Overview

     The topics covered in Quantitative Analysis do not motivate

   students to be benevolent, but the topics can make the most

  of the time and effort put into benevolence.  I encourage you

 to think of original topics, but in case you are stuck for a topic, two alternative paper topics below help you explore how Quantitative Analysis can make benevolence efficient.

Assignment Problem (Chapter 7) 

If all that matters is the production from your labor (say, the number of houses you build), then you should choose those volunteer assignments that are closest to you. 

In some cases, there are non-quantitative elements of problems that may lead you to volunteer your labor in a distant location.  For example, an African missionary I talked to recently said that the best mix of benevolence was money (to buy materials) plus some Americans to encourage the locals.  It may also be a valuable education or chance for personal growth to volunteer your labor in distant lands.

Your paper topic is to describe how some benevolence program was made efficient by reducing the transportation costs of volunteers, or replacing some volunteer labor with cash.  In that example, were non-quantitative elements present?

Queuing theory (Chapter 11) 

Show how Pepperdine (which is a non-profit organization) can better minimize cost.   One way to minimize cost is to determine how many service people Pepperdine should use in one of the various queues (lines) around campus.

Tip: Before trying the following project, first master Lessons 2.5 and 2.6 from Chapter 11, especially Example 2 in Lesson 2.6.  

How many cashiers should Pepperdine use in the student cafeteria?  To answer with the theory in Chapter 11, measure four things:

· The average service time a typical cashier spends on a customer.   For example, if find a typical cashier spending 1 min. on Customer 1, 2 min. each on Customers 2 and 3, and 3 min. on Customer 4.  Then, that is an average of 2 min. for each customer (1/2 customer per minute).  That translates to a service rate of

m = (60 min/ hr.)(1/2 cus./min.) = 30 customers per hour. 

· The average number of students that arrive at the cashiers stations for checkout each hour.  That is the arrival rate, l.

(Measure both of those numbers with at least 20 minutes of observations.)

· The value of an hour of time for a typical student.  (Be creative with that measurement.  Say, set the value of time equal to the average wage earned by Pepperdine students, plus a few dollars per hour as a fudge factor to accommodate students that value their own time so much they choose not to work at all.) 

· The average cost to Pepperdine of employing a cashier for an hour.

With that data, you can compute the total hourly cost of having either k = 1, k = 2, or k = 3 cashiers (channels) open.   Note, it is only possible to have k channels open if km > l.  Because whenever km < l, then it is impossible to serve all your customers with only k channels.  (You need to increase k.)

Tip

Whichever topic you choose, you should first read about the economics of charitable giving, which puts Quantitative Analysis in context.  Specifically, Quantitative Analysis helps one be better at perfect altruism.