PuLP linear programming problem is infeasible
Question:
I am writing a Linear Programming problem to help generate daily fantasy lineups.
The goal is:
- Maximize Fpts projection
The constraints are:
- Salary (Maximum 50,000)
- Positionality (Have to have 1 PG, 1 SG, 1 SF, 1 PF, 1 C, 1 G, 1 F and 1 UTIL player) where "G" players are either PG or SG, "F" are either SF or PF players, and "UTIL" are any position players
I have my problem set up like this:
# Create problem
prob = plp.LpProblem("NBA_DK", plp.LpMaximize)
# Objective function
prob += plp.lpSum([fpts[i] * player_vars[i] for i in players]), 'Objective - Maximize Fpts'
# Salary constraint
prob += plp.lpSum([salaries[i] * player_vars[i] for i in players]) <= 50000, 'Salary Constraints'
# Position constraints
for curr_pos in ['PG', 'SG', 'SF', 'PF', 'C', 'G', 'F', 'UTIL']:
prob += plp.lpSum([player_vars[player] for player in players if curr_pos in positions[player]]) == 1, f'{curr_pos} Positional Constraint'
Here are some of the example variables being referenced above
player_vars
player_vars = plp.LpVariable.dicts("Players", players, lowBound=0, cat='Binary')
projections
projections = pd.read_csv('../dk_data/projections.csv', thousands=',')
...
Name Fpts Position Team Opponent Minutes Salary Pts/$ Value
0 Nikola Jokic 61.52 C/UTIL DEN LAL 33.9 11700 5.26 3.02
1 Giannis Antetokounmpo 58.09 PF/C/F/UTIL MIL NYK 36.1 12000 4.84 -1.91
2 LeBron James 53.05 SF/PF/F/UTIL LAL DEN 35.4 10900 4.87 -1.45
3 Jayson Tatum 52.94 SF/PF/F/UTIL BOS CHI 37.1 10700 4.95 -0.56
4 Domantas Sabonis 52.62 C/UTIL SAC ORL 36.7 10500 5.01 0.12
5 Ja Morant 51.01 PG/G/UTIL MEM SAS 32.6 10300 4.95 -0.49
6 Julius Randle 49.74 PF/F/UTIL NYK MIL 38.0 10400 4.78 -2.26
7 Kristaps Porzingis 44.76 PF/C/F/UTIL WAS NOP 35.0 9400 4.76 -2.24
8 De'Aaron Fox 43.40 PG/G/UTIL SAC ORL 35.3 8700 4.99 -0.10
9 DeMar DeRozan 43.21 SF/PF/F/UTIL CHI BOS 36.8 9000 4.80 -1.79
10 Jaylen Brown 42.45 SG/SF/G/F/UTIL BOS CHI 33.7 9500 4.47 -5.05
11 CJ McCollum 42.05 PG/G/UTIL NOP WAS 35.0 8500 4.95 -0.45
12 Jalen Brunson 41.20 PG/G/UTIL NYK MIL 36.2 8100 5.09 0.70
13 Paolo Banchero 40.34 SF/PF/F/UTIL ORL SAC 34.3 8200 4.92 -0.66
14 Kyle Kuzma 39.88 SF/PF/F/UTIL WAS NOP 34.8 8400 4.75 -2.12
15 Nikola Vucevic 37.51 C/UTIL CHI BOS 32.0 8000 4.69 -2.49
16 Zach LaVine 37.45 SG/SF/G/F/UTIL CHI BOS 34.9 7500 4.99 -0.05
17 Russell Westbrook 37.11 PG/G/UTIL LAL DEN 28.9 7700 4.82 -1.39
18 Jaren Jackson Jr. 36.08 PF/C/F/UTIL MEM SAS 28.3 6800 5.31 2.08
19 Keldon Johnson 35.44 SF/F/UTIL SAS MEM 31.7 7000 5.06 0.44
20 Jrue Holiday 35.32 PG/G/UTIL MIL NYK 32.4 7400 4.77 -1.68
21 Desmond Bane 35.18 SG/G/UTIL MEM SAS 29.2 6600 5.33 2.18
22 Jonas Valanciunas 34.71 C/UTIL NOP WAS 26.4 6600 5.26 1.71
23 Jamal Murray 34.59 PG/G/UTIL DEN LAL 31.9 6800 5.09 0.59
24 Tre Jones 32.40 PG/G/UTIL SAS MEM 30.2 6000 5.40 2.40
25 Aaron Gordon 32.37 PF/F/UTIL DEN LAL 30.1 6600 4.90 -0.63
26 Franz Wagner 32.13 SG/SF/G/F/UTIL ORL SAC 35.1 7100 4.53 -3.37
27 Jakob Poeltl 31.88 C/UTIL SAS MEM 25.8 5900 5.40 2.38
28 Thomas Bryant 31.78 C/UTIL LAL DEN 29.9 6300 5.05 0.28
29 Immanuel Quickley 31.78 PG/SG/G/UTIL NYK MIL 35.9 6200 5.13 0.78
30 Wendell Carter Jr. 31.64 C/UTIL ORL SAC 29.8 6400 4.94 -0.36
31 Steven Adams 29.50 C/UTIL MEM SAS 27.6 6000 4.92 -0.50
32 Naji Marshall 29.14 SF/PF/F/UTIL NOP WAS 34.1 5500 5.30 1.64
33 Michael Porter Jr. 29.10 SF/F/UTIL DEN LAL 29.7 5900 4.93 -0.40
34 Markelle Fultz 29.02 PG/G/UTIL ORL SAC 28.8 6100 4.76 -1.48
35 Bobby Portis 28.49 PF/C/F/UTIL MIL NYK 27.1 6700 4.25 -5.01
36 Kevin Huerter 28.25 SG/SF/G/F/UTIL SAC ORL 32.9 5700 4.96 -0.25
37 Mitchell Robinson 27.48 C/UTIL NYK MIL 29.9 5200 5.28 1.48
38 Malcolm Brogdon 27.16 PG/SG/G/UTIL BOS CHI 24.5 5300 5.12 0.66
