$ondollar title CDOT Generalized Asmt (ILP) Example 11.6 of Rardin (1998)

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

sets
i "districts" /1*6/,
j "ships"  /1*3/;

table c(j,i) "cost of assigning i to j"
   1   2   3   4   5   6
1 130  30 510  30 340  20
2 460 150  20  40  30 450
3  40 370 120 390  40  30;

table t(j,i) "times for assigning i to j"
   1   2   3   4   5   6
1  30  50  10  11  13  9
2  10  20  60  10  10  17
3  70  10  10  15  8   12;

free variable cost;

binary variable x(i,j) "whether i is assigned to j";

equations
obj        "min total cost"
assign(i)  "each i assigned",
cap(j)     "capacities at j";

obj..
cost =e= sum((i,j), c(j,i)*x(i,j));

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

cap(j)..
sum(i, t(j,i)*x(i,j)) =l= 50;

model cdot /all/;

solve cdot using mip minimizing cost;