Mathmatically optimizing court time usage for a pickleball tournament 

This is going to be a unique quesion but I figured i'd ask it here and see if anyone has any ideas. I am in charge of running a pickleball tournament and would like to see if there is a way I can describe it mathmatically and then optimize my equasion for time to get it done as efficiently as possible. I will describe it in detail below.

The Problem:

I have a certain number of courts and a certain number of brackets with a number of games in each (each bracket has a different number of games) that will fill those courts over period of the day. Different brackets can be run at the same time on different courts, but once they are started they must run until completed and on any varying amount of courts as necessary. Brackets should take no longer than 3 hours to complete, each game will be assumed to be 20 mins. The goal is to fill the number of courts perfectly over the course of the day so there is no empty space at any time. Brackets can start on a certain number of courts and increase to more or less as necessary. 

in a large tournament with hundreds of people and only so many hours in a day, it becomes many hours of work to plan these to run as efficiently as possible. If I can describe this problem in an equasion perhaps I can write some software to automate some of the process. I have am an engineer not a mathmatician so this part is a struggle for me. 

  • Erdos Erdos
    0

    Can you elaborate on what you mean by a "bracket"? It is not clear from your description.

  • a bracket is a group of players that will play together, maybe division is a better term, for example, men's doubles is one bracket ( consisting of only men) women's doubles is another (consisting of only women). They will not play each other, think of each "division/bracket" as an inseparable group of games.

  • Erdos Erdos
    0

    How many games does a given team or player play in a bracket? You should also provide more specific details. How many courts are there? How many brackets are being played? How many teams are in each bracket? You might also want to consider offering a higher reward, as answering this post could be quite time-consuming.

  • The goal is to have an equation that can describe this so I can input my variables and optimize for time, I didn’t provide # of courts, brackets, teams etc because I don’t want them as constants. I need to figure out how to describe this mathematically. How much time do you think it could take?

  • Low bounty. Formulating this takes about an hour or a bit less. I would suggest increasing bounty to at least $50.

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Kav10 Kav10
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  • Could you give me a quick example of how you would solve this function? you can input random values.

    • Kav10 Kav10
      0

      You would need to use an optimization software or write code to solve this problem. The optimization software finds the optimal solution by iteratively evaluating different combinations of start times to find possible solutions to the objective function while considering the constraints. The solution would be something like: Bracket 1 starts at time 0 and ends at time 1 hour. Bracket 2 starts at time 0 and ends at time 2 hours and so forth.

    • Kav10 Kav10
      0

      This solution minimizes the total time required to complete all brackets while satisfying all constraints noted above.

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