A constraint is a condition that restricts which values or combinations of variables are feasible. In optimization, it defines a boundary that cannot be breached while another function is minimized or maximized. section 4.1
A roster-selection problem turns constraints into explicit requirements:
- Sign exactly five free agents. section 4.1
- Select one point guard, shooting guard, center, power forward, and small forward. section 4.1
- Keep combined annual salaries at or below $90 million. section 4.6
- Keep the selected group’s average age at or below 30. section 4.6
Choosing an NBA roster
The team is not simply looking for the five highest-rated free agents. It is looking for the strongest group that satisfies every restriction simultaneously. This separates feasible combinations from choices that exceed the salary limit, miss a position, select too many or too few players, or produce an excessive average age. section 4.0 section 4.6
Table 4.1 List of available free agents (view table figure)
Use the free-agent table to compare candidate ages, positions, salaries, and win shares before testing combinations against the constraints. section 4.6
