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JAOT

Sports League Scheduling

Optimize sports scheduling, team selection, and tournament design. Building a fair fixture list that minimizes travel, avoids scheduling conflicts, and satisfies broadcast windows is a classic optimization challenge that scales quickly as teams and venues increase.

When to Use This Guide

This guide is a good fit when you need to:

  • League scheduling -- create a round-robin or partial schedule for a set of teams with home/away balance
  • Team or player selection -- pick a squad from a larger pool subject to budget, skill, and position constraints
  • Tournament bracket design -- seed and schedule elimination rounds with venue and rest-day rules
  • Venue allocation -- assign games to venues considering capacity, availability, and geographic balance

If your problem involves assigning teams or players to time slots and locations under fairness and logistical constraints, start here.

Step-by-Step Walkthrough

  1. List your teams and venues. Record each team's home venue and any venue-sharing arrangements.

  2. Define scheduling rules. Common rules: no back-to-back away games, minimum rest days between matches, and broadcast window preferences.

  3. Set constraints. Every pair of teams must play the required number of times (e.g., home and away). Venue capacity and availability on each date must be respected.

  4. Choose your objective. Minimize total travel distance, maximize broadcast revenue, or maximize schedule fairness (balanced home/away streaks).

  5. Run and review. The solver produces a full fixture list. Check for practical issues like holidays or venue conflicts not captured in the model.

Example: Round-Robin League Schedule

Schedule 8 teams in a round-robin league across 4 venues. Each pair plays once. No team should play more than one game per round. Minimize total travel distance.

import httpx

API_URL = "https://api.jaot.io/api/v2"
headers = {"Authorization": "Bearer ok_live_your_key_here"}

teams = ["alpha", "beta", "gamma", "delta", "echo", "foxtrot", "golf", "hotel"]
rounds = list(range(1, 8))  # 7 rounds for 8 teams
venues = ["venue_1", "venue_2", "venue_3", "venue_4"]

# Travel cost between each team's home city and each venue
travel_cost = {
    (t, v): abs(hash(f"{t}_{v}")) % 50 + 10
    for t in teams for v in venues
}

# Binary variable: does match (team_i vs team_j) happen in round r at venue v?
variables = []
matches = [(teams[i], teams[j]) for i in range(len(teams)) for j in range(i+1, len(teams))]

for (t1, t2) in matches:
    for r in rounds:
        for v in venues:
            variables.append({
                "name": f"{t1}_v_{t2}_r{r}_{v}",
                "type": "binary",
            })

# Minimize total travel
objective = {
    "sense": "minimize",
    "coefficients": {
        f"{t1}_v_{t2}_r{r}_{v}": travel_cost[(t1, v)] + travel_cost[(t2, v)]
        for (t1, t2) in matches for r in rounds for v in venues
    },
}

constraints = []

# Every pair plays exactly once
for (t1, t2) in matches:
    constraints.append({
        "name": f"play_{t1}_{t2}",
        "coefficients": {
            f"{t1}_v_{t2}_r{r}_{v}": 1
            for r in rounds for v in venues
        },
        "sense": "==",
        "rhs": 1,
    })

# Each team plays at most 1 game per round
for t in teams:
    for r in rounds:
        involved = {}
        for (t1, t2) in matches:
            if t in (t1, t2):
                for v in venues:
                    involved[f"{t1}_v_{t2}_r{r}_{v}"] = 1
        constraints.append({
            "name": f"one_game_{t}_r{r}",
            "coefficients": involved,
            "sense": "<=",
            "rhs": 1,
        })

response = httpx.post(f"{API_URL}/solve", headers=headers, json={
    "variables": variables,
    "objective": objective,
    "constraints": constraints,
})
result = response.json()

print(f"Status: {result['status']}")
print(f"Total travel cost: ${result['objective_value']:.2f}")

The solver assigns each match to the round and venue combination that minimizes total travel while ensuring every team plays at most once per round.

Next Steps

  • Workforce Scheduling (intermediate) -- apply similar assignment techniques to employee shift scheduling
  • Education Timetabling (intermediate) -- see how scheduling models extend to class and room assignments