Class date(s):

07 January to 04 February 2015

















References
Dr. Marlin has made a great, short ebook on Linear Programming. You will find reading his notes very rewarding, and a great supplement to the class lectures.
Resources
Scroll down, if necessary, to see the resources.
Date

Class number

Topic

Slides/handouts for class

References and Notes

07 January

01B

 Degrees of freedom
 Terminology related to optimization
 Introductory linear programming problem

Handout from class


12 January

02A

 More terminology related to optimization
 Continue with our introductory LP problem
 Geometric aspects of the optimum
 Moving LP problems into standard form

Handout from class

We covered topics on page 11, 13, 14 and 17 of the notes by Marlin (see comment above).

14 January

02B

 Getting the LP problem into standard form
 Starting to understand the Simplex method to solve LPs

Handout from class

We covered topics on page 21 to 29 of the notes by Marlin, however, I did not focus on the mathematical details; we only consider the geometric viewpoint in 4G3.

19 January

03A

 Running the simplex method to solve LPs
 Interpretation of the optimum solution

21 January

03B

 Interpretation of general LP models
 Understand the effects of changes in the model on the optimum solution (i.e. sensitivity analysis)

Handout from class

See page 37 and 38 in Marlin's notes for an alternative visualization of sensitivity analysis.

26 January

04A

 Understand the effects of changes in the model on the optimum solution (i.e. sensitivity analysis)
 The effect of \(b_i\) changes on the RHS
 The effect of \(A\) changes on the LHS
 The effect of \(c_i\) changes in the objective

Handout from class


28 January and 04 February

04B

 Recapped some concepts on sensitivity analysis
 Considered sensitivity analysis where two or more variables were varied
 Getting a general understanding of LPs
 Allocation problems
 Blending problems

Handout from class


The Rcode used to draw the plot in the class handout 2B and 3A.
plot(c(0, 100), c(0, 70), type = "n", xlab = expression(x[1]), ylab = expression(x[2]), asp = 1)
abline(a=1500/10, b=16/10, lw=7) # Placement
abline(a=1000/12, b=10/12, lw=5) # Solder
abline(a=500/8, b=4/8, lw=3) # Inspection
abline(v=0, h=0)
title(expression("Objective: Maximize 10"~x[1]~"+ 15"~x[2]))
text(20, 55, expression("Inspection: 4"~x[1]~"+ 8"~x[2]~"+ "~x[5]~" = 500"), srt=332.5)
text(35, 57, expression("Solder: 10"~x[1]~"+ 12"~x[2]~"+ "~x[4]~" = 1000"), srt=319.5)
text(65.5, 50, expression("Placement: 16"~x[1]~"+ 10"~x[2]~"+ "~x[3]~" = 1500"), srt=301)
text(2, 30, expression("Nonnegativity: "~x[1]>=~"0"), srt=90)
text(45, 2, expression("Nonnegativity: "~x[2]>=~"0"), srt=0)
delta=2
text(0+delta, 0+delta, "[0]")
text(0+delta, 62.52*delta, "[1]")
text(62.5, 31.251.5*delta, "[2]")
text(87delta, 10.91.0*delta, "[3]")
text(93.752.1*delta, 0+1.0*delta, "[4]")