Jcg Case

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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.

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