Linear programming

From Optimization for Chemical Engineering: 4G3
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Class date(s): 07 January 2015
Download video: Link [610 M]

Download video: Link [812 M]

Download video: Link [840 M]

Download video: Link [820 M]

References

Dr. Marlin has made a great, short e-book 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 Video file References and Notes
07 January 01B
  • Degrees of freedom
  • Terminology related to optimization
  • Introductory linear programming problem

Handout from class

Video
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

Video

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

Video

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.

The R-code used to draw the plot in the class handout

plot(c(0, 100), c(0, 70), type = "n", xlab = expression(x[1]), ylab = expression(x[2]), asp = 1)
abline(a=150, b=-1.6, lw=7)
abline(a=1000/12, b=-10/12, lw=5)
abline(a=500/8, b=-0.5, lw=3)
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("Non-negativity: "~x[1]>=~"0"), srt=90)
text(45, 2, expression("Non-negativity: "~x[2]>=~"0"), srt=0)

delta=2
text(0+delta, 0+delta, "[0]")
text(0+delta, 62.5-2*delta, "[1]")
text(62.5, 31.25-1.5*delta, "[2]")
text(87-delta, 10.9-1.0*delta, "[3]")
text(93.75-2.1*delta, 0+1.0*delta, "[4]")
19 January 03A
  • Running the simplex method to solve LPs
  • Interpretation of the optimum solution
Video