#
# an uncapacitated facility location model, with
# disaggregated constraints
#
param m;  #  number of warehouse locations
param n;  #  number of customers

option randseed 421415;

param f{1..m} = Uniform(10,30);  # fixed cost of opening facility

param c{1..m, 1..n} = Uniform(1,9);
                 #  shipping cost for satisfying all of j's demand

var y{1..m} binary;  #  whether to open facility

var x{1..m, 1..n} >= 0;  #  proportion of demand satisfied by each facility

minimize objective:
  sum{i in 1..m} f[i]*y[i] + sum{i in 1..m, j in 1..n} c[i,j]*x[i,j];

subject to meetdemand{j in 1..n}: sum{i in 1..m} x[i,j] =1;

subject to onlyuseopen{i in 1..m, j in 1..n}: x[i,j] <= y[i];