| Date | Topic | Reading |
| 17 January | Introduction to Network Flows | Chapter 1, 2.1, and 2.2 |
| Transportation Problem Example | ||
| Solving Network Flow Problems with AMPL/CPLEX | AMPL Files | |
| 24 January | Review of MCNFP | Transportation Example
from Jensen and Bard |
| TCC Example
TCC Solution |
||
| Algorithm Design and Analysis | Chapter 2.3 and 3.1 | |
| 31 January | Personnel Scheduling with MCNFP | |
| Node Splitting | Pages 41 and 42 | |
| Search Algorithms | 3.4 | |
| Algorithms for the Shortest Path Problem: Introduction | Chapter 4.1, 4.2, 4.3, and 4.4 | |
| 7 February | Shortest Path Applications: Dynamic Programming | Handouts
PPT |
| The 0-1 Knapsack Problem | Pages 100 - 102 | |
| Equipment Replacement | www.utdallas.edu/~scniu/OPRE-6201 | |
| Cramming for Finals | ||
| Correctness of the Reaching Algorithm | PPT | |
| 14 February | Application: The Oracle of Kevin Bacon | |
| Dijkstra's Algorithm | Chapter 4.5
Handouts PPT |
|
| The Bellman-Ford Algorithm | Chapter 5.4
PPT |
|
| The Floyd-Warshall Algorithm | Chapter 5
PPT Example 1 |
|
| MCNFP and Negative Cycles | Example | |
| 21 February | Overview of Shortest Path Algorithms | |
| Sets in AMPL | ||
| Algorithms in AMPL | ||
| 28 February | The Maximum Flow Problem | Chapter 6.1, 6.2, 6.3, and 6.4 |
| Flows and Cuts | PPT | |
| The Max-Flow Min-Cut Theorem | Handout | |
| The Augmenting Path Algorithm | PPT | |
| Max-Flow Min-Cut Applications | Scheduling on Parallel
Machines and
Distributed Computing |
|
| 7 March | More Max-Flow Min-Cut Applications | |
| Baseball Elimination | Section 8.1
PPT |
|
| Flow on cycles | PPT | |
| All-Pairs Minimum Cut | PPT | |
| Edge Connectivity | ||
| Open-Pit Mining | PPT
AMPL data file |
|
| The Ford-Fulkerson Algorithm | Section 6.5
PPT |
|
| 28 March | Drawbacks to Ford-Fulkerson | PPT |
| Max Flow with Non-Zero Lower Bounds | PPT | |
| Even More Max-Flow Min-Cut Applications | Matchings, Coverings,
and Independent Sets
Minimum Chain Covering Problem |
|
| 4 April | Covers and Such Revisited | PPT |
| Vertex Connectivity | ||
| Formulation Example | Pick Axe Mining Company | |
| Midterm Exam Solutions | (See assignments page) | |
| Review of the Simplex Method | LP in Two Dimensions | |
| LP's in Standard Form | ||
| Basic Solutions | ||
| Preview
of the Simplex Method
Simplex Method Example The Ratio Test |
||
| Cramer's Rule | ||
| 11 April | Introduction to the Network Simplex algorithm | PPT
Chapter 11. |
| Formulation Examples | Distribution
and Worker Assignment
Make-to-Order vs. Make-to-Stock |
|
| Network Models with Integer Variables and/or Side Constraints | Warehouse
Location Problem
Solution |
|
| 18 April | Network Simplex | Chapter 11
Spanning Trees and Basic Feasible Solutions Node Potentials, and Reduced Arc Costs |
| Formulation Example | Network
Design
AMPL output |
|
| Multicommodity Flows | Definition
Examples AMPL: model and data files for examples 1 and 2 output |
|
| 25 April | Guest Lecturer: Thomas McLoud | PPT |
| 25 April | Generalized Network Flows | Jensen and Bard Example
PPT AMPL model, data, and output |
| Final Exam |