Jovan\'s Movers rents out trucks with a crew of two on a daily basis, usually to

Question

Jovan's Movers rents out trucks with a crew of two on a daily basis, usually to homeowners who are moving or to companies with delivery problems. On one particular day Jovan is a truck short and intends to hire one from a local truck rental firm. However, he does not know how large the load is that needs to be moved.

How big a truck should he rent? A large truck costs $200 per day (including insurance, fuel, etc.), a small truck $130 per day. A small truck is cheaper but if the load is too large, the crew may have to make two trips. Jovan assesses the additional cost of making two trips (overtime and truck mileage) at $150 beyond the costs for a single trip. He assesses the probability that two trips will be necessary if he rents a small truck at 0.40. Assume that if Jovan rents a large truck it can accommodate any size load in a single trip.

Assuming there are no other ramifications to the decision, should Jovan rent a large truck or a small truck? Construct a decision tree (manually or using PrecisionTree) to support your answer and explain your recommendation. Would your answer change if the probability that two trips will be necessary is 50% instead of 40%?

What is the most Jovan would pay to know for sure whether a small truck or a large truck would be adequate for the job? For example, suppose he could hire someone to inspect the contents of the move in advance. Construct a second decision tree to support your answer and estimate if the probability of needing two trips with a small truck is set to 40% as in part a).

Suppose Jovan is risk averse, with a risk tolerance value of $1,000 (assume the exponential utility function applies). Would this change your answer to part a)?

Explanation / Answer

If Jovan decides to hire a large truck, it will cost him $ 200

But with a probability of 0.4 that the small truck will need to make two trips with an additional cost of $ 150, i.e. above the normal expense of $ 130, the expected cost = 0.6 * 130 + 0.4 * (130 + 150) = $ 190, which is lower than the cost of hiring a large truck, so Jovan should hire a small truck

Now, if the probability changes to 0.5, then his expected cost = 0.5 * 130 + 0.5 * (130 + 150) = $ 205

So, with a 50 % probability of two trips for small truck, JOvan should hire a large truck

Now , EVPI = EV | PI - EMV = (0.4 * 200 + 0.6 * 130) - 130

EV | PI = maximising the return, when there is a 40 % prob of two trips, hire a large truck, else hire a small truck

= 152 - 130 = $ 22

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