! Keywords: Airlines / Distribution / Network /
! RailRoad Industry / Routing / Scheduling / Shipping /
! Shortest Route / Transportation;
! Fleet routing and assignment with two plane types;
! We want to schedule planes to cover the following
! schedule of 11 flights that repeats every day.
! We have two plane types, A and B, to choose from.
! See the text Optimization Modeling with LINGO for more details.
! City Time
! Flight Depart Arrive Depart Arrive
! 1 221 ORD DEN 0800 0934
! 2 223 ORD DEN 0900 1039
! 3 274 LAX DEN 0800 1116
! 4 105 ORD LAX 1100 1314
! 5 228 DEN ORD 1100 1423
! 6 230 DEN ORD 1200 1521
! 7 259 ORD LAX 1400 1609
! 8 293 DEN LAX 1400 1510
! 9 412 LAX ORD 1400 1959
! 10 766 LAX DEN 1600 1912
! 11 238 DEN ORD 1800 2121
!
! Maximize profit contribution from flights covered;
MAX 105 F221A + 121 F221B + 109 F223A + 108 F223B
+ 110 F274A + 115 F274B + 130 F105A + 140 F105B
+ 106 F228A + 122 F228B + 112 F230A + 115 F230B
+ 132 F259A + 129 F259B + 115 F293A + 123 F293B
+ 133 F412A + 135 F412B + 108 F766A + 117 F766B
+ 116 F238A + 124 F238B
SUBJECT TO
! Conservation of flow constraints,
! for type A aircraft,
! Chicago at 8 am, sources - uses = 0;
2) - F221A - F223A - F105A - F259A - GC1400A + GC2400A = 0
! Chicago at midnight;
3) F228A + F230A + F412A + F238A + GC1400A - GC2400A = 0
! Denver at 11 am;
4) F221A + F223A - F228A - GD1100A + GD2400A = 0
! Denver at high noon;
5) F274A - F230A - F293A - F238A + GD1100A - GD1800A = 0
! Denver at midnight;
6) F766A - GD2400A + GD1800A = 0
! LA at 8 am;
7) - F274A - GL0800A + GL2400A = 0
! LA at 1400;
8) F105A - F412A + GL0800A - GL1400A = 0
! LA at 1600;
9) F293A - F766A + GL1400A - GL1600A = 0
! LA at midnight;
10) F259A - GL2400A + GL1600A = 0
! Aircraft type B, conservation of flow;
! Chicago at 8 am;
11) - F221B - F223B - F105B - F259B - GC1400B + GC2400B = 0
! Chicago at midnight;
12) F228B + F230B + F412B + F238B + GC1400B - GC2400B = 0
! Denver at 11 am;
13) F221B + F223B - F228B - GD1100B + GD2400B = 0
! Denver at high noon;
14) F274B - F230B - F293B - F238B + GD1100B - GD1800B = 0
! Denver at midnight;
15) F766B - GD2400B + GD1800B = 0
! LA at 8 am;
16) - F274B - GL0800B + GL2400B = 0
! LA at 1400;
17) F105B - F412B + GL0800B - GL1400B = 0
! LA at 1600;
18) F293B - F766B + GL1400B - GL1600B = 0
! LA at midnight;
19) F259B - GL2400B + GL1600B = 0
! Can put at most one plane on each flight;
20) F221A + F221B <= 1
21) F223A + F223B <= 1
22) F274A + F274B <= 1
23) F105A + F105B <= 1
24) F228A + F228B <= 1
25) F230A + F230B <= 1
26) F259A + F259B <= 1
27) F293A + F293B <= 1
28) F412A + F412B <= 1
29) F766A + F766B <= 1
30) F238A + F238B <= 1
! Fleet size of type B;
31) GC2400B + GD2400B + GL2400B <= 2
END
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