! Keywords: Blending / Matching / Product Management / Product Mix / Production / Shipping / Sorting / Transportation;
! Maximize no. of barges assigned;
MAX XB11 + XB12 + XB13 + XB14 + XB15 + XB16 + XB21
+ XB22 + XB23 + XB24 + XB25 + XB26 + XB31 + XB32
+ XB33 + XB34 + XB35 + XB36 + XB41 + XB42 + XB43
+ XB44 + XB45 + XB46
SUBJECT TO
! At most 3 per group;
2) XB11 + XB21 + XB31 + XB41 <= 3
3) XB12 + XB22 + XB32 + XB42 <= 3
4) XB13 + XB23 + XB33 + XB43 <= 3
5) XB14 + XB24 + XB34 + XB44 <= 3
6) XB15 + XB25 + XB35 + XB45 <= 3
7) XB16 + XB26 + XB36 + XB46 <= 3
! Assign no more of a type than are available;
8) XB11 + XB12 + XB13 + XB14 + XB15 + XB16 <= 3
9) XB21 + XB22 + XB23 + XB24 + XB25 + XB26 <= 4
10) XB31 + XB32 + XB33 + XB34 + XB35 + XB36 <= 2
11) XB41 + XB42 + XB43 + XB44 + XB45 + XB46 <= 3
! The blending constraints for each group;
12) 29 XB11 + 1201 XB21 - 2370 XB31 + 200 XB41 >= 0
13) - 0.06 XB11 + 0.25 XB21 - 0.52 XB31 + 0.08 XB41 <= 0
14) - 0.94 XB11 + 0.26 XB21 - 2.14 XB31 + 0.16 XB41 <= 0
15) - 0.8 XB11 - 1.9 XB21 - 2.4 XB31 + 0.6 XB41 <= 0
16) 29 XB12 + 1201 XB22 - 2370 XB32 + 200 XB42 >= 0
17) - 0.06 XB12 + 0.25 XB22 - 0.52 XB32 + 0.08 XB42 <= 0
18) - 0.94 XB12 + 0.26 XB22 - 2.14 XB32 + 0.16 XB42 <= 0
19) - 0.8 XB12 - 1.9 XB22 - 2.4 XB32 + 0.6 XB42 <= 0
20) 29 XB13 + 1201 XB23 - 2370 XB33 + 200 XB43 >= 0
21) - 0.06 XB13 + 0.25 XB23 - 0.52 XB33 + 0.08 XB43 <= 0
22) - 0.94 XB13 + 0.26 XB23 - 2.14 XB33 + 0.16 XB43 <= 0
23) - 0.8 XB13 - 1.9 XB23 - 2.4 XB33 + 0.6 XB43 <= 0
24) 29 XB14 + 1201 XB24 - 2370 XB34 + 200 XB44 >= 0
25) - 0.06 XB14 + 0.25 XB24 - 0.52 XB34 + 0.08 XB44 <= 0
26) - 0.94 XB14 + 0.26 XB24 - 2.14 XB34 + 0.16 XB44 <= 0
27) - 0.8 XB14 - 1.9 XB24 - 2.4 XB34 + 0.6 XB44 <= 0
28) 29 XB15 + 1201 XB25 - 2370 XB35 + 200 XB45 >= 0
29) - 0.06 XB15 + 0.25 XB25 - 0.52 XB35 + 0.08 XB45 <= 0
30) - 0.94 XB15 + 0.26 XB25 - 2.14 XB35 + 0.16 XB45 <= 0
31) - 0.8 XB15 - 1.9 XB25 - 2.4 XB35 + 0.6 XB45 <= 0
32) 29 XB16 + 1201 XB26 - 2370 XB36 + 200 XB46 >= 0
33) - 0.06 XB16 + 0.25 XB26 - 0.52 XB36 + 0.08 XB46 <= 0
34) - 0.94 XB16 + 0.26 XB26 - 2.14 XB36 + 0.16 XB46 <= 0
35) - 0.8 XB16 - 1.9 XB26 - 2.4 XB36 + 0.6 XB46 <= 0
END
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