|
Week |
Date |
Read |
Topic 1 |
Topic 2 |
Topic 3 |
Homework |
|
1 |
26-Aug |
Ch. 1
(all), Ch. 2(review), Ch. 3.1-3.3 |
Intro to
OR History
(Morse) Recent
Applications Where to
Look for Info Instructor
Info |
Course
Structure Optimization
taxonomy LP history LP
assumptions (3.1) |
LP
Graphical Solution (3.2) Special
cases (3.3) Admin –
student info Admin –
student survey |
p. 56: 1,4 p. 64: 3,5 p. 69:
1,2,3,7 |
|
2 |
2-Sep |
Ch. 2
(review), Ch. 3.3-3.12, LINDO Handout |
|
|
|
|
|
3 |
9-Sep |
Ch.
3.3-3.12 |
Standard
NPS formulation format Formulation
I Product
mix (3.4, 3.6, 3.7) |
Formulation
II Covering,
Staffing, Scheduling (3.5) Blending
(3.8) |
Formulation
III Multiperiod
planning (3.10) |
p. 73: 1 p. 76: 2,
6 p. 91:6,10 p. 103: 3;4 |
|
4 |
16-Sep |
LINDO
Handout, MPL Tutorial, Ch. 4.1-4.3, 4.12 |
Formulation
IV Recourse
Models (LINDO Handout) |
MPL -
algebraic model language intro, examples |
Standard
Form (4.1) Simplex
Intro (4.2) |
Handout,
#4 (formulate only) Formulate
and solve with MPL/CPLEX: p. 120: 49 p. 127: 3 |
|
5 |
23-Sep |
Ch
4.5-4.6, 4.10-4.11, |
Tableau I
(4.3) Tableau
mechanics, stopping criterion Tableau
adjustments (4.4, 4.12) |
Tableau II
Alternative
optima (4.5) Unbounded
LPs (4.6) Degeneracy
and cycling (4.9) |
Degeneracy
continued (4.9) Big M,
Two-Phase (4.10, 4.11) |
p. 143:
3,5 p. 148:
#2, #5 p. 151: #3 p. 170: find
initial BFS using Two-Phase |
|
6 |
30-Sep |
Ch. 6.2,
10.1-10.2 Ch.
6.5-6.11 |
Matrix
form of simplex (6.2) Revised
Simplex (10.1, 10.2) |
Duality I Formulating
the Dual (6.5) Economic
interpretation (6.6) Dual
Theorems (6.7) |
Duality II Shadow
prices/reduced costs (6.8) Complementary
slackness (6.10) |
p. 247: 2
(find z, x1, x2, s1, s2 via matrix formulas) p. 559:1
(use product form of inverse) p. 275: 5 p: 287: 2a
(also show dual of the dual is the primal) p. 297: 6 |
|
7 |
7-Oct |
Ch 6.10, Review |
Duality
III Elastic
constraints/dual bounds Dual
simplex/adding constraints (6.11) |
Comprehensive
Example I Formulation Dual MPL Setup |
Comprehensive
Example II Solution
Analysis Sensitivity Project
Handout, Discussion |
|
|
8 |
15-Oct |
Ch 7.1-7.3
(formulations only) Ch
8.1-8.3, 8.5, 8.6 |
Formulations:
transportation, transshipment, assignment |
Network
terminology Min cost
network flow formulation |
Network
simplex |
|
|
9 |
21-Oct |
MIDTERM |
|
|
|
|
|
10 |
28-Oct |
Ch. 9.1,
9.2 |
Network
Simplex Cont’d Network
Review |
IP
Formulation I Integral
variables Logical
conditions: fixed charge, either-or, if-then |
IP
Formulation II Limiting
variables Economies
of scale SOS
variables |
|
|
11 |
4-Nov |
Ch. 9.3,
9.4, Handouts |
IP
Formulation III Covers Packs Partitions |
LP
relaxations Network
problem integrality Solution
implications Branch-and-bound:
theory |
Presolve
methods Strong
formulations Branch
priorities Cuts |
|
|
12 |
11-Nov |
MPL Manual
pp. 90-107, CPLEX Handout, Ch. 12.1-12.4 |
Cuts CPLEX MIP
Options |
Detailed
Example MPL
Formulation CPLEX
options Solution
analysis and sensitivity |
NLP I Introduction/Taxonomy Convexity/Concavity Line
Searches |
|
|
13 |
18-Nov |
Ch
12.5-12.8 |
NLP II Multivariate
Unconstrained Optimization Gradients;
steepest ascent |
NLP III Convergence
of steepest ascent; alternatives Lagrange
multiplier methods |
NLP IV Karush-Kuhn-Tucker
Conditions |
|
|
14 |
25-Nov |
Ch 12.9,
12.11 |
NLP V Quadratic
Programming |
NLP VI Survey of
NLP Methods |
NLP VI Survey of
NLP Methods (Cont’d) |
|
|
15 |
2-Dec |
Review |
Total
Course Picture Formulation |
LP Theory Network
Theory |
IP Theory NLP Theory |
|
|
|
16-Dec |
FINAL |
|
|
|
|