How can volunteers maximize their time at Pine Ridge Reservation?

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Intro video:

https://www.youtube.com/watch?v=6QjIbpknBgo&ab_channel=FirstnameLastname

Every summer since 8th grade began, I have had the opportunity to go on a week-long trip to Pine Ridge, South Dakota, U.S.A. Pine Ridge is a Native American reservation, and it is the poorest place in the United States. Consistent with history, they receive little to no help from the government and are currently being plagued with COVID-19 (which is why I couldn’t go last summer, and maybe can’t go this summer either.) The week-long trip was organized through a non-profit organization called Re-Member. Re-Member looks to recreate and strengthen the bonds between the Ogala Lakota people of Pine Ridge and the rest of America. While you are there, you work service hours to help people who call the organization to request help for almost anything. Work consists of: Skirting trailers (because many people use trailers as homes, they are not built into the ground, which is dangerous. Skirting a trailer basically builds it into the ground.), creating and digging an outhouse (dig a 6 foot deep hole, necessary because many people in Pine Ridge do not have a toilet), working in the workshop on site, (building outhouses and bunk beds), and delivering bunk beds to houses in need. This brings me to my question: How can volunteers maximize their time to complete as many jobs as possible?

Well, seeing as this is a game theory project, let’s set up this problem as a game. There are a few key components that must be explained first:

There are approximately 40 volunteers. There are 3 workdays (The other days are for travel, speakers, pow wows, museums. It is important to educate the volunteers and not just work.)  which span for 8 hours each. 

Defining the possible jobs, how long they take and how many people required for each job:

Skirting trailers: 8 people, 8 hours per trailer.

Outhouse holes: 4 people, 4 hours per outhouse. This job can only be completed if there is the creation of an outhouse in the workshop.

Delivering bunk beds: 8 people, 2 hours per bunk bed delivery, again contingent upon the creation of bunk beds in the workshop.

Workshop: 4 people, 2 hours per outhouse, 1 hour per bunk bed built. Does NOT count as a completed job.

An important thing to remember- to optimize this game, we want the highest # of completed jobs possible. 

So what is the optimal strategy to maximize jobs completed?

The first thing to notice is that outhouse holes and bunk bed delivery actually hold the same value- 4 people could get 2 jobs done in 8 hours, so 8 people could get 4 jobs done in 8 hours. Similarly for bunk bed delivery, 8 people could get 4 jobs done per 8 hours.

This means that it does not matter which job is done AS LONG AS THERE ARE ENOUGH OUTHOUSES/BUNK BEDS.

It is clearly more efficient to deliver a bunk bed/dig an outhouse hold than to skirt a trailer, but it is impossible to deliver a bunk bed or an outhouse without them being built, meaning that on Day 1, skirting trailers is the only job that can be completed. 

The maximum number of jobs that can be completed in a day is 20, by delivering bunk beds/outhouses.

It takes one full day of work from each individual group in the workshop to create enough bunk beds/outhouses to satisfy one day of everybody delivering.

Therefore 2 groups can build enough outhouses/bunk beds on Day 1 so that Days 2 and 3 can only go towards bunk bed and outhouse delivery.

Solution:

Day 1:

3 groups (24/40 people) skirt trailers-

4 groups (16/40 people) work in the workshop, creating whatever needs to be delivered on days 2 and 3.

Jobs completed: 3

Day 2:

Any assortment of groups (40/40 people) delivering bunk beds/outhouses

Jobs completed: 20

Day 3:

Any assortment of groups (40/40 people) delivering bunk beds/outhouses

Jobs completed: 20

Total jobs completed: 43.

In conclusion, every week of volunteer work can be maximized to complete 43 jobs. Please leave a comment or leave feedback if you have a different way of solving this. Thank you for reading and learning about Pine Ridge. If this topic interests you further, look up Re-Member on Google. Lastly, I’m going to plug my GoFundMe. 5$ goes a long way to buying these supplies to create bunk beds, outhouses, etc. The money goes directly to the non-profit mentioned in this project.

http://gf.me/u/zhkbib

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