World Cup Team Selection – Integer Optimization Problem A na…
Questions
Wоrld Cup Teаm Selectiоn – Integer Optimizаtiоn Problem A nаtional team preparing for the FIFA World Cup must select a final 23-player squad from a pool of candidates. Each player has a position, an expected performance rating, and a salary cost. The coaching staff aims to maximize total team performance while meeting roster and budget constraints. Player Position Performance Score Salary ($M) P1 Forward 92 12 P2 Forward 88 10 P3 Midfield 90 11 P4 Midfield 85 8 P5 Defense 87 9 P6 Defense 83 7 P7 Defense 80 6 P8 Goalkeeper 91 10 P9 Goalkeeper 84 7 Requirements The team must satisfy the following constraints: Exactly 1 goalkeeper must be selected At least 3 defenders must be selected At least 2 midfielders must be selected At least 2 forwards must be selected Total salary budget cannot exceed $60M Decision Variables Let: xᵢ = 1 if player i is selected, 0 otherwise Part 1 - Formulate the integer programming model. Provide the objective function and constraints. Part 2 - Solve the objective function.
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