Question

Aircraft companies had very difficult times during the pandemic period. In Turkey, Turkish Airlines (THY), Pegasus (PG) and Onur Airlines (OHY) have created some advantages for their loyal customers, especially for the Istanbul-Ankara flight. THY provides 1250 points (flight miles) for each flight to its customers flying from Istanbul to Ankara. However, it gives 4000 (flight miles) extra points to more than 4 flights and 10000 (flight miles) to more than 8 flights within six months. While PG gives 1400 points (flight miles) for each flight, it gives 8000 (flight miles) extra points for every 6 flights within six months. On the other hand, OHY gives 1350 points (flight miles) for each flight, but within 6 months, it gives 5000 (flight miles) extra points for more than 5 flights and 12500 (flight miles) extra points for more than 10 flights. For a person who wants to make an Istanbul-ankara flight 25 times in the next six months, please create an integer programming model to maximize flight miles. (Create only the ILP model, do not solve the problem)

Answer 1

Xp24-1, If Yp> 24,othes, wise Yp2420 Answer:. Decision variables Let It be the no. of flights, the peason should rake Using thy cialines make of flights, the peason using PH aialines Xo be the no-of flights, using oty should Xp be the the peason should make adlines xty 1 af 74, otheswise Xtu :0 X+8=1, it X478, otherwise 48 = 0 Xp6a1, af xp 7=6, otheSwise upb=0 Xp12:1, 7? Xp>=12, othea wise Xp12-0 Xp18=1, If Xp>= 12 others wisexpl8 :o Xo5=1, IL Xpas, othe Gwise you =0 Xolo = 1, it Xpxo, (the swise X10:0 Objective funciona Max 1250x4 +1400%p + 13504 + 4000'+y +1000074? + 8000 Xp6+ 16000 Xp12 + 94000Xp12 + 32000 Xp24 + 5000 X5 + 12500 to lo.

Constraints' X+-5X44 >=0 fihy airlines Caflesion Ps more than 4 flights which means minimum of s : flights will icon 4000 Echa poirls) XE - 9X28>=0 4414180 ttu 7 448231 xp - 6xp6>=0 Xp-12Xp12 >=0 Xp-184 p18>0 Xp-424 Xp24 >=0 Xp6 + Xp12 tX p18TXp24 L=1 Xo - 6x05 >=0 X6 -11x60 2-0 Xos +80 10 L=1 , Xo >=0 XL ,XP, itu , 448, Xp 6, Xp12,Xp 18Xp24, X05, Yolo = = 30,1? Chinosy vorables).

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