robust optimisation

[sh.mojtahedzadeh at gmail.com]

Dear all,

I have a LP model here as follow:


Min = .42*x1 + .56*x2 + .70*x3;


S.t.
x1 + x2 + x3 = 900;

x1 <= 400 * y1;
x2 <= 700 * y2;
x3 <= 600 * y3;

30*x1 <= 12500;
40*x2 <= 20000;
50*x3 <=15000;

.15*x1 + .2*x2 +.15*x3 >= 100;
.2*x1 + .05*x2 + .2*x3 >= 100;
.25*x1 + .15*x2+ .05*x3 >= 150;

y1+y2+y3 = 2;


xi>=0,
yi=0, if x=o
yi=1, if x>=o

The constraints
.15*x1 + .2*x2 +.15*x3 >= 100;
.2*x1 + .05*x2 + .2*x3 >= 100;
.25*x1 + .15*x2+ .05*x3 >= 150;


have uncertainties in x1, x2, and x3 coefficients. I want to know how
can I make a robust optimisation model for this LP model?


for example, if we know that all the coefficients have variations
about 30%.


Thank you,
Shab