39 Dennis Schroder 27.07 PG/G/UTIL LAL DEN 34.6 5700 4.75 -1.43
40 Harrison Barnes 26.88 SF/PF/F/UTIL SAC ORL 32.9 5600 4.80 -1.12
41 Dillon Brooks 26.32 SG/SF/G/F/UTIL MEM SAS 29.1 5800 4.54 -2.68
42 Daniel Gafford 26.22 C/UTIL WAS NOP 24.7 4700 5.58 2.72
43 Brook Lopez 25.35 C/UTIL MIL NYK 28.6 5700 4.45 -3.15
44 Monte Morris 25.13 PG/G/UTIL WAS NOP 27.9 4800 5.23 1.13
45 Jeremy Sochan 25.10 PF/F/UTIL SAS MEM 28.6 5000 5.02 0.10
46 Cole Anthony 25.07 PG/SG/G/UTIL ORL SAC 26.7 5200 4.82 -0.93
47 Derrick White 24.74 PG/SG/G/UTIL BOS CHI 28.7 5100 4.85 -0.76
48 Bones Hyland 24.70 PG/SG/G/UTIL DEN LAL 21.8 4900 5.04 0.20
49 Malik Monk 23.98 SG/G/UTIL SAC ORL 22.1 4500 5.33 1.48
50 Robert Williams 23.88 C/UTIL BOS CHI 21.8 4400 5.43 1.88
51 Al Horford 23.51 PF/C/F/UTIL BOS CHI 29.0 4800 4.90 -0.49
52 Quentin Grimes 23.48 SG/SF/G/F/UTIL NYK MIL 34.4 5400 4.35 -3.52
53 Rui Hachimura 23.25 PF/F/UTIL WAS NOP 24.5 4700 4.95 -0.25
54 Herbert Jones 23.16 SF/F/UTIL NOP WAS 27.5 4900 4.73 -1.34
55 Deni Avdija 22.61 SF/F/UTIL WAS NOP 25.7 4200 5.38 1.61
56 Trey Murphy III 22.56 SG/SF/G/F/UTIL NOP WAS 28.2 5100 4.42 -2.94
57 Patrick Williams 21.92 SF/PF/F/UTIL CHI BOS 30.6 4400 4.98 -0.08
58 Kentavious Caldwell-Pope 21.74 SG/G/UTIL DEN LAL 31.3 4400 4.94 -0.26
59 Josh Richardson 21.62 PG/SG/G/UTIL SAS MEM 21.7 4000 5.40 1.62
60 Keegan Murray 21.61 PF/F/UTIL SAC ORL 27.8 4300 5.03 0.11
61 Bruce Brown 21.01 SG/SF/G/F/UTIL DEN LAL 24.2 5000 4.20 -3.99
62 Moritz Wagner 20.30 PF/C/F/UTIL ORL SAC 19.5 5300 3.83 -6.20
63 Zach Collins 20.08 C/UTIL SAS MEM 17.9 4700 4.27 -3.42
players
players = list(projections['Name'])
fpts, salaries, positions
salaries = dict(zip(players, projections['Salary']))
fpts = dict(zip(players, projections['Fpts']))
positions = dict(zip(players, projections['Position']))
Here is my prob.writeLP() output:
* NBA_DK *
Maximize
OBJ: 32.37 Players_Aaron_Gordon + 23.51 Players_Al_Horford
+ 28.49 Players_Bobby_Portis + 24.7 Players_Bones_Hyland
+ 25.35 Players_Brook_Lopez + 21.01 Players_Bruce_Brown
+ 42.05 Players_CJ_McCollum + 25.07 Players_Cole_Anthony
+ 26.22 Players_Daniel_Gafford + 43.4 Players_De'Aaron_Fox
+ 43.21 Players_DeMar_DeRozan + 22.61 Players_Deni_Avdija
+ 27.07 Players_Dennis_Schroder + 24.74 Players_Derrick_White
+ 35.18 Players_Desmond_Bane + 26.32 Players_Dillon_Brooks
+ 52.62 Players_Domantas_Sabonis + 32.13 Players_Franz_Wagner
+ 58.09 Players_Giannis_Antetokounmpo + 26.88 Players_Harrison_Barnes
+ 23.16 Players_Herbert_Jones + 31.78 Players_Immanuel_Quickley
+ 51.01 Players_Ja_Morant + 31.88 Players_Jakob_Poeltl
+ 41.2 Players_Jalen_Brunson + 34.59 Players_Jamal_Murray
+ 36.08 Players_Jaren_Jackson_Jr. + 42.45 Players_Jaylen_Brown
+ 52.94 Players_Jayson_Tatum + 25.1 Players_Jeremy_Sochan
+ 34.71 Players_Jonas_Valanciunas + 21.62 Players_Josh_Richardson
+ 35.32 Players_Jrue_Holiday + 49.74 Players_Julius_Randle
+ 21.61 Players_Keegan_Murray + 35.44 Players_Keldon_Johnson
+ 21.74 Players_Kentavious_Caldwell_Pope + 28.25 Players_Kevin_Huerter
+ 44.76 Players_Kristaps_Porzingis + 39.88 Players_Kyle_Kuzma
+ 53.05 Players_LeBron_James + 27.16 Players_Malcolm_Brogdon
+ 23.98 Players_Malik_Monk + 29.02 Players_Markelle_Fultz
+ 29.1 Players_Michael_Porter_Jr. + 27.48 Players_Mitchell_Robinson
+ 25.13 Players_Monte_Morris + 20.3 Players_Moritz_Wagner
+ 29.14 Players_Naji_Marshall + 61.52 Players_Nikola_Jokic
+ 37.51 Players_Nikola_Vucevic + 40.34 Players_Paolo_Banchero
+ 21.92 Players_Patrick_Williams + 23.48 Players_Quentin_Grimes
+ 23.88 Players_Robert_Williams + 23.25 Players_Rui_Hachimura
+ 37.11 Players_Russell_Westbrook + 29.5 Players_Steven_Adams
+ 31.78 Players_Thomas_Bryant + 32.4 Players_Tre_Jones
+ 22.56 Players_Trey_Murphy_III + 31.64 Players_Wendell_Carter_Jr.
