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QT-2 Assignment JCG Global Air Services Case 1)CE750 Decision Variables: X1: Fuel to be bought at KMLI (in pounds) X2: Fuel to be bought at KBOS (in pounds) X3: Fuel to be bought at KTEB (in pounds) X4: Fuel to be bought at KDAL (in pounds) X5: Fuel to be bought at KMLI (in pounds) Y1: Binary Variable defining whether ramp fee waved or not at KBOS Y2: Binary Variable defining whether ramp fee waved or not at KTEB Y3: Binary Variable defining whether ramp fee waved or not at KDAL Where, 1 means fee waved and 0 means fee not waved
Objective Function: Minimize total cost of travel Min, Z= (3.97X1+8.35X2+7.47X3+6.01X4+3.97X5)/6.7+(800Y1+450Y2+400Y 3)
Constraints Subject To:
Ramp Fee waiver: At KBOS: 500*6.7*(1-Y1) <=X2 At KTEB: 300*6.7*(1-Y2) <=X3 At KDAL: 350*6.7*(1-Y3) <=X4
Capacity of tank: At KMLI: 7000+X1<=13000 At KBOS: 7000+X1-4800+X2 <= 13000 At KTEB: 7000+X1-4800+X2-2000+X3 <=13000 At KDAL: 7000+X1-4800+X2-2000+X3-5300+X4<=13000 At KMLI: 7000+X1-4800+X2-2000+X3-5300+X4-3100<=13000 Minimum arrival fuel: At KBOS: 7000 + X1-4800>= 2400 At KTEB: 7000+X1-4800+X2-2000>= 2400 At KDAL: 7000 +X1-4800+X2-2000+X3-5300>= 2400 At KMLI: 7000+ X1-4800+X2-2000+X3-5300+X4-3100>=2400 Ramp weight: At KMLI: 22200+7000+X1+2*200<=36400 At KBOS: 22200+7000+X1-4800+X2+4*200<=36400 At KTEB: 22200+7000+X1-4800+X2-2800+X3+8*200<=36400 At KDAL: 22200+7000+X1-4800+X2-2800+X3-5300+X4+8*200<=36400 Landing weight: At KBOS: 22200+7000+X1-4800+2*200<=31800 At KTEB: 22200+7000+X1-4800+X2-2000+4*200<=31800 At KDAL: 22200+7000+X1-4800+X2-2000+X3-5300+8*200<=31800 At KMLI: 3100+8*200<=31800
22200+7000+X1-4800+X2-2000+X3-5300+X4-
Integer: X1, X2, X3, X4, X5,Y1, Y2, Y3 are integers.
Excel Snapshot:
X1 X2 X3 X4 X5 KMLI KBOS KTEB KDAL KMLI 6000 0 2010 2590 4600 3.97 8.35 7.47 6.01 3.97
Fuel to be bought Price of fuel ($/gallon) Ramp Fee Waiver Binary Variable Defining KBOS KTEB KDAL
1 0 0
Objective Function 11645. 16
Minimize Constraints Relation between X and Y – 0 2010 2345
0 2010 2590
13000 8200 8210 5500 7000
13000 13000 13000 13000 13000
8200 6200 2910 2400 Minimum Fuel on arrival at KMLI 7000
2400 2400 2400 2400
Fuel Tank constraints –
Minimum Fuel Constraints –
7000
800 450 400
Y1 Y2 Y3
Maximum Ramp Weight 35600 31200 32010 29300
36400 36400 36400 36400
30800 29200 26710 26200
31800 31800 31800 31800
Maximum Landing weight -
AnswerHence minimum fuel cost = $ 11,645.16 6000 pounds, 0 pounds, 2010 pounds, 2590 pounds, 4600 pounds of fuel have to be bought at KMLI, KBOS, KTEB, KDAL and KMLI.
2) Gulfstream GV Decision Variables: X1: Fuel to be bought at KMLI (in pounds) X2: Fuel to be bought at KBOS (in pounds) X3: Fuel to be bought at KTEB (in pounds) X4: Fuel to be bought at KDAL (in pounds) X5: Fuel to be bought at KMLI (in pounds) Y1: Binary Variable defining whether ramp fee waved or not at KBOS Y2: Binary Variable defining whether ramp fee waved or not at KTEB Y3: Binary Variable defining whether ramp fee waved or not at KDAL Where, 1 means fee waved and 0 means fee not waved Objective Function:
Min, Z=(3.97X1+8.35X2+7.47X3+6.01X4+3.97X5)/6.7+(800Y1+450Y2+4 00Y3)
Subject To: Constraints
Ramp Fee waiver: At KBOS: 500*6.7*(1-Y1) <=X2 At KTEB: 300*6.7*(1-Y2) <=X3 At KDAL: 350*6.7*(1-Y3) <=X4
Capacity of tank: At KMLI: 7000+X1<=41300 At KBOS: 7000+X1-6968+X2 <= 41300 At KTEB: 7000+X1-6968+X2-2903+X3 <=41300 At KDAL: 7000+X1-6968+X2-2903+X3-7694+X4<=41300 At KMLI: 7000+X1-6968+X2-2903+X3-7694+X4-4500<=41300
Minimum arrival fuel: At KBOS: 48800 + X1-4800>= 2400 At KTEB: 48800+X1-6968+X2-2903>= 2400 At KDAL: 48800 +X1-6968+X2-2903+X3-7694>= 2400 At KMLI: 48800+ X1-6968+X2-2903+X3-7694+X4-4500>=2400 Ramp weight: At KMLI: 48800+7000+X1+2*200<=90900 At KBOS: 48800+7000+X1-6968+X2+4*200<=90900 At KTEB: 48800+7000+X1-6968+X2-2903+X3+8*200<=90900
At KDAL: 48800+7000+X1-6968+X2-2903+X3-7694+X4+8*200<=90900 Landing weight: At KBOS: 22200+7000+X1-4800+2*200<=75300 At KTEB: 22200+7000+X1-4800+X2-2000+4*200<=75300 At KDAL: 22200+7000+X1-4800+X2-2000+X3-5300+8*200<=75300 At KMLI: 3100+8*200<=75300
22200+7000+X1-4800+X2-2000+X3-5300+X4-
Integer and Non-negativity: X1, X2, X3, X4, X5, Y1, Y2, Y3 are non-negative and integers.
Excel Snapshot:
Fuel to be bought Price of fuel ($/gallon) Ramp Fee Waiver Binary Variable Defining KBOS KTEB KDAL
Objective Function Minimize
Constraints Relation between X and Y –
Fuel Tank constraints –
Minimum Fuel Constraints –
Minimum Fuel on arrival at KMLI Maximum Ramp Weight -
Maximum Landing weight -
Answ erHenc e mini mum
fuel cost = $ 1649 0 2300 poun ds, 3350 poun ds, 3950 poun ds, 7300 poun ds, 0 poun ds of fuel have to be boug ht at KMLI, KBOS, KTEB, KDAL and KMLI.