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Brady’s Summer Time Well Spent

Grant Allvin, Mennatallah Barghout, Brady Hess, and Erica Zheng

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Decision Problem

What is the most ideal opportunity for Brady Hess to pursue over the summer?
Brady Hess is the decision maker

Some opportunities not yet available to him yet, namely internships
Analysis includes contingency plan dependent on available options
Brady’s values:

minimizing costs
maximizing income
maintaining a work-life balance
maximizing impact on his career

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Alternatives

Internship Opportunities

Northwestern Mutual (Pittsburgh, PA.)
Northwestern Mutual (Columbus, OH.)
Westinghouse (Pittsburgh, PA)
Payliance (Columbus, OH.)

Summer Job Opportunities

Lifeguarding Job (Columbus, OH.)
Landscaping Job (Columbus, OH.)
Golf Course Job (Columbus, OH.)

Summer Course Offerings

70257 - Optimization (Pittsburgh, PA.)
70381 - Marketing (Pittsburgh, PA.)
88300 - Programming and Data Analysis (Pittsburgh, PA.)
Any Combination of 2 courses

Don’t Pursue Any Opportunities

Do Nothing (Stay home in Columbus, OH)

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01 Decision Model

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Data Points - 1

Rent (Opportunities Outside Columbus Only)

Monthly rent information collected from current residents of Brady’s living space

Assume he will stay for 3 months (internships, two courses in different sessions) or 2 months (one summer course to two courses in one session)

Assume he will stay at home for choices in Columbus and thus not pay rent

Tuition (Summer Courses Only)

$499 (From CMU Student Financial Services) x Number of course units taken (From CMU Schedule of Classes)

Transportation Costs (All Except Summer Courses)

Aggregation of distance (assumed from Google Maps), Brady’s car tank and fuel efficiency, times driving (dependent on weekly schedule and assumption that opportunities last 12 weeks) and gas costs per gallon (from AAA, assumed to be ~$3.50 in Columbus and ~$3.80 in Pittsburgh), into the formula below
Assuming Brady will not drive to summer courses

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Data Points - 2

Pay (Internships and Summer Jobs Only)

Aggregate of hourly pay from job descriptions (for internships) and anecdotes (for summer jobs, which Brady has experience in) multiplied by total hours spent working (from proposed/anecdotal weekly hours multiplied by assumed number of weeks spent working [12])

Hours Worked

(Internships and jobs) Divide total pay above by hourly rate
(Courses) Weekly hours for courses from Faculty Course Evaluations

Taken from standard, 14-week semester courses rather than 6-week summer courses
Assume the total work is about the same, since standard classes meet 2-3 times per week while summer classes meet 5 times per week

Pay

Helps with his income maximization

Brady gave us hourly pay rates for internships from job descriptions and for jobs from his previous experience and typical work hours per week. Assuming these weekly hours are consistent and he works at these internships or jobs for 12 weeks, we take the product of the pay rate, weekly hours, and number of weeks to get his total pay

Hours Worked

Helps with measuring maintenance of work-life balance, which Brady partially defined as not working too much or too little.

For internships and jobs, this metric has already been calculated for us, as we just divide his total pay by his hourly pay rate

For courses we look at data from Faculty Course Evaluations, which include data on typical weekly time commitment. There was not much recent data on summer courses, so we took weekly hours from the standard 14-week semester courses instead. This came with some issue about how to convert the hours spent on a 14-week course to a 6-week summer course. From what we observed, 14 week courses tend to meet 2-3 times a week, while summer courses meet every weekday. With that in mind, we made the assumption that the total time commitment for summer courses was about the same as that of standard 14-week courses, so we just multiply the weekly hours from the standard semesters by 14.