+ 20.08 Players_Zach_Collins + 37.45 Players_Zach_LaVine
Subject To
C_Positional_Constraint: Players_Al_Horford + Players_Bobby_Portis
+ Players_Brook_Lopez + Players_Daniel_Gafford + Players_Domantas_Sabonis
+ Players_Giannis_Antetokounmpo + Players_Jakob_Poeltl
+ Players_Jaren_Jackson_Jr. + Players_Jonas_Valanciunas
+ Players_Kristaps_Porzingis + Players_Mitchell_Robinson
+ Players_Moritz_Wagner + Players_Nikola_Jokic + Players_Nikola_Vucevic
+ Players_Robert_Williams + Players_Steven_Adams + Players_Thomas_Bryant
+ Players_Wendell_Carter_Jr. + Players_Zach_Collins = 1
F_Positional_Constraint: Players_Aaron_Gordon + Players_Al_Horford
+ Players_Bobby_Portis + Players_Bruce_Brown + Players_DeMar_DeRozan
+ Players_Deni_Avdija + Players_Dillon_Brooks + Players_Franz_Wagner
+ Players_Giannis_Antetokounmpo + Players_Harrison_Barnes
+ Players_Herbert_Jones + Players_Jaren_Jackson_Jr. + Players_Jaylen_Brown
+ Players_Jayson_Tatum + Players_Jeremy_Sochan + Players_Julius_Randle
+ Players_Keegan_Murray + Players_Keldon_Johnson + Players_Kevin_Huerter
+ Players_Kristaps_Porzingis + Players_Kyle_Kuzma + Players_LeBron_James
+ Players_Michael_Porter_Jr. + Players_Moritz_Wagner + Players_Naji_Marshall
+ Players_Paolo_Banchero + Players_Patrick_Williams + Players_Quentin_Grimes
+ Players_Rui_Hachimura + Players_Trey_Murphy_III + Players_Zach_LaVine = 1
G_Positional_Constraint: Players_Bones_Hyland + Players_Bruce_Brown
+ Players_CJ_McCollum + Players_Cole_Anthony + Players_De'Aaron_Fox
+ Players_Dennis_Schroder + Players_Derrick_White + Players_Desmond_Bane
+ Players_Dillon_Brooks + Players_Franz_Wagner + Players_Immanuel_Quickley
+ Players_Ja_Morant + Players_Jalen_Brunson + Players_Jamal_Murray
+ Players_Jaylen_Brown + Players_Josh_Richardson + Players_Jrue_Holiday
+ Players_Kentavious_Caldwell_Pope + Players_Kevin_Huerter
+ Players_Malcolm_Brogdon + Players_Malik_Monk + Players_Markelle_Fultz
+ Players_Monte_Morris + Players_Quentin_Grimes + Players_Russell_Westbrook
+ Players_Tre_Jones + Players_Trey_Murphy_III + Players_Zach_LaVine = 1
PF_Positional_Constraint: Players_Aaron_Gordon + Players_Al_Horford
+ Players_Bobby_Portis + Players_DeMar_DeRozan
+ Players_Giannis_Antetokounmpo + Players_Harrison_Barnes
+ Players_Jaren_Jackson_Jr. + Players_Jayson_Tatum + Players_Jeremy_Sochan
+ Players_Julius_Randle + Players_Keegan_Murray + Players_Kristaps_Porzingis
+ Players_Kyle_Kuzma + Players_LeBron_James + Players_Moritz_Wagner
+ Players_Naji_Marshall + Players_Paolo_Banchero + Players_Patrick_Williams
+ Players_Rui_Hachimura = 1
PG_Positional_Constraint: Players_Bones_Hyland + Players_CJ_McCollum
+ Players_Cole_Anthony + Players_De'Aaron_Fox + Players_Dennis_Schroder
+ Players_Derrick_White + Players_Immanuel_Quickley + Players_Ja_Morant
+ Players_Jalen_Brunson + Players_Jamal_Murray + Players_Josh_Richardson
+ Players_Jrue_Holiday + Players_Malcolm_Brogdon + Players_Markelle_Fultz
+ Players_Monte_Morris + Players_Russell_Westbrook + Players_Tre_Jones = 1
SF_Positional_Constraint: Players_Bruce_Brown + Players_DeMar_DeRozan
+ Players_Deni_Avdija + Players_Dillon_Brooks + Players_Franz_Wagner
+ Players_Harrison_Barnes + Players_Herbert_Jones + Players_Jaylen_Brown
+ Players_Jayson_Tatum + Players_Keldon_Johnson + Players_Kevin_Huerter
+ Players_Kyle_Kuzma + Players_LeBron_James + Players_Michael_Porter_Jr.
+ Players_Naji_Marshall + Players_Paolo_Banchero + Players_Patrick_Williams
+ Players_Quentin_Grimes + Players_Trey_Murphy_III + Players_Zach_LaVine = 1
SG_Positional_Constraint: Players_Bones_Hyland + Players_Bruce_Brown
+ Players_Cole_Anthony + Players_Derrick_White + Players_Desmond_Bane
+ Players_Dillon_Brooks + Players_Franz_Wagner + Players_Immanuel_Quickley
+ Players_Jaylen_Brown + Players_Josh_Richardson
+ Players_Kentavious_Caldwell_Pope + Players_Kevin_Huerter
+ Players_Malcolm_Brogdon + Players_Malik_Monk + Players_Quentin_Grimes
+ Players_Trey_Murphy_III + Players_Zach_LaVine = 1
Salary_Constraints: 6600 Players_Aaron_Gordon + 4800 Players_Al_Horford
+ 6700 Players_Bobby_Portis + 4900 Players_Bones_Hyland
+ 5700 Players_Brook_Lopez + 5000 Players_Bruce_Brown
+ 8500 Players_CJ_McCollum + 5200 Players_Cole_Anthony
+ 4700 Players_Daniel_Gafford + 8700 Players_De'Aaron_Fox
+ 9000 Players_DeMar_DeRozan + 4200 Players_Deni_Avdija
+ 5700 Players_Dennis_Schroder + 5100 Players_Derrick_White
+ 6600 Players_Desmond_Bane + 5800 Players_Dillon_Brooks
+ 10500 Players_Domantas_Sabonis + 7100 Players_Franz_Wagner
+ 12000 Players_Giannis_Antetokounmpo + 5600 Players_Harrison_Barnes
+ 4900 Players_Herbert_Jones + 6200 Players_Immanuel_Quickley
+ 10300 Players_Ja_Morant + 5900 Players_Jakob_Poeltl
+ 8100 Players_Jalen_Brunson + 6800 Players_Jamal_Murray
+ 6800 Players_Jaren_Jackson_Jr. + 9500 Players_Jaylen_Brown
+ 10700 Players_Jayson_Tatum + 5000 Players_Jeremy_Sochan
+ 6600 Players_Jonas_Valanciunas + 4000 Players_Josh_Richardson
+ 7400 Players_Jrue_Holiday + 10400 Players_Julius_Randle
+ 4300 Players_Keegan_Murray + 7000 Players_Keldon_Johnson
+ 4400 Players_Kentavious_Caldwell_Pope + 5700 Players_Kevin_Huerter
+ 9400 Players_Kristaps_Porzingis + 8400 Players_Kyle_Kuzma
+ 10900 Players_LeBron_James + 5300 Players_Malcolm_Brogdon
+ 4500 Players_Malik_Monk + 6100 Players_Markelle_Fultz
+ 5900 Players_Michael_Porter_Jr. + 5200 Players_Mitchell_Robinson
+ 4800 Players_Monte_Morris + 5300 Players_Moritz_Wagner
+ 5500 Players_Naji_Marshall + 11700 Players_Nikola_Jokic
+ 8000 Players_Nikola_Vucevic + 8200 Players_Paolo_Banchero
+ 4400 Players_Patrick_Williams + 5400 Players_Quentin_Grimes
+ 4400 Players_Robert_Williams + 4700 Players_Rui_Hachimura
+ 7700 Players_Russell_Westbrook + 6000 Players_Steven_Adams
+ 6300 Players_Thomas_Bryant + 6000 Players_Tre_Jones
+ 5100 Players_Trey_Murphy_III + 6400 Players_Wendell_Carter_Jr.
