Question

Stephanie has 3 ways to commute to work - driving, subway, or train. The chart below shows how long it takes her to get to work depending on the weather:

Decision	Clear Skies	Raining	Snowing
Driving	15	30	45
Subway	20	25	35
Train	30	30	30

Suppose the probabilities for clear skies is 50%, rain is 33% and snow is 17%:

Construct a decision tree and solve it using Expected Value Approach. What is the recommended decision alternative?

Answer 1

Stephanie has 3 options

1. Drive:
   1. Time taken is 15 mins. with clear sky (probability=0.50), 30 mins with rain (probability 0.33), 45 mins with snow (probability=0.17)
2. Subway:
   1. Time taken is 20 mins. with clear sky (probability=0.50), 25 mins with rain (probability 0.33), 35 mins with snow (probability=0.17)
3. Train:
   1. Time taken is 30 mins. with clear sky (probability=0.50), 30 mins with rain (probability 0.33), 30 mins with snow (probability=0.17)

The decision tree is below

Moving the from the left to the right

chance node 2: when Driving

The expected value (expected time) is

chance node 3: when taking subway

The expected value (expected time) is

chance node 4: when taking train

The expected value (expected time) is

Decision node 1

The expected time taken for the 3 options are

1. Drive with an expected time of 25.05 minutes
2. Take subway with an expected time of 24.2 minutes
3. Take a train with an expected time of 30 minutes

We want to minimize the expected time taken to get to work. Taking subway has the least expected time of the 3 choices. Hence Stephanie should take the subway.