SA305: Linear Models and Optimization
Spring 2013
Syllabus
Operations Research (OR) is a wide field which, loosely, seeks to investigate how mathematical techniques can be used
to aid in solving ”real-life” problems. This course provides an introduction to linear programming, which is a fundamental
technique used in OR. The foci of the course are formulating mathematical optimization models (also called mathematical
programs, and understanding the mathematical underpinnings of linear optimization algorithms.
Course textbook: Deterministic Operations Research: Models and Methods in Linear Optimization, by David
Rader.
Course website: http://www.usna.edu/Users/math/dphillip/sa305.s13/index.html. This has links to information for your individual sections.
The course schedule is as follows:
Day
1
2
3
4
5
6
8
9
10
11
12
13
14
15
16
17
18
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
Date
1/8/13
1/9/13
1/11/13
1/14/13
1/16/13
1/18/13
1/23/13
1/25/13
1/28/13
1/30/13
2/1/13
2/4/13
2/6/13
2/8/13
2/11/13
2/13/13
2/15/13
2/20/13
2/22/13
2/25/13
2/27/13
3/1/13
3/4/13
3/6/13
3/8/13
3/18/13
3/20/13
3/22/13
3/25/13
3/27/13
3/29/13
4/1/13
4/3/13
4/5/13
4/8/13
4/10/13
4/12/13
4/15/13
4/17/13
4/19/13
4/22/13
4/24/13
4/26/13
4/29/13
Weekday
Tuesday
Wednesday
Friday
Monday
Wednesday
Friday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Wednesday
Friday
Monday
Lecture topic
The cycle of operations research
Example 1.1
definitions, gusek
Resource allocation
Work scheduling
Blending
Production Process
Multiperiod models
Multiperiod models
Sets, indices, and summations, oh my
Resource allocation redux
Work scheduling redux
Blending redux
Production process redux
Multiperiod redux
review
Test 1
Optimization algorithms-local search
Improving search, optimality, gradients
Convexity, global optimality
Geometry/algebra of extreme points
Geometry, continued
Fundamental theorem of LP
Basic solutions in canonical form
Basic solutions continued
Simplex method
Simplex method, continued
Degeneracy, convergence
Two-phase method
review
Test 2
Bounds
The dual
duality theorems
Zero-sum games
Zero-sum games
Modeling with excel
introduction to network models
optimality and shortest paths
shortest paths interdiction
open
open
open
review
1
DOR
1.1
1.2
1.3
2.1
2.2
2.3
2.5
2.6
2.6
2.3
2.1
2.2
2.3
2.5
2.6
5.1-5.4
6.1-6.2
6.3
7.1
7.1
7.2
2.8,7.3
7.3
8.1
8.1
8.3
8.4
9.1
9.2
9.3
2.7
2.9
12.2
Homework
Bonus
1.1(a)-1.1(d)
1.2
2.1,2.3*
2.6
2.11*, 2.12
2.9,2.10*
2.20
2.22
diet*
2.7,2.8
2.13*, 2.14
TBD
2.16,2.24,inventory,finco
na
na
6.1, 6.2, 6.8, 6.9
6.14,6.18
7.2,7.3
7.4
handout
7.14,7.16
7.17
TBD
TBD
TBD
TBD
na
na
TBD
TBD
TBD
TBD
TBD
TBD
TBD
TBD
TBD
6.15,6.19
7.24