+ 4700 Players_Zach_Collins + 7500 Players_Zach_LaVine <= 50000
UTIL_Positional_Constraint: Players_Aaron_Gordon + Players_Al_Horford
+ Players_Bobby_Portis + Players_Bones_Hyland + Players_Brook_Lopez
+ Players_Bruce_Brown + Players_CJ_McCollum + Players_Cole_Anthony
+ Players_Daniel_Gafford + Players_De'Aaron_Fox + Players_DeMar_DeRozan
+ Players_Deni_Avdija + Players_Dennis_Schroder + Players_Derrick_White
+ Players_Desmond_Bane + Players_Dillon_Brooks + Players_Domantas_Sabonis
+ Players_Franz_Wagner + Players_Giannis_Antetokounmpo
+ Players_Harrison_Barnes + Players_Herbert_Jones + Players_Immanuel_Quickley
+ Players_Ja_Morant + Players_Jakob_Poeltl + Players_Jalen_Brunson
+ Players_Jamal_Murray + Players_Jaren_Jackson_Jr. + Players_Jaylen_Brown
+ Players_Jayson_Tatum + Players_Jeremy_Sochan + Players_Jonas_Valanciunas
+ Players_Josh_Richardson + Players_Jrue_Holiday + Players_Julius_Randle
+ Players_Keegan_Murray + Players_Keldon_Johnson
+ Players_Kentavious_Caldwell_Pope + Players_Kevin_Huerter
+ Players_Kristaps_Porzingis + Players_Kyle_Kuzma + Players_LeBron_James
+ Players_Malcolm_Brogdon + Players_Malik_Monk + Players_Markelle_Fultz
+ Players_Michael_Porter_Jr. + Players_Mitchell_Robinson
+ Players_Monte_Morris + Players_Moritz_Wagner + Players_Naji_Marshall
+ Players_Nikola_Jokic + Players_Nikola_Vucevic + Players_Paolo_Banchero
+ Players_Patrick_Williams + Players_Quentin_Grimes + Players_Robert_Williams
+ Players_Rui_Hachimura + Players_Russell_Westbrook + Players_Steven_Adams
+ Players_Thomas_Bryant + Players_Tre_Jones + Players_Trey_Murphy_III
+ Players_Wendell_Carter_Jr. + Players_Zach_Collins + Players_Zach_LaVine = 1
Binaries
Players_Aaron_Gordon
Players_Al_Horford
Players_Bobby_Portis
Players_Bones_Hyland
Players_Brook_Lopez
Players_Bruce_Brown
Players_CJ_McCollum
Players_Cole_Anthony
Players_Daniel_Gafford
Players_De'Aaron_Fox
Players_DeMar_DeRozan
Players_Deni_Avdija
Players_Dennis_Schroder
Players_Derrick_White
Players_Desmond_Bane
Players_Dillon_Brooks
Players_Domantas_Sabonis
Players_Franz_Wagner
Players_Giannis_Antetokounmpo
Players_Harrison_Barnes
Players_Herbert_Jones
Players_Immanuel_Quickley
Players_Ja_Morant
Players_Jakob_Poeltl
Players_Jalen_Brunson
Players_Jamal_Murray
Players_Jaren_Jackson_Jr.
Players_Jaylen_Brown
Players_Jayson_Tatum
Players_Jeremy_Sochan
Players_Jonas_Valanciunas
Players_Josh_Richardson
Players_Jrue_Holiday
Players_Julius_Randle
Players_Keegan_Murray
Players_Keldon_Johnson
Players_Kentavious_Caldwell_Pope
Players_Kevin_Huerter
Players_Kristaps_Porzingis
Players_Kyle_Kuzma
Players_LeBron_James
Players_Malcolm_Brogdon
Players_Malik_Monk
Players_Markelle_Fultz
Players_Michael_Porter_Jr.
Players_Mitchell_Robinson
Players_Monte_Morris
Players_Moritz_Wagner
Players_Naji_Marshall
Players_Nikola_Jokic
Players_Nikola_Vucevic
Players_Paolo_Banchero
Players_Patrick_Williams
Players_Quentin_Grimes
Players_Robert_Williams
Players_Rui_Hachimura
Players_Russell_Westbrook
Players_Steven_Adams
Players_Thomas_Bryant
Players_Tre_Jones
Players_Trey_Murphy_III
Players_Wendell_Carter_Jr.
Players_Zach_Collins
Players_Zach_LaVine
End
When trying to .solve() this problem`:
prob.solve(plp.PULP_CBC_CMD(msg=0))
print(f'Status: {plp.LpStatus[prob.status]}')
score = str(prob.objective)
for v in prob.variables():
score = score.replace(v.name, str(v.varValue))
score = eval(score)
lineup = [v.name for v in prob.variables() if v.varValue != 0]
print(score, lineup)
it outputs:
Status: Infeasible
23.570000000000004 ['Players_Giannis_Antetokounmpo', 'Players_Immanuel_Quickley', 'Players_Ja_Morant', 'Players_Jaylen_Brown', 'Players_Malcolm_Brogdon']
I know the issue lies within the positionality constraints, because commenting them out or altering them produces an optimal result.
Answers:
You’ll need to re-index your problem with a second index such that the assignment binary variable is as:
assign[player, position]
currently you are double/triple counting people which is leading to the infeasibility. Specifically, if player X can play 3 positions, you are (inadvertently) assigning them to play all 3 positions at once, so when you total up by position the result is > 1, which busts your position constraint.
After you change your variable, then it will be easy to also sum across all positions for each player and ensure they are only assigned once, which will address the second issue of avoiding multiple assignments where feasible.
This is pretty similar, with an added twist, but is shows most of the general construct:
Python PULP optimization – Limiting total number of one variable chosen
And this:
Python PULP – Positional Constraints for a Lineup Generator
(I guess I’ve looked at a couple of these fantasy teams!)