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Data Points - 3

Difficulty

Based on anecdotes (for summer jobs) or perceived difficulty from internship/course descriptions
Subjective scale of 1-to-5 (1 is very easy, 5 is very hard)

Enjoyment

Based on anecdotes (for summer jobs) or perceived difficulty from job/course descriptions
Subjective scale of 1-to-5 (1 is very unenjoyable, 5 is very enjoyable)

Distance

Attribute based on location
Dichotomous scale of being “close” to home (Columbus) or “far” from home (Pittsburgh)

In addition to how long Brady works, we felt it also important to think about how hard or how enjoyable an opportunity might be. The difficulty and enjoyment parameters were both similar in that they both come with some subjectivity. For the summer jobs, Brady has decent experience working with them, so he is confident with how difficult and enjoyable they are. However, for the internships and courses, he has less experience or has never taken such courses, so his perception of difficulty for such opportunities were made by assumptions based on the internship or course descriptions. Both data are ranked from 1 to 5. For difficulty, 1 indicates an opportunity being very easy, while 5 indicates an opportunity being very hard. For enjoyment, 1 indicates something very unenjoyable and 5 indicates something very enjoyable.

Distance

Brady told us that he would prefer to work someplace close to home, as he could spend more time with family and friends in Columbus, implying the benefits that come with that would positively impact his work-life balance. We decided upon a dichotomous scale for this variable of opportunities being close to home or far from home, since all our opportunities tend to be in two areas (Columbus and Pittsburgh) and the effects of two opportunities in the same relative location being some miles apart from each other was negligible to him.

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Data Points - 4

Probability of full-time employment after having the opportunity

(From NACE 2019 Student Survey Report) 53.2% of graduates get job offers, 57.2% of graduates with internship experience get offers, 43.7% of graduates without internship experience get offers.

Apply proportional changes in log odds to a baseline employment rate for Tepper graduates (86%, from CMU post-grad dashboard)
Assume the rate of full-time employment after completing an internship is 88% and rate for not doing so is 81%.

Relevance to career aspirations

Based on perceived relevance from job/course descriptions
Subjective 1-to-3 scale (1 is irrelevant, 2 is relevant, 3 is very relevant)

Probability of full time employment

For Brady’s goal of maximizing impact on his career, we felt is crucial to see how an opportunity would impact his chances of employment. This was a bit difficult to define by one data point so we did some aggregation on two data sources. [NACE] We felt these changes could be applicable to CMU data so we then went about trying to apply these percentage changes to a baseline rate of employment for Tepper graduates, which turned out to be 86% from CMU’s post-graduate dashboard data from 2019 to 2022. To avoid issues with using a bounded range like percentages, we first converted the changes from the NACE study and the CMU baseline to log odds, applied changes to CMU’s log odds proportionally from the national study, and then converted back into probability to get an employment rate after completing an internship being 88% and 81% if not completing an internship

Relevance to career aspirations

In addition to something subjective, we felt it necessary to do a subjective reading. Since, for example, an internship could improve one’s employment rate, but not necessarily be related to one’s career aspirations and thus feel like a waste of time. These were measured based on responses educated by job or course descriptions on a scale of 1 to 3

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Analysis

02

Putting it all together

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Consequences Table

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Even Swaps

Note:

Brady did not rate any options with a rigor score of 5, so we disregard its large difference from his other even swaps
Full time employment swap is negative, implying that Brady is willing to pay $15 for each percentage

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Adjusted Benefits Table

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Assumptions and Uncertainties

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Assumptions

Unless he was taking a summer course (except when he’s taking two courses in different sessions), Brady would engage in an opportunity for 12 weeks
He would stay at home for opportunities in Columbus and thus not pay rent
Other living expenses (food, leisure, etc.) unaffected or provided by parents
Gas prices in both locations would stay relatively the same and be the prices given on average
Brady will start each opportunity on a full tank of gas

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Uncertainties

Probability of employment after having an opportunity - measurements estimated from an aggregate of data, may threaten model validity
Even swaps for being close to home - Brady told us he was the least confident about this even swap, could this have affected Brady’s choices?
Duration of internship - we are operating under the assumption that the internship and the jobs (excluding summer courses) will last 12 weeks, but the timeline may be shorter

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Sensitivity Analysis - 1

Chance of full-time employment after completion of internship for the first most preferred option

% chance of full time employment

$ value of each percentage point

Erica

For the first sensitivity analysis, we looked at changes of Brady’s chances of full time employment after completing an internship for his first most preferred option which is an internship at Payliance in Columbus. For the columns we have the percent change in chances of Brady’s full time employment, which we calculated earlier, so we have values ranging from 81 to 90%. For the rows, we took note of how much Brady values each percent increase or decrease from ranging dollar values of 10 to 20 dollars. We can see that no matter the chance of full time employment or how much Brady values each percent, he will still prefer his first most preferred option of Payliance.

