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pythonconstraintspulp

pulp constraint: exactly N in a category, up to X of a second choice, same category

I have a problem I'm trying to solve for where I want N players from one team, and up to X players from a second team, but I don't particularly care which team fills those constraints. For example, if N=5 and X=2, I could have 5 from one team and up to 2 from a second, different, team. How would I write such a constraint?

example dataframe:

team pos name ceil salary
0 NYY OF Aaron Judge 21.6631 6500
1 HOU OF Yordan Alvarez 21.6404 6100
2 ATL OF Ronald Acuna Jr. 21.5363 5400
3 HOU OF Kyle Tucker 20.0992 4700
4 TOR 1B Vladimir Guerrero Jr. 20.0722 6000
5 LAD SS Trea Turner 20.0256 5700
6 LAD OF Mookie Betts 19.5231 6300
7 SEA OF Julio Rodriguez 19.3694 5200
8 MIN OF Byron Buxton 19.3412 5600
9 LAD 1B Freddie Freeman 19.3393 5600
10 TOR OF George Springer 19.1429 5100
11 NYM OF Starling Marte 19.0791 5200
12 ATL 1B Matt Olson 19.009 4800
13 ATL 3B Austin Riley 18.9091 5200
14 SF OF Austin Slater 18.9052 3700
15 NYM 1B Pete Alonso 18.8921 5700
16 TEX OF Adolis Garcia 18.7115 4200
17 TEX SS Corey Seager 18.6957 5100
18 TOR OF Teoscar Hernandez 18.6834 5200
19 CWS 1B Jose Abreu 18.497 4600
20 ATL SS Dansby Swanson 18.4679 4900
21 TEX 2B/SS Marcus Semien 18.4389 4100
22 NYY 1B Anthony Rizzo 18.4383 5300
23 NYY 2B Gleyber Torres 18.39 4500
24 CHC C Willson Contreras 18.3452 5800

existing code snippet:

        #problem definition
        prob = LpProblem(name="DFS", sense=LpMaximize)
        prob += lpSum(player_vars[i] * slate['ceil'].iloc[i] for i in player_ids), "FPTS"
        
        #salary and total player constraints
        prob += lpSum(player_vars[i] * slate['salary'].iloc[i] for i in player_ids) <= 50000, "Salary"
        prob += lpSum(player_vars[i] for i in player_ids) == 10, "Total Players"
        
        #position constraints
        prob += lpSum(player_vars[i] for i in player_ids if slate['pos'].iloc[i] == 'P') == 2, "Pitcher"
        prob += lpSum([player_vars[i] for i in player_ids if slate['name'].iloc[i] in slate['name'][slate['pos'].str.contains('C')].to_list()]) == 1, "Catcher"
        prob += lpSum([player_vars[i] for i in player_ids if slate['name'].iloc[i] in slate['name'][slate['pos'].str.contains('1B')].to_list()]) == 1, "1B"
        prob += lpSum([player_vars[i] for i in player_ids if slate['name'].iloc[i] in slate['name'][slate['pos'].str.contains('2B')].to_list()]) == 1, "2B"
        prob += lpSum([player_vars[i] for i in player_ids if slate['name'].iloc[i] in slate['name'][slate['pos'].str.contains('3B')].to_list()]) == 1, "3B"
        prob += lpSum([player_vars[i] for i in player_ids if slate['name'].iloc[i] in slate['name'][slate['pos'].str.contains('SS')].to_list()]) == 1, "SS"
        prob += lpSum([player_vars[i] for i in player_ids if slate['name'].iloc[i] in slate['name'][slate['pos'].str.contains('OF')].to_list()]) == 3, "OF"
        
       
        #no opposing pitcher constraint
        for pid in player_ids:
            if slate['pos'].iloc[pid] == 'P':
                prob += lpSum([player_vars[i] for i in player_ids if 
                    slate['team'].iloc[i] == slate['opp'].iloc[pid]] + [9 * player_vars[pid]]) <= 9, "P{pid}".format(pid=pid)

        #three team max constraint
        unique_teams = slate['team'].unique()
        player_in_team = slate['team'].str.get_dummies()        
        team_vars = LpVariable.dicts('team', unique_teams, cat = 'Binary')
        
        for team in unique_teams:
            prob += lpSum([player_in_team[team][i] * player_vars[i] for i in player_ids if slate['pos'].iloc[i] != 'P']) >= team_vars[team], "Team{team}Min".format(team=team)
            
        
        prob += lpSum(team_vars[team] for team in unique_teams) == 3, "3 Teams"
Solution

  • Here's how I would attack this... In pseudocode....

    1. make a set of teams that you can use to index a couple of new variables.

    2. Make subsets of your players grouped by team, or use pandas data frame filters to limit summations of players to the team of interest.

    3. Make 2 new variables, that are binary "indicator" variables, one call it use5from[team] and one called use[team] to indicate that the team has been used at all.

    4. Make appropriate constraints to link those to the selection variables. Something like:

    for team in teams:
    5 * use5from[team] <= pulp.lpSum(x[i] for i in team[i])
    1. And for the other, a constraint to indicate any use...

    for team in teams:
    use[team] <= pulp.lpSum(x[i] for i in team[I])
    1. And then make constraints that those two variables sum to over 1 and 3 respectively.