I am writing a Linear Programming problem to help generate daily fantasy lineups.
The goal is:
- Maximize Fpts projection
The constraints are:
- Salary (Maximum 50,000)
- Positionality (Have to have 1 PG, 1 SG, 1 SF, 1 PF, 1 C, 1 G, 1 F and 1 UTIL player) where "G" players are either PG or SG, "F" are either SF or PF players, and "UTIL" are any position players
I have my problem set up like this:
# Create problem
prob = plp.LpProblem("NBA_DK", plp.LpMaximize)
# Objective function
prob += plp.lpSum([fpts[i] * player_vars[i] for i in players]), 'Objective - Maximize Fpts'
# Salary constraint
prob += plp.lpSum([salaries[i] * player_vars[i] for i in players]) <= 50000, 'Salary Constraints'
# Position constraints
for curr_pos in ['PG', 'SG', 'SF', 'PF', 'C', 'G', 'F', 'UTIL']:
prob += plp.lpSum([player_vars[player] for player in players if curr_pos in positions[player]]) == 1, f'{curr_pos} Positional Constraint'
Here are some of the example variables being referenced above
player_vars
player_vars = plp.LpVariable.dicts("Players", players, lowBound=0, cat='Binary')
projections
projections = pd.read_csv('../dk_data/projections.csv', thousands=',')
...
Name Fpts Position Team Opponent Minutes Salary Pts/$ Value
0 Nikola Jokic 61.52 C/UTIL DEN LAL 33.9 11700 5.26 3.02
1 Giannis Antetokounmpo 58.09 PF/C/F/UTIL MIL NYK 36.1 12000 4.84 -1.91
2 LeBron James 53.05 SF/PF/F/UTIL LAL DEN 35.4 10900 4.87 -1.45
3 Jayson Tatum 52.94 SF/PF/F/UTIL BOS CHI 37.1 10700 4.95 -0.56
4 Domantas Sabonis 52.62 C/UTIL SAC ORL 36.7 10500 5.01 0.12
5 Ja Morant 51.01 PG/G/UTIL MEM SAS 32.6 10300 4.95 -0.49
6 Julius Randle 49.74 PF/F/UTIL NYK MIL 38.0 10400 4.78 -2.26
7 Kristaps Porzingis 44.76 PF/C/F/UTIL WAS NOP 35.0 9400 4.76 -2.24
8 De'Aaron Fox 43.40 PG/G/UTIL SAC ORL 35.3 8700 4.99 -0.10
9 DeMar DeRozan 43.21 SF/PF/F/UTIL CHI BOS 36.8 9000 4.80 -1.79
10 Jaylen Brown 42.45 SG/SF/G/F/UTIL BOS CHI 33.7 9500 4.47 -5.05
11 CJ McCollum 42.05 PG/G/UTIL NOP WAS 35.0 8500 4.95 -0.45
12 Jalen Brunson 41.20 PG/G/UTIL NYK MIL 36.2 8100 5.09 0.70
13 Paolo Banchero 40.34 SF/PF/F/UTIL ORL SAC 34.3 8200 4.92 -0.66
14 Kyle Kuzma 39.88 SF/PF/F/UTIL WAS NOP 34.8 8400 4.75 -2.12
15 Nikola Vucevic 37.51 C/UTIL CHI BOS 32.0 8000 4.69 -2.49
16 Zach LaVine 37.45 SG/SF/G/F/UTIL CHI BOS 34.9 7500 4.99 -0.05
17 Russell Westbrook 37.11 PG/G/UTIL LAL DEN 28.9 7700 4.82 -1.39
18 Jaren Jackson Jr. 36.08 PF/C/F/UTIL MEM SAS 28.3 6800 5.31 2.08
19 Keldon Johnson 35.44 SF/F/UTIL SAS MEM 31.7 7000 5.06 0.44
20 Jrue Holiday 35.32 PG/G/UTIL MIL NYK 32.4 7400 4.77 -1.68
21 Desmond Bane 35.18 SG/G/UTIL MEM SAS 29.2 6600 5.33 2.18
22 Jonas Valanciunas 34.71 C/UTIL NOP WAS 26.4 6600 5.26 1.71
23 Jamal Murray 34.59 PG/G/UTIL DEN LAL 31.9 6800 5.09 0.59
24 Tre Jones 32.40 PG/G/UTIL SAS MEM 30.2 6000 5.40 2.40
25 Aaron Gordon 32.37 PF/F/UTIL DEN LAL 30.1 6600 4.90 -0.63
26 Franz Wagner 32.13 SG/SF/G/F/UTIL ORL SAC 35.1 7100 4.53 -3.37
27 Jakob Poeltl 31.88 C/UTIL SAS MEM 25.8 5900 5.40 2.38
28 Thomas Bryant 31.78 C/UTIL LAL DEN 29.9 6300 5.05 0.28
29 Immanuel Quickley 31.78 PG/SG/G/UTIL NYK MIL 35.9 6200 5.13 0.78
30 Wendell Carter Jr. 31.64 C/UTIL ORL SAC 29.8 6400 4.94 -0.36
31 Steven Adams 29.50 C/UTIL MEM SAS 27.6 6000 4.92 -0.50
32 Naji Marshall 29.14 SF/PF/F/UTIL NOP WAS 34.1 5500 5.30 1.64
33 Michael Porter Jr. 29.10 SF/F/UTIL DEN LAL 29.7 5900 4.93 -0.40
34 Markelle Fultz 29.02 PG/G/UTIL ORL SAC 28.8 6100 4.76 -1.48
35 Bobby Portis 28.49 PF/C/F/UTIL MIL NYK 27.1 6700 4.25 -5.01
36 Kevin Huerter 28.25 SG/SF/G/F/UTIL SAC ORL 32.9 5700 4.96 -0.25
37 Mitchell Robinson 27.48 C/UTIL NYK MIL 29.9 5200 5.28 1.48
38 Malcolm Brogdon 27.16 PG/SG/G/UTIL BOS CHI 24.5 5300 5.12 0.66
39 Dennis Schroder 27.07 PG/G/UTIL LAL DEN 34.6 5700 4.75 -1.43