First most preferred option (internship) - probability of full-time employment given changing percentage

Chance of full time employment after completing internship

X - how much he values each percentage point

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Sensitivity Analysis - 2

Chance of full-time employment after completion an internship for the fifth most preferred option

% chance of full time employment

$ value of each percentage point

Erica

For the second sensitivity analysis, we looked at changes of Brady’s chances of full time employment after completing an internship for his fifth most preferred option, the golf course job in Columbus. We choose to look at this as we noticed the adjusted benefit for the 4th and 5th ranked options are close by a grand, so we did the analysis to see if Brady’s plans would change. Again for the columns we have the percent change in chances of Brady’s full time employment and for the rows, how much Brady values each percent. We can see that no matter the chance of full time employment or how much Brady values each percent, he will prefer the fifth most preferred option of working at the golf course in Columbus.

How much Brady values being close to home - how would fourth and fifth rank would change

Doesn’t matter for the first and second most preferred - are in Columbus
Adjusted benefit is higher than third and fourth by a couple thousand
If he values close to home then northwestern mutual pittsburgh and gold course would change rank

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Sensitivity Analysis - 3

How much Brady values being close to home for the fifth most preferred option

$ value of distance from home

The job Brady will take

Erica

For the third sensitivity analysis, We also looked at how much Brady values being close to home, again seeing if his fourth ranked option, the Northwestern Mutual in Pittsburgh internship and his fifth ranked option the golf course job, would change. We examined Brady’s willingness to pay to be closer to home, currently Brady’s even swap for distance is at 2 thousand dollars to be closer to home and from the previous analysis we know that the adjusted benefit for the 4th and 5th ranked options are close by a grand. So from the analysis we can see that the more Brady is willing to pay, around the $3000 to the $3500 of his willingness to pay, his preferences would change and the Northwestern Mutual in Pittsburgh internship would now become the fifth most preferred option and the golf course job will move up and become the fourth most preferred option.

How much Brady values being close to home - how would fourth and fifth rank would change

Doesn’t matter for the first and second most preferred - are in Columbus
Adjusted benefit is higher than third and fourth by a couple thousand
If he values close to home then northwestern mutual pittsburgh and gold course would change rank
Negative b/c in even swaps for distance -2000 if it is far rather than close, in exchange of it being far, it is how much Brady would quantify being farther from home, spending 2K to make it closer
Initial findings all internships are better than everything else
Pays more money to it closer to home - far rather than close

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Sensitivity Analysis - 4

How long Brady would be working at Payliance for the most preferred option

# of weeks at Payliance

The job Brady will take

Erica

Lastly, for the fourth sensitivity analysis we made the assumption that all the opportunities excluding the summer courses, will last for 12 weeks. We didn’t know how long the duration of the opportunity would impact Brady’s rankings. So for the column we have the job that Brady will take and for the rows we have the range of weeks over the summer. The maximum number of weeks is 12 cause the summer can only last so long, and a minimum of 9 weeks as a 8 week internship seems to short. From the sensitivity analysis, we can see that if the Payliance internship was 9 or 10 weeks long, then Brady would now prefer his second most preferred option at Northwestern Mutual, Columbus, but if the Payliance internship was 11 or 12 weeks, then his currently rank would be the same. We deem 10 weeks to be a fairly reasonable duration for an internship, which may produce some concern regarding this assumption’s sensitivity. But since this analysis is on the change of a measurement for one alternative leaving all other durations for other alternatives constant, its threat to our model’s validity remains inconclusive.

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Final Recommendation

Brady should take the best internship he is offered, by rank (most preferred being Payliance). If he is offered any internship positions, Brady should accept the most preferred/highest ranked out of them. If not offered any internships, Brady should take the golf course job in Columbus.

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Thank You!

Questions?