ENGINEERING OPTIMIZATION Methods and Applications. A. Ravindran, K. M. Ragsdell, G. V. Reklaitis. Book Review. Chapter 4: Linear Programming. Part 1: Abu (Sayeem) Reaz Part 2: Rui (Richard) Wang. Review Session June 25, 2010. Finding the optimum of any given world – how cool is that?!.
Methods and Applications
A. Ravindran, K. M. Ragsdell, G. V. Reklaitis
Part 1: Abu (Sayeem) Reaz
Part 2: Rui (Richard) Wang
June 25, 2010
– how cool is that?!
The constraints of the system can be expressed as linear equations or inequalities and the objective function is a linear function of the design variables
Linear Program (LP): all variables are real
Integer Linear Program (ILP): all variables are integer
Mixed Integer Linear Program (MILP): variables are a mix of integer and real number
Binary Linear Program (BLP): all variables are binary
“Model building is not a science; it is primarily an art that is developed mainly by experience”
25 inspections/hour, accuracy = 98%, wage=$4/hour
15 inspections/hour, accuracy= 95%, wage=$3/hour
Let’s get experienced!!
“During each period, up to 50,000 MWh of electricity can be sold at $20.00/MWh, and excess power above 50,000 MWh can only be sold for $14.00/MW”
Piecewise Linear in the regions (0, 50000) and (50000, ∞)
Property: If there exists an optimum solution to a linear programming problem, then at least one of the corner points of the feasible region will always qualify to be an optimal solution!
(A is the coefficient matrix, x is the decision vector, b is
the requirement vector, and c is the profit (cost) vector)
In some situations, it may become necessary to introduce a variable that can assume both positive and negative values!
100 hr of labor, 600 lb of material, and 300hr of administration per day
A. Felt, ‘‘LINDO: API: Software Review,’’ OR/MS Today, vol. 29, pp. 58–60, Dec. 2002.
For any optimization problem in linear form with feasible solution time!
Every linear programming problem has an associated linear program called its dual such that a solution to the original linear program also gives a solution to its dual
Solve one, get one free!!
Columns into constraints and constraints into columns
Find a Dual: Example 4.10
x takes the value of y if both the ranges are true
Now Part 2 begins….