Originally posted by: Abdelkader

Hi Alex,

I am wondering whether it is possible to use Cplex for max-min optimization. Something like:

$\max_{x \in S}\big\{\min_{1\leq i \leq m}\{f_i(x)\}\big\}$

s.t to G(x) <= c

x \in S

Thanks for your help,

Abdelkader

Hi,

let me take the question https://www.ibm.com/developerworks/community/forums/html/topic?id=dac107d0-54fd-4500-9591-b51fd1abbce5&ps=25#repliesPg=0

in order to show you an example:

int N = 3;
int NbPeriods = 2;
 
range Periods = 1..NbPeriods;
 
// Parameters
 
float p[i in 1..N] = i;
float s[i in 1..N+1] = i;
 
float Demand [p in Periods] = rand(p);

// Decision Variables

dvar int x2 [Periods];  //Variable Price Quantity

// Objective function

dexpr float TotalCost [t in Periods] =
piecewise ( i in 1..N){
     s[i] -> p[i];
     s[N+1]
 } (1, 1) x2[t];

 

 
minimize max(p in Periods)TotalCost[p] ;

 

subject to {

forall ( t in Periods)
  Demand [t] == x2[t];

forall ( t in Periods) {
 
  x2[t] >= 0;
}  
}

regards

Originally posted by: Abdelkader

Dear Alex,

Great. Many thanks for your help.

Cheers,

Abdelkader