The RedGold company

RedGold is a major cider producer with sales representing about 30% the UK cider market. The company, which is located in the West Midlands of England, sells its product in bottles and cans, and on draught in clubs and public houses.

In the financial year 2001/2 the company achieved excellent results. The value of sales increased by 28% to $60 million and pre-tax profits of $6 million represented and increase of 55% on the previous year. Much of the company's success was based on sales of draught cider. The number of outlets selling the product had increased substantially over recent years and the upward trend in sales had been accelerating.

The growth in draught cider sales had, however, created some problems for the company's managers. In particular, there was concern that in August, when sales reached a seasonal peak, there might not be enough kegs available to meet demand. Kegs are 11 gallon, stainless steel containers in which draught cider is supplied to customers. After use, empty kegs are returned to the cider mill where they are inspected for damage, cleaned and refilled. In 2002, Applegold owned about 100,000 kegs, but in view of the expansion of sales, it was felt by some managers that this stock should be increased.

In June 2002, the recently formed Keq Steering Committee met to consider the position for the coming summer. This committee consisted of managers from the Operations, Computing, Accounting, Sales and Marketing departments. Rick Fleetwood, the Operations Manager, put forward a proposal that 8000 new kegs should be ordered immediately from the manufacturer in Birmingham so that they would be available in time for the peak summer demand (the manufacturer would only supply in batches of 1000 kegs).

Ted Mitchell, the accountant was less sure. At $40 per keg this would amount to expenditure of $320,000 and there was no certainty that all these kegs would be needed. Fleetwood pointed out that, even if they were not needed this year, the kegs might be required in the following year.

'In that case," retorted Mitchell, "we'll have tied up $320,000 for a year unnecessarily. Given a 10% rate of interest, that would cost us $32,000."

At this point Colin Jewel, the Data Processing Manager, intervened. "Surely there are intermediate positions. We could presumably order any number of batches from 0 to 8. What we need is some estimate of the likely levels of demand in August and the consequences of having given number of kegs available to meet these levels of demand."

Phil Skills, the Sales Manager, pointed out that the sales forecasts were really only reliable one month ahead, partly because this was linked to the long-range weather forecast. In hot, dry summers, sales rocketed. "Perhaps we should delay our decision until July when we'll get the August forecast," he said.

"If we do that," replied Fleetwood, "it may well be too late. Other brewers might be placing orders with the keg manufacturers and I reckon there'd only be an 80% chance that they could get the kegs produced for us in time for August. Surely you must have some idea of what sales are likely to do. After all, your reps are constantly touring the country, talking to people in the trade."

Skills was silent for a few moments. "Well, if you really twist my arm, the best I can say is this. I reckon there's about a 60% chance that sales in August this year will be at least 10% up on August last year, a 30% chance that increase by less than this amount and a 10% chance that we will see no increase. But remember, these are only rough guestimates."

Jewel turned to Mitchell. "OK, can we do some calculations on what the consequences are of having different numbers of kegs available for August assuming first no increase in sales, secondly a less than 10% increase and thirdly an increase of at least 10%?"

Mitchell was sceptical, but under pressure he agreed to do some rough calculations. For simplicity, he assumed that:

i) either 0, 4000 or 8000 kegs would be ordered;

ii) if sales increased by more than 10%, all extra kegs purchased would be used during August, while if sales increased by less than this amount, only 4000 extra kegs would be needed.

iii) if it was needed, each new keg would make only one journey in August thereby supplying 11 gallons of cider to customers and earning a contribution of $8.

The results of his calculations are shown in the table below. This shows the estimated changes in profit which would result for different decisions and different levels of sales.

(Changes in profit)

Sales in August 2002

No increase onUp less than10%Up at least 10%

Previous yearon previous yearon previous year

No of

new kegs

purchased

0$0$0$0

4000-$16000$16000$16000

8000-$32000$0$32000

Jen Martin, from the Marketing department, was quick to point out that these calculations took no account of the customer goodwill which would be lost if the Company was unable to meet demand because of a shortage of available kegs. "In the long run," she said,"we could see customers asking us to remove the pumping equipment we have installed in their bars and that could prove costly!"

"I still think it might be worth delaying our decision until we get the August sales forecast," said Skills,"even if that does mean taking a risk that the kegs will not be available."

"How reliable are these one month ahead forecasts?" asked Jewel.

"They're not bad. If you can give me a couple of days I'll let you have a summary of their recent performance."

After some further discussion, it was agreed to reconvene the committee at the end of the week when Skills' figures could be looked at. A decision would then be made on whether to go ahead and order a specific number of kegs immediately or to delay the purchasing decision until the sales forecast was available. The results which Skills put to the meeting are appended.

Appendix Details of sales forecast performance for past 72 months

For example, in 22 of these months there was no increase in sales over the previous year.

The forecast had correctly predicted this for 12 of the months, but:

for 6 of the months an increase of less than 10% had been forecast, and

for 4 of the months an increase of at least 10% had been forecast.

QUESTIONS:

#4.Use the information from the above case study to devise values for all terminal

nodes for the decision tree (T1-T29); grey boxes.The change in profit amounts are

given within the case study.

Report all values as integers - include negatives where needed.The responses should be dollar amounts (Ex:$63,000 should be 63)

#5.Use the information from the above case study to devise values for all posterior

probabilities for the decision tree (P1-P29); blue boxes.Responses are derived in the previous BAYES analysis questions.

Report all values to 3 decimals with leading zero (ex:0.326)

Use the responses from question 1, 2, and 3 to populate the probabilities for

P1-P29.

#6.Use the information from the above case study to devise values for all probability nodes

for the decision tree (Q1-Q15); yellow boxes.The Q values are given; those values are

provided within the case study.

The values are based on calculations; keep the maximum value