Daily Archives: June 19, 2021

Explain why the model is likely to be a simplification of the real problem.

The managers of a food company are about to install a number of automatic vending machines at various locations in a major city. A number of types of machine are available and the managers would like to choose the design which will minimize the profit that will be lost because the machine is out of order. The following model is to be used to represent the lost profit:

Cost of lost profit per month= (number of breakdowns per month)× (time to repair machine after each breakdown, in hours)× (profit lost per hour)

One machine that is being considered is the Supervend, and the following probability distributions have been estimated for this machine:

(a) Use a table of random numbers, or the random number button on a calculator,….

Compare the risk analysis results for the six designs and discuss how a decision could be made between them.

Trentware plc is a medium-sized pottery manufacturer which is based in the English Potteries. The company has fared badly over the last 10 years mainly as a result of Japanese competition, and recently this has led to major changes at the senior management level. The new Managing Director is determined to increase the company’s market share, and you are a member of the ambitious new management team which intends to extend the company’s range of tableware designs. Trentware’s immediate objective is to launch a new high-quality product for the Christmas market in 18 months’ time. Over 30 possible designs have been subjected to both technical analysis (to assess their production implications) and extensive market research. As a result of this analysis, the number of potential designs has now….

The number of days that the machine will be hired out in year 1 and in year 2;

(This exercise is really designed to be carried out by a group of people, with each individual using a different set of random numbers. The individual results can then be combined by using the table at the end of the question.) An equipment hire company has to decide whether to buy a specialized piece of earth-digging machinery for $6000. The machine would be sold after two years. The main factors which it is thought will affect the return on the investment are:

(i) The revenue generated by hiring the machine out for a day: it is certain that this will be $40;

(ii) The number of days that the machine will be hired out in year 1 and in year 2;

(iii) The costs of having the machine….

Compare the two distributions, and stating any necessary assumptions, determine the option that the management should choose.

The managers of a chemical company have to decide whether to extend their existing plant or replace it with completely new equipment. A simulation of the two alternatives gives the following probability distributions of net present value:

(a) Compare the two distributions, and stating any necessary assumptions, determine the option that the management should choose.

(b) After the above simulations have been carried out a third possible course of action becomes available. This would involve the movement of some of the company’s operations to a new site.

A simulation of this option generated the following probability distribution. Is this option worth considering?

 

Explain why the estimate from the model might differ from the ‘holistic’ estimate of the marketing manager and discuss how the conflict might be resolved.

A publisher is considering launching a new magazine for women in the 18–25 years age group. It is thought to be vital to the long-term success of the magazine that its sales should reach break-even point within its first year. When asked to make an estimate of the risk of this target not being achieved, the marketing manager, after some thought, states that she thinks the risk is only about 1 in 10.

(a) Sketch out the key features of a risk analysis model which might be appropriate for this estimate and explain how the estimate would be obtained from the model.

(b) Suppose that your risk analysis model suggests that the risk of not achieving the target is about 1 in 4. Explain why the estimate from….

How much would it be worth paying for the information from the test?

A company has just received some ‘state of the art’ electronic equipment from an overseas supplier. The packaging has been damaged during delivery and the company must decide whether to accept the equipment. If the equipment itself has not been damaged, it could be sold for a profit of $10 000. However, if the batch is accepted and it turns out to be damaged, a loss of −$5000 will be made. Rejection of the equipment will lead to no change in the company’s profit. After a cursory inspection, the company’s engineer estimates that there is a 60% chance that the equipment has not been damaged. The company has another option. The equipment could be tested by a local specialist company. Their test, however, is not perfectly reliable and….

Calculate the expected value of imperfect information and hence determine whether the company should test market the product.

The managers of Red Valley Auto Products are considering the national launch of a new car-cleaning product. For simplicity, the potential average sales of the product during its lifetime are classified as being either high, medium or low and the net present value of the product under each of these conditions is estimated to be $80 million, $15 million and −$40 million, respectively. The company’s marketing manager estimates that there is a 0.3 probability that average sales will be high, a 0.4 probability that they will be medium and a 0.3 probability that they will be low. It can be assumed that the company’s objective is to maximize expected net present value.

(a) On the basis of the marketing manager’s prior probabilities, determine:

(i) Whether the product should….

Explain the rationale behind your recommended decision rule in non-technical terms.

A food company runs a computerized processing plant and needs to formulate a series of decision rules to advise its managers on how they should react if the control panel indicates particular problems with the system. Because there is always a possibility that an indicated problem is in fact caused by a fault in the control panel itself, there is some concern that unnecessary losses will be incurred if production is halted because of a non-existent problem.

Light number 131 will illuminate on the panel if the computer detects that packs of a frozen food are being filled to below the legal weight. However, it is known that there is a 0.15 probability that this light will give a false alarm. In the event of this light illuminating,….

Discuss the extent to which the expected monetary value (EMV) criterion is likely to be appropriate to Central’s decision.

When the demand for electricity exceeds a particular level the Central Electricity Company has to bring an additional power station on line at a fixed cost of $10 000. Excessive demand only occurs on cold winter weekdays between 4.30 and 5.30 pm. To try to avoid bringing the additional station on line Central has made a deal with its largest industrial customer. According to the deal the customer will reduce its electricity usage by an agreed amount between 4.30 and 5.30 pm on any day that they receive a request from Central. In return they will receive a reduction in their bill of $6000 for any day that a request is received. However, the request will need to be made by 9.30 am. At 9.00 am on 26….

Determine the expected value of the information from the test, assuming that the food company’s objective is to minimize expected costs.

A worker in a food plant has a rash on his left arm and the company doctor is concerned that he may be suffering from Flaubert’s disease. This can only occur as a result of biological contamination of the raw materials that the worker handles in his job. However, the disease is rare and has not occurred in the plant during the ten years of its operation so the doctor estimates that the probability that contamination exists in the plant to be only 2%, while there is a 98% chance that the contamination is not present. The doctor has now to advise the company’s board on whether they should close the plant for two days to enable fumigation to be carried out. This would certainly eradicate any contamination….