Assignment: Probabilities

Respond to…

Looking at the situation, I am conflicted about how to answer. My first response is to calculate probabilities of the sample of their drive for the first 20 days and then calculate in the winter months’ delays into the probability, and then factor in the smart-phone app.

Sample Month Probability = 3 / 20 = 15%
Expected time along I-20 = 25 minutes x 85% + 45 minutes x 15% = (21.25 + 6.75) minutes = 28 minutes
Expected time along Boulevard = 35 minutes
Highway 1-20 takes less expected time and is the better option.

Winter Months Probability = 6 / 20 = 30%
Expected time along I-20 = 25 minutes x 70% + 45 minutes x 30% = (17.5 + 13.5) minutes = 31 minutes
Expected time along Boulevard = 35 minutes
Highway 1-20 takes less expected time and is the better option.

App Probability =  1 / 20 = 5%
Expected time along I-20 = 25 minutes x 95% + 45 minutes x 5% = (23.75 + 2.25) minutes = 26 minutes
Expected time along Boulevard = 35 minutes
Highway1-20 takes less expected time and is the better option.

When I think deeper into the question, I want to factor in the utility associated with the decision. Does it yield a higher utility for the drivers to know that taking the Boulevard route that offers less probabilities of traffic jams, that could possible take up to 45 minutes and cause them to be late to work, which in turn, could cost them their job if they had a job where they had to clock-in each day. Does it hold a higher utility if they consider highway traffic to be stressful compared to a more scenic route of the Boulevard. These drivers are not held to the maximin decision rule where they are looking out for shareholders and the best interest for a company, but their decisions are driven by other factors. On a personal level, the drivers have to weigh their degree of risk aversion, which can vary from zero degrees of risk aversion to being extremely risk-averse.

The problem presented is outside of the business management spectrum which constitutes looking at personal utility. The problem also only offers sample data from their own experience within 20 days. Would it make for a better judgment of probabilities to look at information supplied by the Department of Transportation of accidents on those particular routes over a period of a year or over certain months during that year?

References

Douglas, E. (2012). Managerial Economics (1st ed.) [Electronic version]. Retrieved May 8, 2019, from https://content.ashford.edu/ (Links to an external site.)Links to an external site. (Links to an external site.)

Respond to…

I-20 without traffic jams (25 min * 17 days) = 425 minutes

I-20 with traffic jams (45 min * 3 days) = 135 minutes

Shea Boulveard (35 minutes * 20 days) = 700 minutes

Winter weather

I-20 without traffic jams (25 min * 14 days) = 350 minutes

I-20 with traffic jams (45 min * 6 days) = 270 minutes

Highway total drive time  (425 + 135) = 560 mins

Winter weather total drive time (350 + 270) = 620 mins

Based on the calculations above we can answer the following:

should Edith and Mathew continue to use the highway for traveling to work?

The highway is deemed to be the most efficient route for Edit and Matthew to take to work. Data supports that they are only utilizing 560 total minutes each month in drive time even with a few traffic jam delays. This is ower than taking the shea boulevard route of 700 minutes.

How would your conclusion change for the winter months, if bad weather makes it likely for traffic jams on the highway to increase to 6 days per month?

In regards to the increase of delays on the highway during the winter months, the highway route is still the most efficient route to take. With the added delay days the total monthly drive time is 620 minutes. This is still lower than taking the Shea Boulevard route of 700 minutes.

How would your conclusion change if Mathew purchased a new smart-phone app that could show the status of the highway traffic prior to their drive each morning, thus reducing the probability of them getting into a jam down to only 1day per month (where on this day, the app showed no traffic jam, but a jam developed in the meantime as they were driving along the highway).

The app is a good resource to use in planning your route and getting an overview of what to expect, however, it is not real-time data and you could be in transit and an accident happens which is deemed an unforeseen event. The app is a tool but it cannot predict risks or uncertainties. According to Douglas (2012), risks are the potential outcomes and the probability of each outcome is known in advance. Uncertainty is when the potential outcomes are not entirely predictable or probabilities are not estimated in advance. With that being said Edith and Matthew should stick to the Highway route and utilize the app Matthew downloaded on a case by case basis. I would not recommend them to change their route due to the uncertainty of the app.

Reference

Douglas, E. (2012). Managerial Economics (1st ed.) [Electronic version]. Retrieved May 8, 2019, from https://content.ashford.edu/ 

 
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