Lec #  Date  Topic(s)  Scribe  Panopto 
1 
Jan 8 
syllabus,
optimization in calculus, the system \(A\mathbf{x} =
\mathbf{b}\), EROs, basic/nonbasic variables, parametric vector
form

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video

2 
Jan 10 
matrix transpose, multiplication, linear independence (LI),
rank, inverse, general form of GaussJordan (GJ) method

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video

3 
Jan 15 
GJ example, Homework 1, LP formulation,
decision variables (d.v.'s), objective function, constraints,
sign restrictions

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video

4 
Jan 17 
second formulation of Jones LP , assumptions of LP, graphical
solution, feasible region, optimal solution, convex set

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video

5 
Jan 22 
extreme point/vertex of LP, cases of LP, alternative optimal
solutions, infeasible LP, unbounded LP, a full 2D example

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video

6 
Jan 24 
LP formulation problems: staffing, blending: average quality,
inventory planning: unified flow balance constraints

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video

7 
Jan 29 
computer leasing problem, hints on Homework 3 problems,
introduction to AMPL, model for Farmer Jones
LP

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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

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video

10 
Feb 7 
correspondence of bfs's and corner points, adjacent bfs, steps
of simplex method for a max LP with \(\leq\) constraints

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video

11 
Feb 12 
simplex method: entering variable, minratio test, leaving
variable, pivoting, optimal bfs, tableau simplex method

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video

12 
Feb 14 
makeup: simplex for minLP, describing all alternative
optima, unbounded LP, bigM simplex, artificial variable

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video

13 
Feb 19 
infeasibility in bigM simplex, handling unrestricted
in sign (urs) vars: \(x_i \leftarrow x_i^+  x_i^\), for
\(x_i^+, x_i^ \geq 0\), full example

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video

14 
Feb 21 
review: problems from the Practice midterm

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video

15 
Feb 26 
Midterm exam

16 
Feb 28 
more AMPL: Chukee toys LP;
sensitivity analysis in graphical LP, changing objective
function coefficient

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video

17 
Mar 5 
changing coefficient of wheat, changing rhs of constraint \(b_i
\rightarrow b_i + \Delta\), shadow price, economic
interpretation

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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

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video

19 
Mar 19 
video: sensitivity analysis in matrix form:
changing \(c_j\) for nonbasic \(x_j\), reduced cost, changing
\(c_j\) for basic \(x_j\)

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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

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video

21 
Mar 26 
video: LP duality, normal constraints/variables, dual of
normal max LP, primaldual relations, motivation for the dual

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video

22 
Mar 28 
economic interpretation of Farmer Jones and Gaseous LPs
(Hw2),
duality in matrix form, weak and stroing duality

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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

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video

24 
Apr 4 
hints on Homework 10 problems,
complementary slackness conditions (CSCs), using CSCs to solve
LPs

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video

25 
Apr 9 
discussion on Project, integer programming
(IP), IP formulation: basketball starting lineup, ifthen
constaints

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video

26 
Apr 11 
fixed charge MIP, forcing constraint, general eitheror
constraint, OR vs XOR, modeling more than two options

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video

27 
Apr 16 
more discussion on Project, general ifthen
statement, \(A \Rightarrow B ~\equiv~ \mbox{not} A ~\mbox{OR}~
B\), warehouse location MIP

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video

28 
Apr 18 
modeling general eitheror and general ifthen statements using
extra binary variables

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video

29 
Apr 23 
problems from Homework 8
and Homework
10, review of practice final exam

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video

30 
Apr 25 
more review of practice final exam

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video
