Sports schedule: home/away alternation

[fredericgirod]

Hi again,
I've been spending my days trying to create a sports schedule with pyschedule, but I cannot implement a home/away alternation constraint. Each matches calendar should get the teams to alternate home and away matches in order not to play e.g. 5 times at home or away in a row.
I know a capacity constraint should do the job, but I don't see how.
Any thoughts about this ?
I would really appreciate any tips or advice.

[timnon]

In the following script, we restrict each team to play in each stadium at most once every 3 rounds. Thats comes pretty close to what you want. Exactly matching your requirements is probably not possible at the moment.

import sys
sys.path.append('../src')
from pyschedule import Scenario, solvers, plotters, alt

n_teams = 8
n_stadiums = n_teams
n_slots = n_teams-1

S = Scenario('sports_scheduline',horizon=n_slots)
Stadiums = S.Resources('S',num=n_stadiums)
Teams = S.Resources('T',num=n_teams)

Games = list()
for T1 in Teams:
	count = 1
	for T2 in Teams:
		if str(T1) >= str(T2):
			continue
		Game = S.Task('%s%s'%(T1,T2),completion_time_cost=2**count)
		Game['team_%s'%str(T1)] = 1
		Game['team_%s'%str(T2)] = 1
		Games.append(Game)
		count += 1
		Game += T1, T2
		Game += alt(Stadiums)


for Stadium in Stadiums:
	for T in Teams:
		S += Stadium['team_%s'%T][0:n_slots:3] <= 1

print(S)

#print(S)
solvers.mip.solve(S,time_limit=600,msg=1)
plotters.matplotlib.plot(S,show_task_labels=True,img_filename='tmp.png')

[timnon]

Here might be a better solution for 10 teams:

• each team plays at least 4 times at home (in the Stadium with the same number)
• in at most 3 consecutive rounds it doesnt play at home (this includes not playing at all, which is not exactly your requirement, but its pretty close). This is the minimum such that still a solution exists. I also allow a game only happening in one of the two stadiums of the participating teams. This makes finding a solution much easier and is probably also a requirement.

from pyschedule import Scenario, solvers, plotters, alt

n_teams = 10
n_stadiums = n_teams
n_slots = n_teams-1

n_plays_at_home = 4
max_n_not_at_home_periods = 3

S = Scenario('sports_scheduline',horizon=n_slots)
Stadiums = S.Resources('Stadium',num=n_stadiums)
Teams = S.Resources('T',num=n_teams)
Team2Stadium = dict(zip(Teams,Stadiums))

Games = list()
for Team0 in Teams:
	count = 1
	for Team1 in Teams:
		if Team0.name >= Team1.name:
			continue
		Game = S.Task('%s%s'%(Team0,Team1),completion_time_cost=2**count)
		Game[Team0.name] = 1
		Game[Team1.name] = 1
		Games.append(Game)
		Game += Team0, Team1
		Game += Team2Stadium[Team0] | Team2Stadium[Team1]
		count += 1

for Team in Team2Stadium:
	Stadium = Team2Stadium[Team]
	S += Stadium[Team.name] >= n_plays_at_home
	S += Stadium[Team.name][0:n_slots:max_n_not_at_home_periods] >= 1

print(S)
solvers.mip.solve(S,time_limit=600,msg=1)
plotters.matplotlib.plot(S,show_task_labels=True,hide_resources=Teams)

Note that i am hiding the Team resources in the following plot, the Stadiums are the interesting ones: