operations research question

QUESTION 1) To simplify the following problem, let's assume that your team plays a special version of the basketball game under following rules. The basketball court is divided into eight zones. As can be seen in the following figure, one of the two assigned players may possess ball at each zone (e.g. only Players A or B may possess ball at Zone 2). ZONE 1 ZONE 2 ZONE 3 ZONE 4 A-B A-D A-C ZONE 5 ZONE 6 ZONE 7 B-E D-E C-E ZOMER In this special game, a player is not allowed to dribble the basketball out of the zone s/he stands. The player should pass the basketball to another player at a neighbor zone only and then s/he may go to any other zone. A zone is considered to be a neighbor zone if it is next to another one in vertical or diagonal positions toward the basketball rim: neighbor zones of Zone 1 are Zones 2, 3, and 4: neighbor zones of Zone 2 are Zones 5 and 6: neighbor zones of Zone 3 are Zones 5, 6 and 7: neighbor zones of Zone 4 ore Zones 6 and 7: neighbor zone of Zone 5 is Zone 8; neighbor zone of Zone 6 is Zone 8: neighbor zone of Zone 7 is Zone 8. Please notice that a player cannot be at more than one zone at the same time (i.e. cannot pass herself/himself) In the beginning, Player A or B will possess the basketball at Zone 1 and then passes the basketball to a player at Zones 2, 3, or 4. Then, the player who takes the basketball will pass the basketball to a player at a neighbor zone only. The player who takes the basketball at that moment passes the basketball to a player at Zone 8 and finally that player at Zone 8 takes the basketball and shoots into the basket. The statistical data on the passing performance (passes completed / passes attempted) of each player in each possible direction are given in the following table. Vertical Diagonal 95% 98% 93% 95% 100% 88% B D E 97% 83% 96% 100% The shooting performance of Player Dat Zone 8 is 72% and that of Player E is 84%. a) (20 pts.) Formulate an Integer Programming model to find a route which gets the basketball from Zone 1 to the basketball rim to maximize the average performance value of players on the court. Formulate your model in opened form (there is no need to use and V notations). QUESTION 1) To simplify the following problem, let's assume that your team plays a special version of the basketball game under following rules. The basketball court is divided into eight zones. As can be seen in the following figure, one of the two assigned players may possess ball at each zone (e.g. only Players A or B may possess ball at Zone 2). ZONE 1 ZONE 2 ZONE 3 ZONE 4 A-B A-D A-C ZONE 5 ZONE 6 ZONE 7 B-E D-E C-E ZOMER In this special game, a player is not allowed to dribble the basketball out of the zone s/he stands. The player should pass the basketball to another player at a neighbor zone only and then s/he may go to any other zone. A zone is considered to be a neighbor zone if it is next to another one in vertical or diagonal positions toward the basketball rim: neighbor zones of Zone 1 are Zones 2, 3, and 4: neighbor zones of Zone 2 are Zones 5 and 6: neighbor zones of Zone 3 are Zones 5, 6 and 7: neighbor zones of Zone 4 ore Zones 6 and 7: neighbor zone of Zone 5 is Zone 8; neighbor zone of Zone 6 is Zone 8: neighbor zone of Zone 7 is Zone 8. Please notice that a player cannot be at more than one zone at the same time (i.e. cannot pass herself/himself) In the beginning, Player A or B will possess the basketball at Zone 1 and then passes the basketball to a player at Zones 2, 3, or 4. Then, the player who takes the basketball will pass the basketball to a player at a neighbor zone only. The player who takes the basketball at that moment passes the basketball to a player at Zone 8 and finally that player at Zone 8 takes the basketball and shoots into the basket. The statistical data on the passing performance (passes completed / passes attempted) of each player in each possible direction are given in the following table. Vertical Diagonal 95% 98% 93% 95% 100% 88% B D E 97% 83% 96% 100% The shooting performance of Player Dat Zone 8 is 72% and that of Player E is 84%. a) (20 pts.) Formulate an Integer Programming model to find a route which gets the basketball from Zone 1 to the basketball rim to maximize the average performance value of players on the court. Formulate your model in opened form (there is no need to use and V notations)