Contabilidad

Glenn Abbot, the CEO of RPG, is faced with the following dilemma: should he choose project A with a certain payoff of $2.5 million, or choose project B where RPG could make $10.8 million if the project is completed on time but would lose $1.8 million if the project is completed late. The best estimate is that the probability is 0.6 that RPG would finish project B on time. It is possible to generate a better estimate through a quick-and-dirty experiment at a cost of $100,000. If the experiment yields favorable result the probability of finishing project B on time would increase to 0.8. On the other hand, should the experiment yield unfavorable result the probability of finishing project B on time would decline to 0.4. The probability of favorable result is 0.5 and the probability of unfavorable result is 0.5. The experiment would have no other material effect on any other parameter of the problem described above. As a decision maker, Abbot is a maximizer of EMV (expected monetary value).

OR-Notes

J E Beasley

OR-Notes are a series of introductory notes on topics that fall under the broad heading of the field of operations research (OR). They were originally used by me in an introductory OR course I give at Imperial College. They are now available for use by any students and teachers interested in OR subject to the following conditions.

A full list of the topics available in OR-Notes can be found here.

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Decision trees examples

Decision tree example 1995 UG exam

Your company is considering whether it should tender for two contracts (MS1 and MS2) on offer from a government department for the supply of certain components. The company has three options:

• tender for MS1 only; or

• tender for MS2 only; or

• tender for both MS1 and MS2.

If tenders are to be submitted the company will incur additional costs. These costs will have to be entirely recouped from the contract price. The risk, of course, is that if a tender is unsuccessful the company will have made a loss.

The cost of tendering for contract MS1 only is £50,000. The component supply cost if the tender is successful would be £18,000.

The cost of tendering for contract MS2 only is £14,000. The component supply cost if the tender is successful would be £12,000.

The cost of tendering for both contract MS1 and contract MS2 is £55,000. The component supply cost if the tender is successful would be £24,000.

For each contract, possible tender prices have been determined. In addition, subjective assessments have been made of the probability of getting the contract with a particular tender price as shown below. Note here that the company can only submit one tender and cannot, for example, submit two tenders (at different prices) for the same contract.

Option Possible Probability

tender of getting

prices (£) contract

MS1 only 130,000 0.20

115,000 0.85

MS2 only 70,000 0.15

65,000 0.80

60,000 0.95

MS1 and MS2 190,000 0.05

140,000 0.65

In the event that the company tenders for both MS1 and MS2 it will either win both contracts (at the price shown above) or no contract at all.

• What do you suggest the company should do and why?

• What are the downside and the upside of your suggested course of action?

• A consultant has approached your company with an offer that in return for £20,000 in cash she will ensure that if you tender £60,000 for contract MS2 only your tender is guaranteed to be successful. Should you accept her offer or not and why?

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Solution

The decision tree for the problem is shown below.

Below we carry out step 1 of the decision tree solution procedure which (for this example) involves working out the total profit for each of the paths from the initial node to the terminal node (all figures in £'000).

Step 1

• path to terminal node 12, we tender for MS1 only (cost 50), at a price of 130, and win the contract, so incurring component supply costs of 18, total profit 130-50-18 = 62

• path to terminal node 13, we tender for MS1 only (cost 50), at a price of 130, and lose the contract, total profit -50

• path to terminal node 14, we tender for MS1 only (cost 50), at a price of 115, and win the contract, so incurring component supply costs of 18, total profit 115-50-18 = 47

• path to terminal node 15, we tender for MS1 only (cost 50), at a price of 115, and lose the contract, total profit -50

• path to terminal node 16, we tender for MS2 only (cost 14), at a price of 70, and win the contract, so incurring component supply costs of 12, total profit 70-14-12 = 44

• path to terminal node 17, we tender for MS2 only (cost 14), at a price of 70, and lose the contract, total profit -14

• path to terminal node 18, we tender for MS2 only (cost 14), at a price of 65, and win the contract, so incurring component supply costs of 12, total profit 65-14-12 = 39

• path to terminal node 19, we tender for MS2 only (cost 14), at a price of 65, and lose the contract, total profit -14

• path to terminal node 20, we tender for MS2 only (cost 14), at a price of 60, and win the contract, so incurring component supply costs of 12, total profit 60-14-12 = 34

• path to terminal node 21, we tender for MS2 only (cost 14), at a price of 60, and lose the contract, total profit -14

• path to terminal node 22, we tender for MS1 and MS2 (cost 55), at a price of 190, and win the contract, so incurring component supply costs of 24, total profit 190-55- 24=111

• path to terminal node 23, we tender for MS1 and MS2 (cost

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