Originally posted by: SystemAdmin

Hi, everyone!
My problem is :
X = http://x1, x2,....xn, x1 ---- xn are float variables, another binary variable y has the following relationship with X:
if one of xn is greater than 0, then y = 1
otherwise, y = 0, i.e., x1 = x2 =... = xn = 0;
how to represent this in cplex?

Thanks in advance.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

I sorry, i made a type error! X = http:// x1, x2, .... xn
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

Assuming you have upper bound ui on each of the xi this does what you want:

x1 <= y * u1
  x2 <= y * u2
  ...
  xn <= y * un

Moreover, y should have a positive coefficient in the objective function (assuming you problem is a minimization instance).
Then xi>0 requires y=1 and if all xi=0 then y will be 0 in any optimal solution.
#CPLEXOptimizers
#DecisionOptimization

Originally posted by: SystemAdmin

> dju358 wrote:

> ... and if all xi=0 then y will be 0 in any optimal solution

... provided that y is penalized (directly or indirectly) in the objective function; otherwise x1 = ... = xn = 0 and y = 1 is feasible (which is usually, but not always, harmless in models where y is not penalized).

/Paul
#CPLEXOptimizers
#DecisionOptimization