40 Harrison Barnes 26.88 SF/PF/F/UTIL SAC ORL 32.9 5600 4.80 -1.12
41 Dillon Brooks 26.32 SG/SF/G/F/UTIL MEM SAS 29.1 5800 4.54 -2.68
42 Daniel Gafford 26.22 C/UTIL WAS NOP 24.7 4700 5.58 2.72
43 Brook Lopez 25.35 C/UTIL MIL NYK 28.6 5700 4.45 -3.15
44 Monte Morris 25.13 PG/G/UTIL WAS NOP 27.9 4800 5.23 1.13
45 Jeremy Sochan 25.10 PF/F/UTIL SAS MEM 28.6 5000 5.02 0.10
46 Cole Anthony 25.07 PG/SG/G/UTIL ORL SAC 26.7 5200 4.82 -0.93
47 Derrick White 24.74 PG/SG/G/UTIL BOS CHI 28.7 5100 4.85 -0.76
48 Bones Hyland 24.70 PG/SG/G/UTIL DEN LAL 21.8 4900 5.04 0.20
49 Malik Monk 23.98 SG/G/UTIL SAC ORL 22.1 4500 5.33 1.48
50 Robert Williams 23.88 C/UTIL BOS CHI 21.8 4400 5.43 1.88
51 Al Horford 23.51 PF/C/F/UTIL BOS CHI 29.0 4800 4.90 -0.49
52 Quentin Grimes 23.48 SG/SF/G/F/UTIL NYK MIL 34.4 5400 4.35 -3.52
53 Rui Hachimura 23.25 PF/F/UTIL WAS NOP 24.5 4700 4.95 -0.25
54 Herbert Jones 23.16 SF/F/UTIL NOP WAS 27.5 4900 4.73 -1.34
55 Deni Avdija 22.61 SF/F/UTIL WAS NOP 25.7 4200 5.38 1.61
56 Trey Murphy III 22.56 SG/SF/G/F/UTIL NOP WAS 28.2 5100 4.42 -2.94
57 Patrick Williams 21.92 SF/PF/F/UTIL CHI BOS 30.6 4400 4.98 -0.08
58 Kentavious Caldwell-Pope 21.74 SG/G/UTIL DEN LAL 31.3 4400 4.94 -0.26
59 Josh Richardson 21.62 PG/SG/G/UTIL SAS MEM 21.7 4000 5.40 1.62
60 Keegan Murray 21.61 PF/F/UTIL SAC ORL 27.8 4300 5.03 0.11
61 Bruce Brown 21.01 SG/SF/G/F/UTIL DEN LAL 24.2 5000 4.20 -3.99
62 Moritz Wagner 20.30 PF/C/F/UTIL ORL SAC 19.5 5300 3.83 -6.20
63 Zach Collins 20.08 C/UTIL SAS MEM 17.9 4700 4.27 -3.42
players
players = list(projections['Name'])
fpts, salaries, positions
salaries = dict(zip(players, projections['Salary']))
fpts = dict(zip(players, projections['Fpts']))
positions = dict(zip(players, projections['Position']))
Here is my prob.writeLP() output:
* NBA_DK *
Maximize
OBJ: 32.37 Players_Aaron_Gordon + 23.51 Players_Al_Horford
+ 28.49 Players_Bobby_Portis + 24.7 Players_Bones_Hyland
+ 25.35 Players_Brook_Lopez + 21.01 Players_Bruce_Brown
+ 42.05 Players_CJ_McCollum + 25.07 Players_Cole_Anthony
+ 26.22 Players_Daniel_Gafford + 43.4 Players_De'Aaron_Fox
+ 43.21 Players_DeMar_DeRozan + 22.61 Players_Deni_Avdija
+ 27.07 Players_Dennis_Schroder + 24.74 Players_Derrick_White
+ 35.18 Players_Desmond_Bane + 26.32 Players_Dillon_Brooks
+ 52.62 Players_Domantas_Sabonis + 32.13 Players_Franz_Wagner
+ 58.09 Players_Giannis_Antetokounmpo + 26.88 Players_Harrison_Barnes
+ 23.16 Players_Herbert_Jones + 31.78 Players_Immanuel_Quickley
+ 51.01 Players_Ja_Morant + 31.88 Players_Jakob_Poeltl
+ 41.2 Players_Jalen_Brunson + 34.59 Players_Jamal_Murray
+ 36.08 Players_Jaren_Jackson_Jr. + 42.45 Players_Jaylen_Brown
+ 52.94 Players_Jayson_Tatum + 25.1 Players_Jeremy_Sochan
+ 34.71 Players_Jonas_Valanciunas + 21.62 Players_Josh_Richardson
+ 35.32 Players_Jrue_Holiday + 49.74 Players_Julius_Randle
+ 21.61 Players_Keegan_Murray + 35.44 Players_Keldon_Johnson
+ 21.74 Players_Kentavious_Caldwell_Pope + 28.25 Players_Kevin_Huerter
+ 44.76 Players_Kristaps_Porzingis + 39.88 Players_Kyle_Kuzma
+ 53.05 Players_LeBron_James + 27.16 Players_Malcolm_Brogdon
+ 23.98 Players_Malik_Monk + 29.02 Players_Markelle_Fultz
+ 29.1 Players_Michael_Porter_Jr. + 27.48 Players_Mitchell_Robinson
+ 25.13 Players_Monte_Morris + 20.3 Players_Moritz_Wagner
+ 29.14 Players_Naji_Marshall + 61.52 Players_Nikola_Jokic
+ 37.51 Players_Nikola_Vucevic + 40.34 Players_Paolo_Banchero
+ 21.92 Players_Patrick_Williams + 23.48 Players_Quentin_Grimes
+ 23.88 Players_Robert_Williams + 23.25 Players_Rui_Hachimura
+ 37.11 Players_Russell_Westbrook + 29.5 Players_Steven_Adams
+ 31.78 Players_Thomas_Bryant + 32.4 Players_Tre_Jones
+ 22.56 Players_Trey_Murphy_III + 31.64 Players_Wendell_Carter_Jr.
