Allegheny Mountain Power and Light is an electric utility company with a large fleet of vehicles including automobiles, light trucks, and construction equipment. The company is evaluating four alternative strategies for maintaining its vehicles at the lowest cost: (1) take no preventive maintenance at all and repair vehicle components when they fail; (2) take oil samples at regular intervals and perform whatever preventive maintenance is indicated by the oil analysis; (3) change the vehicle oil on a regular basis and perform repairs when needed; and (4) change the oil at regular intervals and take oil samples regularly, performing maintenance repairs as indicated by the sample analysis.

For autos and light trucks, strategy 1 (no preventive maintenance) cost nothing to implement and results in two possible outcomes: There is a 0.08 probability that a defective component will occur, requiring emergency maintenance at a cost of $1,600, or there is 0.92 probability that no defects will occur and no maintenance will be necessary.

Strategy 2 (take oil samples) cost $40 to implement (i.e. take a sample), and there is a 0.08 probability that there will be a defective part and 0.92 probability that there will not be a defect. If there is actually a defective part, there is a 0.7 probability the sample will correctly identify it, resulting in preventive maintenance at a cost of $500. However, there is a 0.3 probability that the sample will not identify the defect and indicate everything is okay, resulting in emergency maintenance later at a cost of $1,600. On the other hand, if there are actually no defects, there is a 0.2 probability that the sample will erroneously indicate that there is a defect, resulting in unnecessary maintenance at a cost of $230. There is a 0.8 probability that the sample will correctly indicate there are no defects, resulting in no maintenance and no costs.

Strategy 3 (changing the oil regularly) cost $34.80 to implement and has two outcomes: a 0.04 probability of a defective component, which will require emergency maintenance at a cost of $1,600, and a 0.96 probability that no defects will occur, resulting in no maintenance and no cost.

Strategy 4 (changing the oil and sampling) cost $74.80 to implement and results in the same probability of defects and no defects as in strategy 3. If there is a defective component, there is a 0.7 probability that the sample will detect it and $500 in preventive maintenance cost will be incurred. Alternatively, there is a 0.3 probability that the sample will not detect the defect, resulting in emergency maintenance at a cost of $1,600. If there is no defect, there is a 0.2 probability the sample will indicate there is a defect, resulting in an unnecessary maintenance cost of $250, and a 0.8 probability that the sample will correctly indicate no defects, resulting in no cost.

a) Develop a decision tree for Allegheny Mountain Power and Light and indicate the expected value. Which strategy should be adopted?

For heavy construction equipment, emergency maintenance is much more expensive and cost $15,000. Required maintenance cost $2,000 and unnecessary maintenance cost $1,200. The cost of an oil change is $200 and the cost of taking an oil sample and analyzing it is $50. All the probabilities remain the same as for the autos and light trucks.

b) Determine the strategy the company should use for its heavy equipment using another decision tree.  

c) From the example above, discuss why the strategy for heavy construction equipment is similar with or different from that of autos and light trucks.