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DS601 Project NFL Schedules

Introduction:

In the dynamic and competitive landscape of professional sports, efficient scheduling plays a crucial role in ensuring fair play and optimal performance for teams. For the National Football League (NFL), where teams are geographically dispersed, the challenge lies in creating a schedule that minimizes travel distances for teams throughout the season. This optimization problem is essential not only for the well-being and performance of the athletes but also for the overall sustainability of the league.

1.Problem Description:

The NFL consists of eight teams: MIA, BUF, NYJ, NE, KC, LV, LAC, and DEN. Each team is associated with a home city, and the distances between these cities are provided in a distance matrix. The objective of this scheduling optimization problem is to design a season schedule that minimizes the total travel distance for all teams.

Objective:

Minimize the total travel distance for all teams during the NFL season.

Constraints:

Each team should play half of its games at home and half away.

Each team should play a certain number of games during the season.

No team should play against itself.

The scheduling should be symmetric, meaning that playing at home against team A is equivalent to playing away against team A.

2.Description of model & tools:

The problem will be formulated as a linear programming optimization model.

Decision variables will represent whether a team plays at home or away against another team.

The objective function will aim to minimize the total travel distance, subject to the defined constraints.

Excel Solver can be used to find the optimal schedule that satisfies the given conditions and minimizes travel for NFL teams. This approach ensures a fair and balanced schedule, contributing to the overall success and competitiveness of the league.

Mathematical Model:

Decision Variables:

Decision Variables

Define binary variables for each possible game, indicating whether it takes place (1) or not (0).

xij = 1 if team i plays a home game against team j

xij = 0 otherwise

Objective Function

Objective：

Minimize the total travel distance：

Minimize

Constraints:

1. Home and GAMES:

Each team should paly half of its games at home and half away:

2. Number of Games:

Each team should play a certain number of game

3. Avoid self-play:

The objective function seeks to minimize the total travel distance for all teams.

Constraints ensure a balanced schedule, avoiding self-play, maintaining symmetry, and accommodating specific matchup preferences.

3．A discussion of the Results