+ 20.08 Players_Zach_Collins + 37.45 Players_Zach_LaVine
Subject To
C_Positional_Constraint: Players_Al_Horford + Players_Bobby_Portis
+ Players_Brook_Lopez + Players_Daniel_Gafford + Players_Domantas_Sabonis
+ Players_Giannis_Antetokounmpo + Players_Jakob_Poeltl
+ Players_Jaren_Jackson_Jr. + Players_Jonas_Valanciunas
+ Players_Kristaps_Porzingis + Players_Mitchell_Robinson
+ Players_Moritz_Wagner + Players_Nikola_Jokic + Players_Nikola_Vucevic
+ Players_Robert_Williams + Players_Steven_Adams + Players_Thomas_Bryant
+ Players_Wendell_Carter_Jr. + Players_Zach_Collins = 1
F_Positional_Constraint: Players_Aaron_Gordon + Players_Al_Horford
+ Players_Bobby_Portis + Players_Bruce_Brown + Players_DeMar_DeRozan
+ Players_Deni_Avdija + Players_Dillon_Brooks + Players_Franz_Wagner
+ Players_Giannis_Antetokounmpo + Players_Harrison_Barnes
+ Players_Herbert_Jones + Players_Jaren_Jackson_Jr. + Players_Jaylen_Brown
+ Players_Jayson_Tatum + Players_Jeremy_Sochan + Players_Julius_Randle
+ Players_Keegan_Murray + Players_Keldon_Johnson + Players_Kevin_Huerter
+ Players_Kristaps_Porzingis + Players_Kyle_Kuzma + Players_LeBron_James
+ Players_Michael_Porter_Jr. + Players_Moritz_Wagner + Players_Naji_Marshall
+ Players_Paolo_Banchero + Players_Patrick_Williams + Players_Quentin_Grimes
+ Players_Rui_Hachimura + Players_Trey_Murphy_III + Players_Zach_LaVine = 1
G_Positional_Constraint: Players_Bones_Hyland + Players_Bruce_Brown
+ Players_CJ_McCollum + Players_Cole_Anthony + Players_De'Aaron_Fox
+ Players_Dennis_Schroder + Players_Derrick_White + Players_Desmond_Bane
+ Players_Dillon_Brooks + Players_Franz_Wagner + Players_Immanuel_Quickley
+ Players_Ja_Morant + Players_Jalen_Brunson + Players_Jamal_Murray
+ Players_Jaylen_Brown + Players_Josh_Richardson + Players_Jrue_Holiday
+ Players_Kentavious_Caldwell_Pope + Players_Kevin_Huerter
+ Players_Malcolm_Brogdon + Players_Malik_Monk + Players_Markelle_Fultz
+ Players_Monte_Morris + Players_Quentin_Grimes + Players_Russell_Westbrook
+ Players_Tre_Jones + Players_Trey_Murphy_III + Players_Zach_LaVine = 1
PF_Positional_Constraint: Players_Aaron_Gordon + Players_Al_Horford
+ Players_Bobby_Portis + Players_DeMar_DeRozan
+ Players_Giannis_Antetokounmpo + Players_Harrison_Barnes
+ Players_Jaren_Jackson_Jr. + Players_Jayson_Tatum + Players_Jeremy_Sochan
+ Players_Julius_Randle + Players_Keegan_Murray + Players_Kristaps_Porzingis
+ Players_Kyle_Kuzma + Players_LeBron_James + Players_Moritz_Wagner
+ Players_Naji_Marshall + Players_Paolo_Banchero + Players_Patrick_Williams
+ Players_Rui_Hachimura = 1
PG_Positional_Constraint: Players_Bones_Hyland + Players_CJ_McCollum
+ Players_Cole_Anthony + Players_De'Aaron_Fox + Players_Dennis_Schroder
+ Players_Derrick_White + Players_Immanuel_Quickley + Players_Ja_Morant
+ Players_Jalen_Brunson + Players_Jamal_Murray + Players_Josh_Richardson
+ Players_Jrue_Holiday + Players_Malcolm_Brogdon + Players_Markelle_Fultz
+ Players_Monte_Morris + Players_Russell_Westbrook + Players_Tre_Jones = 1
SF_Positional_Constraint: Players_Bruce_Brown + Players_DeMar_DeRozan
+ Players_Deni_Avdija + Players_Dillon_Brooks + Players_Franz_Wagner
+ Players_Harrison_Barnes + Players_Herbert_Jones + Players_Jaylen_Brown
+ Players_Jayson_Tatum + Players_Keldon_Johnson + Players_Kevin_Huerter
+ Players_Kyle_Kuzma + Players_LeBron_James + Players_Michael_Porter_Jr.
+ Players_Naji_Marshall + Players_Paolo_Banchero + Players_Patrick_Williams
+ Players_Quentin_Grimes + Players_Trey_Murphy_III + Players_Zach_LaVine = 1
SG_Positional_Constraint: Players_Bones_Hyland + Players_Bruce_Brown
+ Players_Cole_Anthony + Players_Derrick_White + Players_Desmond_Bane
+ Players_Dillon_Brooks + Players_Franz_Wagner + Players_Immanuel_Quickley
+ Players_Jaylen_Brown + Players_Josh_Richardson
+ Players_Kentavious_Caldwell_Pope + Players_Kevin_Huerter
+ Players_Malcolm_Brogdon + Players_Malik_Monk + Players_Quentin_Grimes
+ Players_Trey_Murphy_III + Players_Zach_LaVine = 1
Salary_Constraints: 6600 Players_Aaron_Gordon + 4800 Players_Al_Horford
+ 6700 Players_Bobby_Portis + 4900 Players_Bones_Hyland
+ 5700 Players_Brook_Lopez + 5000 Players_Bruce_Brown
+ 8500 Players_CJ_McCollum + 5200 Players_Cole_Anthony
+ 4700 Players_Daniel_Gafford + 8700 Players_De'Aaron_Fox
+ 9000 Players_DeMar_DeRozan + 4200 Players_Deni_Avdija
+ 5700 Players_Dennis_Schroder + 5100 Players_Derrick_White
+ 6600 Players_Desmond_Bane + 5800 Players_Dillon_Brooks
+ 10500 Players_Domantas_Sabonis + 7100 Players_Franz_Wagner
+ 12000 Players_Giannis_Antetokounmpo + 5600 Players_Harrison_Barnes
+ 4900 Players_Herbert_Jones + 6200 Players_Immanuel_Quickley
+ 10300 Players_Ja_Morant + 5900 Players_Jakob_Poeltl
+ 8100 Players_Jalen_Brunson + 6800 Players_Jamal_Murray
+ 6800 Players_Jaren_Jackson_Jr. + 9500 Players_Jaylen_Brown
+ 10700 Players_Jayson_Tatum + 5000 Players_Jeremy_Sochan
+ 6600 Players_Jonas_Valanciunas + 4000 Players_Josh_Richardson
+ 7400 Players_Jrue_Holiday + 10400 Players_Julius_Randle
+ 4300 Players_Keegan_Murray + 7000 Players_Keldon_Johnson
+ 4400 Players_Kentavious_Caldwell_Pope + 5700 Players_Kevin_Huerter
+ 9400 Players_Kristaps_Porzingis + 8400 Players_Kyle_Kuzma
+ 10900 Players_LeBron_James + 5300 Players_Malcolm_Brogdon
+ 4500 Players_Malik_Monk + 6100 Players_Markelle_Fultz
+ 5900 Players_Michael_Porter_Jr. + 5200 Players_Mitchell_Robinson
+ 4800 Players_Monte_Morris + 5300 Players_Moritz_Wagner
+ 5500 Players_Naji_Marshall + 11700 Players_Nikola_Jokic
+ 8000 Players_Nikola_Vucevic + 8200 Players_Paolo_Banchero
+ 4400 Players_Patrick_Williams + 5400 Players_Quentin_Grimes
+ 4400 Players_Robert_Williams + 4700 Players_Rui_Hachimura
+ 7700 Players_Russell_Westbrook + 6000 Players_Steven_Adams
+ 6300 Players_Thomas_Bryant + 6000 Players_Tre_Jones
+ 5100 Players_Trey_Murphy_III + 6400 Players_Wendell_Carter_Jr.
