Software Search, Categories and Specials

Linear Program

Microsoft Excel - From Beginner to Expert in 6 Hours/ EXCEL DASHBOARD REPORTS

B linear programming GIPALS Start

A Linear Program (LP) is a program that can be expressed as the following:

   Minimize    f(x) = cx

Subject to   Ax  = b  and  x >= 0

where

x = [x₁, x₂, .. , x_n] vector of optimization variables

c = [c₁, c₂, .. , c_n] vector of objective coefficients (so-called "cost coefficients")

	a₁₁	a₁₂	a₁₃	...	a_1n
	a₂₁	a₂₂	a₂₃	...	a_2n
A =	a₃₁	a₃₂	a₃₃	...	a_3n	m x nmatrix of constraint coefficients
	:	:	:	:	:
	a_m1	a_m2	a_m3	...	a_mn

b = [b₁, b₂, .. , b_n] >= 0 vector of right-hand sides of constraint.This type of linear program is called Standard Form of linear program.The function f(x) is called the objective function of linear program and the equations Ax = b are called the constraints. The dimension of all these entities must be consistent. The dimension of vectors x, c and column count of the matrix A are the same and equal to n. The dimension of vector b and row count of the matrix A are the same and equal to m. The matrix A has more columns than rows usually. It allows to choose such values of x which minimize the objective function of linear program f(x).Linear program in the Standard Form can be solve by two most wide known methods: the Simplex Method and Interior Point Methods. The Simplex Method was introduced by Dantzig in the late 1940s and it continues to be widely used method for of all optimization tools.The basic idea of the Simplex Method is to have a basic feasible solution of linear program that satisfies all constrains and try to improve the solution at each iteration of the method. "Improve" suppose to get the objective function with lower value than it has at the current basic solution. At each iteration a new non-basic variable replaces one of basic variables in the linear program. Once a variable went out from the basic solution it should not entry basic solution again, otherwise there is a risk to get an infinite loop. The Simplex Method looks like moving from one feasible solution to another along the edges of the boundary. Interior Point methods by contrast of the Simplex Method go to descent direction until an optimum reached. The most known methods are Affine Scaling Method and Mehrotra Predictor - Corrector algorithm. Unfortunately, the most of the real world linear programs are not in standard form. To be able to solve those linear problems they have to be converted to Standard Form

linear programming GIPALS Start

Linear programming examples

There are several examples of linear programming intended to make the users of GIPALS familiar with it. These examples are included in GIPALS installation and can be found in ..\GIPALS\Examples folder.

Transport problem

Production (profit maximization) problem

Dietary optimization

Alloy mixture optimization

GIPALS Linear Programming $197.95 - 15000 Constraints & Variables | $297.00 - Unlimited Number of Constraints & Variables

Special ! Free Choice of Complete Excel Training Course or Excel Add-ins Collection on all purchases totaling over $70.00. ALL purchases totaling over $150.00 gets you BOTH! Purchases MUST be made via this site. Send payment proof to [email protected] 31 days after purchase date.

Instant Download and Money Back Guarantee on Most Software

Excel Trader Package Technical Analysis in Excel With $139.00 of FREE software!

Microsoft ® and Microsoft Excel ® are registered trademarks of Microsoft Corporation. OzGrid is in no way associated with Microsoft

Linear Program

Microsoft Excel - From Beginner to Expert in 6 Hours/ EXCEL DASHBOARD REPORTS

Blinear programming GIPALS Start

B linear programming GIPALS Start