$ondollar title AA Crew Scheduling (ILP) Model 11.4 of Rardin (1998)

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

sets
j  "crew pairings"  /1*15/,
f  "flights" /101, 109, 203, 204, 211, 212, 305, 308, 310, 402, 406, 407/;

table cov(j,f) "whether pairing j covers flight f"
   101 109 203 204 211 212 305 308 310 402 406 407
1   1       1                   1           1
2   1       1                                   1
3   1           1           1                   1
4   1           1               1
5           1                       1       1
6       1   1                                   1
7       1       1           1                   1
8       1       1               1
9       1               1   1                   1
10      1               1       1
11              1           1           1
12              1    1              1   1
13      1            1          1           1
14                   1              1       1
15      1            1                          1;

parameter c(j) "cost of pairing j"
/1 2900, 2 2700, 3 2600, 4 3000, 5 2600, 6 3150, 7 2550, 8 2500,
9 2600, 10 2050, 11 2400, 12 3600, 13 2550, 14 2650, 15 2350/; 

free variable cost "total crew cost";

binary variables x(j) "whether to use pairing j";

equations
obj    "min total cost",
fly(f) "cover flight f";

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

fly(f)..
sum(j, cov(j,f)*x(j)) =e= 1;

model aacrew /all/;

solve aacrew using mip minimizing cost;