+ 4700 Players_Zach_Collins + 7500 Players_Zach_LaVine <= 50000
UTIL_Positional_Constraint: Players_Aaron_Gordon + Players_Al_Horford
+ Players_Bobby_Portis + Players_Bones_Hyland + Players_Brook_Lopez
+ Players_Bruce_Brown + Players_CJ_McCollum + Players_Cole_Anthony
+ Players_Daniel_Gafford + Players_De'Aaron_Fox + Players_DeMar_DeRozan
+ Players_Deni_Avdija + Players_Dennis_Schroder + Players_Derrick_White
+ Players_Desmond_Bane + Players_Dillon_Brooks + Players_Domantas_Sabonis
+ Players_Franz_Wagner + Players_Giannis_Antetokounmpo
+ Players_Harrison_Barnes + Players_Herbert_Jones + Players_Immanuel_Quickley
+ Players_Ja_Morant + Players_Jakob_Poeltl + Players_Jalen_Brunson
+ Players_Jamal_Murray + Players_Jaren_Jackson_Jr. + Players_Jaylen_Brown
+ Players_Jayson_Tatum + Players_Jeremy_Sochan + Players_Jonas_Valanciunas
+ Players_Josh_Richardson + Players_Jrue_Holiday + Players_Julius_Randle
+ Players_Keegan_Murray + Players_Keldon_Johnson
+ Players_Kentavious_Caldwell_Pope + Players_Kevin_Huerter
+ Players_Kristaps_Porzingis + Players_Kyle_Kuzma + Players_LeBron_James
+ Players_Malcolm_Brogdon + Players_Malik_Monk + Players_Markelle_Fultz
+ Players_Michael_Porter_Jr. + Players_Mitchell_Robinson
+ Players_Monte_Morris + Players_Moritz_Wagner + Players_Naji_Marshall
+ Players_Nikola_Jokic + Players_Nikola_Vucevic + Players_Paolo_Banchero
+ Players_Patrick_Williams + Players_Quentin_Grimes + Players_Robert_Williams
+ Players_Rui_Hachimura + Players_Russell_Westbrook + Players_Steven_Adams
+ Players_Thomas_Bryant + Players_Tre_Jones + Players_Trey_Murphy_III
+ Players_Wendell_Carter_Jr. + Players_Zach_Collins + Players_Zach_LaVine = 1
Binaries
Players_Aaron_Gordon
Players_Al_Horford
Players_Bobby_Portis
Players_Bones_Hyland
Players_Brook_Lopez
Players_Bruce_Brown
Players_CJ_McCollum
Players_Cole_Anthony
Players_Daniel_Gafford
Players_De'Aaron_Fox
Players_DeMar_DeRozan
Players_Deni_Avdija
Players_Dennis_Schroder
Players_Derrick_White
Players_Desmond_Bane
Players_Dillon_Brooks
Players_Domantas_Sabonis
Players_Franz_Wagner
Players_Giannis_Antetokounmpo
Players_Harrison_Barnes
Players_Herbert_Jones
Players_Immanuel_Quickley
Players_Ja_Morant
Players_Jakob_Poeltl
Players_Jalen_Brunson
Players_Jamal_Murray
Players_Jaren_Jackson_Jr.
Players_Jaylen_Brown
Players_Jayson_Tatum
Players_Jeremy_Sochan
Players_Jonas_Valanciunas
Players_Josh_Richardson
Players_Jrue_Holiday
Players_Julius_Randle
Players_Keegan_Murray
Players_Keldon_Johnson
Players_Kentavious_Caldwell_Pope
Players_Kevin_Huerter
Players_Kristaps_Porzingis
Players_Kyle_Kuzma
Players_LeBron_James
Players_Malcolm_Brogdon
Players_Malik_Monk
Players_Markelle_Fultz
Players_Michael_Porter_Jr.
Players_Mitchell_Robinson
Players_Monte_Morris
Players_Moritz_Wagner
Players_Naji_Marshall
Players_Nikola_Jokic
Players_Nikola_Vucevic
Players_Paolo_Banchero
Players_Patrick_Williams
Players_Quentin_Grimes
Players_Robert_Williams
Players_Rui_Hachimura
Players_Russell_Westbrook
Players_Steven_Adams
Players_Thomas_Bryant
Players_Tre_Jones
Players_Trey_Murphy_III
Players_Wendell_Carter_Jr.
Players_Zach_Collins
Players_Zach_LaVine
End
When trying to .solve() this problem`:
prob.solve(plp.PULP_CBC_CMD(msg=0))
print(f'Status: {plp.LpStatus[prob.status]}')
score = str(prob.objective)
for v in prob.variables():
score = score.replace(v.name, str(v.varValue))
score = eval(score)
lineup = [v.name for v in prob.variables() if v.varValue != 0]
print(score, lineup)
it outputs:
Status: Infeasible
23.570000000000004 ['Players_Giannis_Antetokounmpo', 'Players_Immanuel_Quickley', 'Players_Ja_Morant', 'Players_Jaylen_Brown', 'Players_Malcolm_Brogdon']
I know the issue lies within the positionality constraints, because commenting them out or altering them produces an optimal result.
You’ll need to re-index your problem with a second index such that the assignment binary variable is as:
assign[player, position]
currently you are double/triple counting people which is leading to the infeasibility. Specifically, if player X can play 3 positions, you are (inadvertently) assigning them to play all 3 positions at once, so when you total up by position the result is > 1, which busts your position constraint.
After you change your variable, then it will be easy to also sum across all positions for each player and ensure they are only assigned once, which will address the second issue of avoiding multiple assignments where feasible.
This is pretty similar, with an added twist, but is shows most of the general construct:
Python PULP optimization – Limiting total number of one variable chosen
And this:
Python PULP – Positional Constraints for a Lineup Generator
(I guess I’ve looked at a couple of these fantasy teams!)