Question

You are planning an activity which requires the use of a crane. You can rent either a small or large crane. The small crane costs less to rent ($10,000 versus $16,000 for the large crane) but will be slower. As currently planned the activity is not on the critical path, however, an analysis has indicated that there is a 30% probability that the activity will become critical. If it does go critical the table below applies; each day's delay in the activity will cost the project $5000. The table indicates the delay probabilities (short, medium or long) and their respective delays associated with the small or large crane. Small Crane Large Crane Delay Probability Delay in Days Probability Delay in Days Long 0.2 10 0.2 3 Medium 0.5 5 0.5 Short 0.3 0.3 Draw a properly labeled decision tree and using expected value determine which crane should be chosen.

Answer 1

Answer:

Rent for small Crane is $10,000 Rent for large Crane is $16,000 Expected Delay in case of small Crane = 2*10 + .5*5 +.3*2 = 5.1 days, therefore expected cost of delay is $25,500 (5.1*5000) and hence Total expected cost in case of small crane is $35,500 (10000+25500). Expected Delay in case of large Crane = .2*3+.5*2 + .3*1 = 1.9 days, therefore expected cost of delay is $9,500 (1.9*5000) and hence Total expected cost in case of small crane is $25,500 (16000+9500). Even if we round of expected number of days of delay as 5 in case of small crane and 2 in case of large crane, it is found that expected total cost in case large crane is less than that in case of small crane. Therefore based on expected value of total cost (rent+delay) Large Crane should be selected. Diagram of the decision tree has one Decision box having two branches showing two options of hiring small and large crane. Both the branches three states representing three types of delays (long, medium, short) with respective probabilities. long delay(-2, 10) Small Crane (10000) State circle (25500) medium delay(-5,5) Short delay(.3, 2) Decision Box long delay(-2,3) State circle(9500) medium delay(-5, 2) Large Crane(16000) Short delay(-3,1)