COURSE OUTLINE 
(Tentative) 

Class# 
Date 
Topics 
Reading 
HW Assigned 
1 
1/22 
Introduction,
Administration, Examples of mathematical programs 
Chapter 1 

2 
1/26 
Formulation of LP, solving 2d LPs graphically, extreme points, feasible and infeasible LPs, bounded and unbounded LPs 
Chapter
3.1 3.3 

R1 

Review of linear algebra 
Chapter 2 

3 
1/29 
Some examples from remainder of Chapter 3 

HW 1 
4 
2/2 
Standard form, basic and nonbasic variables, basic feasible sloutions, beginning of simplex algorithm 
Chapter
4.1 4.6 
HW 2 
R2 

Examples of linear programs 
Chapter
4.1 4.6 

5 
2/5 
Simplex algorithm 
Chapter
4.9 4.10 

6 
2/9 
Simplex algorithm 

HW 3 
R3 

The simplex algorithm 


7 
2/12 
Degeneracy, unrestricted variables, cycling, complexity of simplex algorithm 


8 
2/16 
Big M method, recap of simplex, LINDO, goal programming LPs on computers 
Chapter 4.7,
4.14, 4.15 
HW4 
R4 

Simplex algorithm 


9 
2/19 
More LP examples, Sensitivity analysis 
Chapter 3.10,
3.11, 5.1 

10 
2/23 
Sensitivity Analysis, LINDO 
Chapter 5, 6.2 

R5 

Midterm Review 


11 
2/26 
Midterm 1 


12 
3/1 
Sensitivity analysis, computing an optimal basis, duality 
chapter
6.3 6.10 
HW 5 
R6 

modeling, sensitivity analysis 


13 
3/4 
duality, economic interpretations 
Chapter
6.8 6.10 

14 
3/8 
Complimentary slackness 


R7 

Sensitivity analysis, duality and complimentary slackness 


15 
3/11 
Sensitivityduality 


Spring Break 



16 
3/22 
Transportation problems 
Chapter
7.1 7.2 
HW 6 
R8 

Transportation problems 


17 
3/25 
Transportation simplex 
Chapter 7.3 

18 
3/29 
Assignment problems 
Chapter 7.5 
HW 7 
R9 

Transportation simplex, assignment problems 


19 
4/1 
Network models, max flow 
Chapter
8.1, 8.3 

20 
4/5 
Max flow min cut theorem 
Chapter
8.1, 8.3 
HW 8 
R10 

Midterm review 


21 
4/8 
Midterm 2 


22 
4/12 
Other flow problems, mincost flows, multicommodity flows 
Chapter 8 

R11 

Network problems 


23 
4/15 
Dynamic programming, knapsack 
Chapter 13 

24 
4/19 
DP, shortest paths, Dijkstra, acyclic graphs, greedy algorithms 
Chapter 8.2 
HW 9 
R12 

Dynamic programming, Shortest paths 


25 
4/22 
Integer Programming 
Chapter 9 

26 
4/26 
IP, brach and bound 
Chapter 9 

R13 

IP 


27 
4/29 
more IP examples, cutting planes, Advanced Topics 
Chapter 9 

28 
5/5 
Review 




Final Exam 


All
readings are from Wayne L. Winston and Munirpallam Venkataramanan,
"Introduction to Mathematical Programming,” Duxbury, Fourth Edition, 2003.
All exams are closed book
closed notes, no electronic or hard copy cheat sheets are allowed. Please go
over the Rutgers Academic
Integrity Policy. 
