| Lec # | Date | Topic(s) | Scribe | Panopto |
| 1 |
Jan 8 |
syllabus,
optimization in calculus, the system \(A\mathbf{x} =
\mathbf{b}\), EROs, basic/non-basic variables, parametric vector
form
|
scribe
|
video
|
| 2 |
Jan 10 |
matrix transpose, multiplication, linear independence (LI),
rank, inverse, general form of Gauss-Jordan (GJ) method
|
scribe
|
video
|
| 3 |
Jan 15 |
GJ example, Homework 1, LP formulation,
decision variables (d.v.'s), objective function, constraints,
sign restrictions
|
scribe
|
video
|
| 4 |
Jan 17 |
second formulation of Jones LP , assumptions of LP, graphical
solution, feasible region, optimal solution, convex set
|
scribe
|
video
|
| 5 |
Jan 22 |
extreme point/vertex of LP, cases of LP, alternative optimal
solutions, infeasible LP, unbounded LP, a full 2D example
|
scribe
|
video
|
| 6 |
Jan 24 |
LP formulation problems: staffing, blending: average quality,
inventory planning: unified flow balance constraints
|
scribe
|
video
|
| 7 |
Jan 29 |
computer leasing problem, hints on Homework 3 problems,
introduction to AMPL, model for Farmer Jones
LP
|
scribe
|
video
|
| 8 |
Jan 31 |
video lecture: more AMPL, Farmer Jones LP using
# crops, inventory planning LP: all balance constraints in one
go
|
software
|
video
|
| 9 |
Feb 5 |
LP standard form, slack/excess vars, basic solutions, basic
feasible solution (bfs), corner point \(\equiv\) bfs, optimal
bfs
|
scribe
|
video
|
| 10 |
Feb 7 |
correspondence of bfs's and corner points, adjacent bfs, steps
of simplex method for a max LP with \(\leq\) constraints
|
scribe
|
video
|
| 11 |
Feb 12 |
simplex method: entering variable, min-ratio test, leaving
variable, pivoting, optimal bfs, tableau simplex method
|
scribe
|
video
|
| 12 |
Feb 14 |
make-up: simplex for min-LP, describing all alternative
optima, unbounded LP, big-M simplex, artificial variable
|
scribe
|
video
|
| 13 |
Feb 19 |
infeasibility in big-M simplex, handling unrestricted
in sign (urs) vars: \(x_i \leftarrow x_i^+ - x_i^-\), for
\(x_i^+, x_i^- \geq 0\), full example
|
scribe
|
video
|
| 14 |
Feb 21 |
review: problems from the Practice midterm
|
scribe
|
video
|
| 15 |
Feb 26 |
Midterm exam
|
| 16 |
Feb 28 |
more AMPL: Chukee toys LP;
sensitivity analysis in graphical LP, changing objective
function coefficient
|
scribe
|
video
|
| 17 |
Mar 5 |
changing coefficient of wheat, changing rhs of constraint \(b_i
\rightarrow b_i + \Delta\), shadow price, economic
interpretation
|
scribe
|
video
|
| 18 |
Mar 7 |
simplex in matrix
form, \(\mathbf{x}^T = [\mathbf{x}_B^T~\mathbf{x}_N^T ]\),
optimal \(\mathbf{x}_B = B^{-1}\mathbf{b},\, z^* =
\mathbf{c}_B^T B^{-1}\mathbf{b}\), optimal tableau given optimal
basis
|
scribe
|
video
|
| 19 |
Mar 19 |
video: sensitivity analysis in matrix form:
changing \(c_j\) for non-basic \(x_j\), reduced cost, changing
\(c_j\) for basic \(x_j\)
|
scribe
|
video
|
| 20 |
Mar 21 |
\(b_i \rightarrow b_i + \Delta\), new \(\mathbf{x}_B =\) old
\(\mathbf{x}_B + \Delta [B^{-1}]_{\cdot i}\), shadow price,
changing \(c_j\) and \(A_{ij}\) for nonbasic \(x_j\)
simultaneously
|
scribe
|
video
|
| 21 |
Mar 26 |
video: LP duality, normal constraints/variables, dual of
normal max LP, primal-dual relations, motivation for the dual
|
scribe
|
video
|
| 22 |
Mar 28 |
economic interpretation of Farmer Jones and Gaseous LPs
(Hw2),
duality in matrix form, weak and stroing duality
|
scribe
|
video
|
| 23 |
Apr 2 |
dual theorem: \(\mathbf{y}^T = \mathbf{c}_B^T B^{-1}\) is
optimal for (D), read off
optimal dual solution (Jones LP), shadow price\(_i =
y_i\), AMPL
|
scribe
|
video
|
| 24 |
Apr 4 |
hints on Homework 10 problems,
complementary slackness conditions (CSCs), using CSCs to solve
LPs
|
scribe
|
video
|
| 25 |
Apr 9 |
discussion on Project, integer programming
(IP), IP formulation: basketball starting line-up, if-then
constaints
|
scribe
|
video
|
| 26 |
Apr 11 |
fixed charge MIP, forcing constraint, general either-or
constraint, OR vs XOR, modeling more than two options
|
scribe
|
video
|
| 27 |
Apr 16 |
more discussion on Project, general if-then
statement, \(A \Rightarrow B ~\equiv~ \mbox{not} A ~\mbox{OR}~
B\), warehouse location MIP
|
scribe
|
video
|
| 28 |
Apr 18 |
modeling general either-or and general if-then statements using
extra binary variables
|
scribe
|
video
|
| 29 |
Apr 23 |
problems from Homework 8
and Homework
10, review of practice final exam
|
scribe
|
video
|
| 30 |
Apr 25 |
more review of practice final exam
|
scribe
|
video
|