$ondollar title Tmark (ILP) Example 11.10 of Rardin (1998)

$offsymxref offsymlist offuelxref offuellist offupper
option limrow = 0, limcol = 0;

sets
j "calling zone" /1*14/,
i "possible centers" /1*8/;

table c(j,i) "unit calling cost from i to j"
    1    2    3    4    5    6    7    8
1  1.25 1.40 1.10 0.90 1.50 1.90 2.00 2.10
2  0.80 0.90 0.90 1.30 1.40 2.20 2.10 1.80
3  0.70 0.40 0.80 1.70 1.60 2.50 2.05 1.60
4  0.90 1.20 1.40 0.50 1.55 1.70 1.80 1.40
5  0.80 0.70 0.60 0.70 1.45 1.80 1.70 1.30
6  1.10 1.70 1.10 0.60 0.90 1.30 1.30 1.40
7  1.40 1.40 1.25 0.80 0.80 1.00 1.00 1.10
8  1.30 1.50 1.00 1.10 0.70 1.50 1.50 1.00
9  1.50 1.90 1.70 1.30 0.40 0.80 0.70 0.80
10 1.35 1.60 1.30 1.50 1.00 1.20 1.10 0.70
11 2.10 2.90 2.40 1.90 1.10 2.00 0.80 1.20
12 1.80 2.60 2.20 1.80 0.95 0.50 2.00 1.00
13 1.60 2.00 1.90 1.90 1.40 1.00 0.90 0.80
14 2.00 2.40 2.00 2.20 1.50 1.20 1.10 0.80;

parameter d(j) "demand at j"
/1 250, 2 150, 3 1000, 4 80, 5 50, 6 800, 7 325,
8 100, 9 475, 10 220, 11 900, 12 1500, 13 430, 14 200/;

parameter f(i) "fixed charge for a center at i"
/1 2400, 2 7000, 3 3600, 4 1600, 5 3000, 6 4600, 7 9000, 8 2000/;

scalars
mincalls  "minimum number of calls per center" /1500/,
maxcalls  "maximum number of calls per center" /5000/;

free variable totcost "total cost";

positive variable
x(i,j)  "fraction of j serviced from i";

binary variable
y(i)    "whether a center is opened at i";

equations
obj      "min total cost"
serv(j)  "each j serviced from somewhere",
minc(i)  "minimum number of calls at i",
maxc(i)  "maximum number of calls at i";

obj..
totcost =e= sum((i,j), c(j,i)*d(j)*x(i,j)) + sum(i, f(i)*y(i));

serv(j)..
sum(i, x(i,j)) =e= 1;

minc(i)..
mincalls*y(i) =l= sum(j, d(j)*x(i,j));

maxc(i)..
sum(j, d(j)*x(i,j)) =l= maxcalls*y(i); 

model tmark /all/;

solve tmark using mip minimizing totcost;