Question

Dorothy Stanyard has three major routes to take to work. She can take Tennessee Street the entire way, she can take several back streets to work, or she can use the expressway. The traffic patterns are, however, very complex. Under good conditions, Tennessee Street is the fastest route. When Tennessee is congested, one of the other routes is preferable. Over the past two months, Dorothy has tried each of route several times under different traffic conditions. This information is summarized in minutes of travel time to work in the following table: + No Traffic Congestion (Minutes) Mild Traffic Congestion (Minutes) 30 Severe Traffic Congestion (Minutes) 15 45 Tennessee Street Back roads Expressway 20 25 35 30 30 In the past 60 days, Dorothy encountered severe traffic congestion 10 days and mild traffic congestion 20 days. Assume that the past 60 days are typical of traffic conditions. a. What route should Dorothy take. Use the EP criterion. (10 points) b. Dorothy is about to buy a radio for her car that would tell her the exact traffic conditions before she started to work each morning. How much time in minutes on the average would Dorothy save by buying the radio? (i.e. Calculate the EVPI) (5 points).

Answer 1

(a)

Probability of mild congestion = 20/60 = 1/3

Probability of severe congestion = 10/60 = 1/6

Probability of no congestion = 1 - 1/3 - 1/6 = 1/2

Alternative \ States of nature	No congestion	Mild congestion	Severe congestion	Expected minutes
Tennessee Street	15	30	45	15*1/2+30*1/3+45*1/6 = 25.00
Back roads	20	25	35	20*1/2+25*1/3+35*1/6 = 24.17
Expressway	30	30	30	30*1/2+30*1/3+30*1/6 = 30.00
Probability	1/2	1/3	1/6

Based on minimum expected minutes (the EP criterion in this case), the best alternative is to use the Expressway.

(b)

Expected minutes with perfect information = Min(15, 20, 30)*1/2 + Min(30, 25, 30)*1/3 + Min(45, 35, 30)*1/6 = 20.833 minutes

Expected value without perfect information = 24.17

So, EVPI = 24.17 - 20.833 = 3.33 minutes