Distributing People Across Days w/ Conflicts (scheduling marching band)

Gabriel97

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Aug 4, 2018
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This isn't a math problem from my teacher, but a literal real world problem I have to solve fairly.

For those of you who know how marching band works, I am on a drum major team of 5 people and we are auditioning for who will be head drum major. Essentially, there are 5 people auditioning for a role in the band. The way the audition works is each of us leads a rehearsal for an entire day this week. Person A leads rehearsal on Monday, Person B on Tuesday, and so on. We decided we want to randomly assign who goes on what day. So far, the solution is just picking straws, but there are some caveats.

Number one, two of us have conflicts on Monday and aren't at rehearsal all day, meaning two of us can't audition on Monday and have to go on a different day. We can refer to these people as A and B if needed.

Secondly, all five of us have to miss an hour of rehearsal on Tuesday (for band people, we have a master class on our respective instruments on that day), making it a less/more desirable day (depending on your perspective), but also isn't a fair audition because one person has less time.
Lastly, Friday is a more desirable day (for band nerds, we are doing our first full run of 1/3 of the show!!).

If it were up to random chance who got what day, those last two caveats wouldn't matter because it's up to random chance who gets them, but because we have to consider that the two people who can't go Monday are basically more likely to get those days, the system is unfair.

The question is, what can we do that'll fairly assign who goes on what day? The important part is incorporating a system for that first conflict, but if someone can come up with something that'll work to include the second and third one, that'll be great!


If you have any questions, let me know below; I'll reply quickly for today! Thank you!!!
 
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