Linear Programing
What is linear programing?
Linear programing is a mathematical method you can apply to find best possible results such as maximum profit or minimum cost. Linear programing practically use as one of the optimization problem solvers. In general, to solve a optimization problem, you need to have an objective (what do you want to solve? Do you want to maximize or minimize your function?) and constraints related to your function. Putting objective and constraints function together on a graph will generate a feasible region.
For example,
Objective function max -1/2x + 7
Constraints y=3x y=x-2
(source: http://www.purplemath.com/modules/linprog.htm)
The shade area is the feasible region
There are many software that help you solve optimization problems. In this page, I will focus on how to use GAMS.
GAMS
GAMS can be accessed through ITAP software remote (https://goremote.itap.purdue.edu/Citrix/XenApp/auth/login.aspx)
variables
objval "objective function value" x1 "new wood pulp" x2 "recycled office paper" x3 "recycled newsprint" y1 "# of products produced by method 1" y2 "# of products produced by method 2" y3 "# of products produced by method 3" y4 "# of products produced by method 4"
free variables
objval;
positive variables
x1,x2,x3,y1,y2,y3,y4;
equations
obj "total cost" method_1 "produce from method 1" method_2 "produce from method 2" method_3 "produce from method 3" rest_80 "process 1 has to bw lesser than or equal to 80" atleast_100 "the # of products must be at least 100";
obj ..
objval =e= 100*x1+50*x2+20*x3;
method_1 ..
x1 =e= 3*y1+y2+y3;
method_2 ..
x2 =e= 4*y2+8*y4;
method_3 ..
x3 =e= 12*y3;
rest_80 ..
x1 =l= 80;
atleast_100 ..
y1+y2+y3+y4 =g= 100;
model absmall /all/;
solve absmall using lp minimizing objval;
My experience with linear programing
I have learned linear programing from a class in school of industrial engineering, IE335
1. From my experience with Linear Programing, I have used it for optimization problems. 2. Linear programing and non-linear programing is a very active area in research….finding a quick possible ways to calculate….
Courses for linear programing
If you are interested more in Linear programing and would like to take a course. I have listed the courses that relates to Linear programming.
IE 335 - Operation Research - Optimization Introduction to deterministic optimization modeling and algorithms in operations research. Emphasis on formulation and solution of linear programs, networks flows, and integer programs. Typically offered Fall Spring.
CS 51500 - Numerical Linear Algebra. (was CS 515: Numerical Analysis of Linear Systems till 2009) Computational aspects of linear algebra; linear equations and matrices, direct and iterative methods; eigenvalues and eigenvectors of matrices; error analysis.
ECE 580 - Optimization Methods for Systems and Control. Introduction to various methods of obtaining the extremum of a nondynamic or a dynamic system and their use in control system design. Linear programming, various search methods, nonlinear programming and dynamic programming. Various real-life applications are discussed, and appropriate case studies are investigated.
IE 535 - Linear Programming. Optimization of linear objective functions subject to linear constraints. Development of theory and algorithmic strategies for solving linear programming problems.
Further studies
If you are interested in reading about Linear programming this link will give you the list of textbooks you can look at.
Stapel, Elizabeth. "Linear Programming: Introduction." Purplemath. Available from
http://www.purplemath.com/modules/linprog.htm. Accessed 11 December 2011
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