CODEWITHSUNDEEP
or-toolscp-sat
pmueller
pmueller

Reputation: 323

OR tools Sports Scheduling problem and modeling constraints

I'm enjoying learning about or-tools, and hope someone can help me out a bit. I've got a problem that's a bit like the nurse-scheduling problem, but instead it's for sports-scheduling. Here's what I've got so far to generate the combinations of possible games.

# Create schedule variables
for h in range(divisions):
    for i in range(teams_per_division):
        for j in range(i+1, teams_per_division):
            for k in range(weeks):
                for l in range(venues):
                    schedule[h, i, j, k, l] = model.NewBoolVar( f"schedule_div{h}_team{i}_team{j}_week{k}_venue{l}")

The constraints I'm trying to add are:

So far, I've tried introducing a new variable, 'played', like this: played[h, i, k, l] = model.NewBoolVar( f"played_div{h}_team{i}_week{k}_venue{l}")

but I'm having trouble linking this 'played' to 'schedule', and then modeling the constraints.

Any and all help much appreciated!

Upvotes: 1

Views: 148

Answers (1)

pmueller
pmueller

Reputation: 323

Looks like I figured it out.

First I created a new variable like so:

for h in range(divisions):
    for i in range(teams_per_division):
        for k in range(weeks):
            weekPlayed[h, i, k] = model.NewIntVar( 0, 10, f"played_div{h}_team{i}_week{k}")
            for l in range(venues):
                played[h, i, k, l] = model.NewBoolVar( f"played_div{h}_team{i}_week{k}_venue{l}")

Now, with the 'played' variable, I could just increment these counters during schedule-creation, like so (note that both i and j are incremented):

...
                    # Increment key counters
                    weekPlayed[h, i, k] = weekPlayed[h, i, k] + schedule[h, i, j, k, l]
                    weekPlayed[h, j, k] = weekPlayed[h, j, k] + schedule[h, i, j, k, l]

Finally, the needed constraint:

# Each team plays once per week
for h in range(divisions):
    for i in range(teams_per_division):
        for k in range(weeks):
            model.Add(weekPlayed[h, i, k] <= 1)

I hope this is helpful to someone else trying to link offshoot variables, and then constrain them independently.

Upvotes: 0

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