IEOR 3608
Fall 2007

Introduction to Mathematical Programming

Professor David Phillips

Syllabus (Tentative and subject to change)

Class Number Date Topics Reading HW Assigned HW Due
1 9/4 Introduction, Administration, Examples of mathematical programs Chapter 1
2 9/6 Formulation of LP, solving 2-d LPs graphically, extreme points, feasible and infeasible LPs, bounded and unbounded LPs Chapter 3.1 - 3.3
3 9/11 Examples and modelling Chapter 3.4 - 3.7 HW 1
4 9/13 Standard form, basic and non-basic variables, basic feasible solutions, directions, beginning of simplex algorithm Chapter 4.1,4.2, note on BFS and theorem 1
R1 Review of linear algebra Chapter 2
5 9/18 Simplex algorithm:directions, BFS existence and Representation theorems, geometry of basic solutions Chapter 4.2-4.4, proofs of theorems 2 and 3 HW 2 HW 1
6 9/20 Simplex algorithm: the tableau, examples Chapter 4.5- 4.8
R2 Examples of linear programs. Chapter 3.8
7 9/25 Simplex algorithm, degeneracy, complexity, Big M Chapter 4.8, 4.11, 4.12, 4.14 HW 3 HW 2
8 9/27 degeneracy continued, multiple optimal solutions, free variables, multiperiod LP examples. Cycling handout, chapter 4.8, 4.14, 3.10-3.12
R3 The simplex algorithm with Big-M Chapter 4.12
9 10/2 LINDO, LPs in Excel, Duality Chapter 4.9, 4.10, 4.17, 6.5, files from class, mcdiet.xls HW 4 HW 3
10 10/4 Duality Chapter 6.2, 6.5, 6.7
R4 Multiperiod models, Duality Chapters 3.12, 6.5
11 10/9 Midterm Review HW 4
12 10/11 Midterm 1
R5 Midterm Review (Wed.)
13 10/16 Sensitivity analaysis Chapter 6.1-6.2 HW 5
14 10/18 Sensitivity analysis, shadow prices Chapter 6.3,6.6,6.8
R6 Duality
15 10/23 Duality and sensitivity analysis, Dual Simplex Chapter 6.8, 6.9, 6.11 HW 6 HW 5
16 10/25 Transportation problems, transportation simplex Chapter 7.1-7.3
R7 Complementary Slackness Chapter 6.10
17 10/30 Transportation simplex, LINGO. Chapter 7.3, Chapter 4:appendices B-C HW 7 HW 6
18 11/1 Assignment problem and Hungarian Algorithms Chapter 7.5
R8 Sensitivity Analysis in transportation problems Chapter 7.4
11/6 NO CLASS
19 11/8 Network models, shortest paths Chapter 8.1, 8.2 HW 8 HW 7
R9 Shortest paths, Dijkstra
20 11/13 Maximum Flow, Minimum Cuts, Duality revisited Chapter 8.3
21 11/15 Mincost flows, Multicommodity flows Chapter 8.5 HW 8
R10 Midterm review
22 11/20 Midterm 2
NO CLASS 11/22
23 11/27 Minimum Cost Flows, Integer Programming, Total Unimodularity Chapters 8.5, 9.1 HW 9
24 11/29 Branch and Bound Chapter 9.3-9.6
R11 Min. Cost Flows and Integer Programming Models Chapters 8.5, 9.2
25 12/4 Min. Cost Flows, Brance & Bound, Dynamic Prorgramming Chapters 8.5,9.6, 13.1-2 HW 10 (not to be handed in) HW 9
26 12/6 Dynamic Programming Chapter 13.3-6
R12 Branch & Bound
12/20, 1:10PM (209 Havemeyer, 233 Mud, 644 Mudd) Final
All readings are from Winston & Venkataraman Introduction to Mathematical Programming, 4th edition