
5
Sept. 24

Module 1 : Lecture 1.5
-Simplex method [Chapter 4 about Simplex Method (4.1-mainly 4.1-4.8+Note #3 (Simplex Method)

 

Homework #5 assigned, homework #4 due

6 Oct. 1

Module 2 : Lecture 2.1
-Integer Programming
[9.1-9.2]]

-Note #4 (Total Unimodularity and Integer Solutions to LPs)

 

Homework #6 assigned, homework #5 due
7
Oct. 8

Module 2 : Lecture 2.2

-Integer Programming, Branch and Bound method for solving integer programs
[9.1-9.2]]

-Nonlinear Programming Fundamentals
[Chapter 11+ Sections 14.1-14.6+Gabriel et al. (2013)]

Homework #7 assigned, homework #6 due
8 Oct. 15

Module 2 : Lecture 2.3
-Nonlinear Programming Fundamentals
[Chapter 11+ Sections 14.1-14.6+Gabriel et al. (2013)]


Homework #8 assigned, homework #7 due
9
Oct. 22

Module 2 : Lecture 2.4
-Energy network problems (natural gas, power), reading provided
-Pooling problem (petroleum refinery) , reading provided
-Constrained Optimization, Karush-Kuhn-Tucker (KKT) conditions
-Introduction to Game Theory
-Market Equilibria and Optimization
-Complementarity Problems

[Sections 14.1-14.6+Gabriel et al. (2013)], natural gas and power networks with engineering considerations (Gabriel et al. Appendices + handouts)]

Nonlinear Programming Fundamentals
Introduction to Game Theory
Market Equilibria and Optimization
Complementarity Problems
Two-Level Optimization Problems
[Chapter 11+ Sections 14.1-14.6+Gabriel et al. (2013)], natural gas and power networks with engineering considerations (Gabriel et al. Appendices + handouts)

Guest lecture

Homework #9 assigned, homework #8 due

10
Oct. 29

Exam #1: during class time

 
11
Nov. 5

Module 2 : Lecture 2.5
-Introduction to Game Theory
-Market Equilibria and Optimization
-Complementarity Problems

[Sections 14.1-14.6+Gabriel et al. (2013)], natural gas and power networks with engineering considerations (Gabriel et al. Appendices + handouts)]

work on projects

homework #9 due

12
Nov. 12

Module 2 : Lecture 2.6
-Market Equilibria and Optimization
-Complementarity Problems

[Sections 14.1-14.6+Gabriel et al. (2013)], natural gas and power networks with engineering considerations (Gabriel et al. Appendices + handouts)]


 

work on projects

 

13
Nov. 19

Module 2: Lecture 2.7

-Market Equilibria and Optimization
-Complementarity Problems

[Sections 14.1-14.6+Gabriel et al. (2013)], natural gas and power networks with engineering considerations (Gabriel et al. Appendices + handouts)]



work on projects

 


14
Nov. 26

Open class for discussion on projects

work on projects

15

Dec. 3

 

Project Presentations (students)

 

project presentations (in class)+ project reports due

    Exam #2: during time assigned by the registar  

Class Text

Operations Research Applications and Algorithms, W.L. Winston (4th edition)

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