How to define multi variable linear programming ??

For a random example:

Variable X from 1 to 3 and Z 0 to 2

I want to minimize 5*x1+2*x2+3*x3+Z0

and the constraints are:

3*x1+2*x2+4*x3-Z1+Z0>=15

10*x1+7*x2+6*x3-Z2+Z1>=10

5*x1+5*x2+5*x3+Z2>=8

X1,X2,X3,Z0,Z1,Z2 >= 0.

I have no problem defining the matrix if there were no Z variable and minimize it.

And I can get the minimized value using the function [x, fval] = linprog(c, A, b, Aeq, beq, lb, ub) where c what I want to minimize, A is the constraint matrix, b is the value of constraints, Aeq, Beq if LHS is only equal to RHS of constraints, lb is lower limite and ub is upper limit for the variables.

With the addition of the variable Z I am not sure how to define and optimize this problem.

Answer 1

[Torsten]

Set Z0 = x4, Z1= x5, Z2 = x6. Can you solve the problem now ?

[Ran Hu]

yes, thought about it. but when when there are say x1 to x20, and z1 to z20. Just seems like the presentation is really bad. I can do x1 to x40. But doesnt look great..

Answer 2

[Alan Weiss]

You have two choices. One is to follow Torsten's advice and use linprog to solve the resulting problem.

The other is to use the new problem-based approach, which allows you to use any set of optimization variables that you like. For linear programming examples using this approach, see Problem-based Linear Programming Applications in Linear Programming and Mixed-Integer Linear Programming.

Alan Weiss

MATLAB mathematical toolbox documentation