# Bivariate mathematical induction for n-consecutive game athletic schedules

Andrew Felt

Union 250

## Start Date

24-4-2015 1:20 PM

## Description

When creating athletic schedules a common request that is made is to limit the number of consecutive home and away games, ignoring bye dates. In many cases, this means that a team cannot have more than the specified number of home or away games in a row, regardless of the byes between them. In the past, we solved this by creating many separate constraints in the integer linear program. Each constraint would require varying window sizes – referring to the number of games being observed – to accomplish the work of our new single constraint. Once cumbersome, this request is now easy to implement with our new single family of constraints using mathematical induction. We found that this new family of constraints could easily be adapted to any requests regardless of the number of consecutive games. We found this to be most helpful when there are an odd number of teams, because in this case byes are required. During this presentation we will walk through a proof by induction showing how this powerful constraint works. Further, we will demonstrate the effectiveness of the constraint through a sample athletic schedule in the context of the mathematical programming language AMPL.

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Apr 24th, 1:20 PM

Bivariate mathematical induction for n-consecutive game athletic schedules

Union 250

When creating athletic schedules a common request that is made is to limit the number of consecutive home and away games, ignoring bye dates. In many cases, this means that a team cannot have more than the specified number of home or away games in a row, regardless of the byes between them. In the past, we solved this by creating many separate constraints in the integer linear program. Each constraint would require varying window sizes – referring to the number of games being observed – to accomplish the work of our new single constraint. Once cumbersome, this request is now easy to implement with our new single family of constraints using mathematical induction. We found that this new family of constraints could easily be adapted to any requests regardless of the number of consecutive games. We found this to be most helpful when there are an odd number of teams, because in this case byes are required. During this presentation we will walk through a proof by induction showing how this powerful constraint works. Further, we will demonstrate the effectiveness of the constraint through a sample athletic schedule in the context of the mathematical programming language AMPL.