纸浆限制：至少一个团队满足最低标准

Question

I have a lineup generator where I'm trying to add a constraint where every lineup I generate has at least 3 players who belong to the same team.

For example: The generator has a total of 60 players to choose from (10 individuals from 6 different teams), I don't want the line up it builds (each lineup has 9 players) to be valid unless one of the teams is represented in at least 3 of the 9 positions.

I currently am able to ensure it does not allow more than 5 players from any team, but I'm unsure how to enforce the minimum from at least one team.

My current max per team constraint is as follows:

    used_team = [pulp.LpVariable("u{}".format(i + 1), cat="Binary") for i in range(self.num_teams)]
    for i in range(self.num_teams):
        prob += (used_team[i] <= pulp.lpSum(
            self.players_teams[k][i] * players_lineup[k] for k in range(self.num_players)))
        prob += (pulp.lpSum(self.players_teams[k][i] * players_lineup[k] for k in range(self.num_players)) <= max_per_team *
                    used_team[i])

Answer 1

The constraint you are giving is successfully forcing the used_team variable to be active when there are active players, bound these active players by the upper bound and forces used_team to be off when there are no active players.

To ensure your other constraint you will need to add an additional binary variable used_3_in_team for each team indicating whether the 3 players from that team are reached. Then you need to do something like the following to add the constraints.

for i in range(self.num_teams):
        prob += (3*used_3_in_team[i] <= pulp.lpSum(
            self.players_teams[k][i] * players_lineup[k] for k in range(self.num_players)))
prob += pulp.lpSum(self.used_3_in_team) >= 1

The first set of inequalities forces used_3_in_team to be only active when there are at least 3 players chosen. And the last inequality ensures at least one of the teams has at least 3 players active.

I hope this solves your problem.

As you did not provide a minimum working example I did not check my code, but I hope the idea is clear.