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 November outside temperatures are below freezing. As a result, Central’s staff estimate that there is a 0.7 probability that the additional station will be required later in the day if no request is made to the customer. If the customer is asked to reduce usage it is virtually certain that the additional station will not be required. Before making the decision on whether to send the request to the customer Central has another option. It could purchase a forecast from the local weather center at a cost of $1500. For this payment the weather center will use a model to indicate whether the additional station will be required. The accuracy of its forecasts is shown by the following table of probabilities.
(a) (i) For the day in question, determine the expected value of the imperfect information from the weather center and explain your result.
(ii) Assuming that Central’s objective is to minimize expected costs, advise them on the course of action they should take.
(b) Discuss the extent to which the expected monetary value (EMV) criterion is likely to be appropriate to Central’s decision.