MSCI 224 Techniques for Management Decision Making

PART A: Answer Question A1 in this section of the paper.

Question A1 (25 marks)

A record label have the money to sign a single new act. They are considering a Country Pop artist, a Rock band and a Jazz artist. They are unsure of the demand for new music but believe that demand will high with probability 0.65. The payoff for signing each of the bands is summarised in the following payoff table

a) Consider the decision criterion of EV, Maximin and Maximax, what decision should the record label make under each decision criterion?

(5 marks)

b) Let p denote the probability of high demand. For what range of values of p would your decision under the expected value decision criterion remain the same as the decision chosen in part a) of this question?

(5 marks)

A) No change in the value of p would change our decision.

B) p > 0.571

C) p > 0.533

D) p < 0.672

c) The record label have the option of using a market research company to predict whether demand for new music will be high. At the end of their investigation the market research company will produce a report indicating whether demand will be high or low (e.g. a positive report is analogous to them predicting high demand). The market research company have worked in the music industry in the past, their past record for predicting an high/low demand is summarised in the following table

What is the probability of the market research company returning:

i) a positive report

ii) a negative report

Additionally what is the probability of

iii) demand being high given a positive report

iv) demand being low given a negative report

(5 of marks)

d) Draw a decision tree to represent whether the record label should use the market research company and which act they should sign.

(5 of marks)

e) Provide the record label with advice on which action they should take using the decision tree to support your recommendation.

(5 of marks)

PART B: Answer two of the three questions in this section of the paper.

Question B1 (25 marks)

A construction project has a deadline of 21 weeks. It consists of the following activities, with their predecessors and the optimistic, most likely and pessimistic times (in weeks):

a. activity durations calculate the earliest and latest start and finish times for each activity, and the total float and free float for each activity. State the project duration and the critical path.

(10 marks)

b. Using P.E.R.T., what is the probability of the project meeting its deadline of 21 weeks?

(5 marks)

A) 0.932

B) 0.644

C) 0.836

D) 0.798

c. There is a 90% probability of completing the project within x weeks. What is the value of x? Calculate the value of x using P.E.R.T to two decimal places.

(3 marks)

A) 21.61

B) 23.33

C) 20.17

D) 25.12

d. Explain why the P.E.R.T. method gives slightly optimistic results. How serious is this limitation likely to be for this project and how can it be overcome?

(2 marks)

e. Without doing any calculations, if the estimates of the times for activities D and F increase or decrease (for example, by changing the resources allocated to them) explain how this would affect the likelihood of the project meeting its deadline.

(5 marks)

Question B2 (25 marks)

A Table Manufacturing Company has discontinued the production of some unprofitable products. This has created excess production capacity for their other products. Management is thinking to devote this excess capacity to three types of tables: luxury, standard and compact. The available capacity of three machines that might limit the output is summarised in the table below:

The Table Manufacturing Company introduced luxury tables very recently to the market and plan to produce no more than 20 of them next week. The unit profit for standard, compact and luxury tables are 50GBP, 20GBP and 100GBP per product respectively.

The Table Manufacturing Company is asking the question how much of each product it should produce to maximise its profit?

(a) Formulate the problem as a linear programme, which maximizes the total profit.

(8 marks)

After solving the problem optimally, the Excel Solver gives the following Answer and Sensitivity reports. Please use them to answer rest of the questions:

(b) What is the optimal solution and optimal objective function value? How many tables of each type should be produced in order to maximise the profit? What is the remaining hours from milling machine, lathe and grinder?

(6 marks)

A) Produce 20 standard, 40 luxury tables and 0 compact tables. Total profit is 4000 GBP. There are an extra 20 machine hours of milling and 40 machine hours of grinding left.

B) Produce 40 standard, 20 luxury tables and 0 compact tables. Total profit is 4000 GBP. There are an extra 40 machine hours of milling and 80 machine hours of grinding left.

C) Produce 40 standard, 20 luxury tables and 20 compact tables. Total profit is 4400 GBP. There are an extra 40 machine hours of milling and 80 machine hours of grinding left.

D) Produce 20 standard, 40 luxury tables and 20 compact tables. Total profit is 4500 GBP. There are an extra 80 machine hours of milling and 40 machine hours of grinding left.

(c) After the marketing team had investigated your solution they have realised that you have underestimated the profit from compact tables. They told you the profit per compact table is 30GBP per table. How should you change your mathematical model and how should you change your solution after this increase?

(4 marks)

(d) The production team have realised they forgot to include finishing operations on each table. Each standard, compact and luxury table need 5, 3 and 9 hours in finishing department respectively and there are only 350 hours available. How many extra hours do you need from the finishing department to realise your production plan?

(2 marks)

A) 15 hours

B) 20 hours

C) 25 hours

D) 30 hours

(e) You have solved the problem with the finishing department and do not need to consider its capacity anymore. Now the marketing team has contacted you to inform you that one of the retailers has shown interest in ordering more luxury tables. They told to your marketing team representative that if you can discount additional tables by 20GBP, they could order 12 more tables. What should be your decision if your aim is still to maximise your profit? If you decide to produce 12 more tables, what would be your new profit and production mix?

(5 marks)

Question B3 (25 marks)

An online retail company selling home appliances have been operating for the last 14 months. During that time they have monitored the number of hits on their website as they believe this information is useful for investigating possible lost sales. This data is recorded in thousands in the following table:

a) Plot the data. What (if any) pattern/s do you see in the data?

(3 marks)

A) There is trend and seasonality in the data

B) There is a trend but no seasonality in the data

C) There is seasonality but no trend in the data

D) There is no trend or seasonality in the data

b) Given the context, comment on any patterns that you see in the data and explain what may have caused them.

(2 marks)

c) Use exponentially weighted moving averages with smoothing parameter α=0.2 to forecast the number of hits on the company’s website for the next three months.

(5 marks)

d) Using Holt’s method with smoothing parameter α=0.3 and β = 0.3 re-forecast the number of hits on the company’s website for the next three months

(5 marks)

e) What is the mean absolute deviation (MAD) and root mean square error (RMSE) for the forecasts for the last 6 months (months 8 -14)?

(5 marks)

A) Exponentially weighted moving average: MAD = 2.77, RMSE = 3.52, Holt’s method: MAD = 1.95, RMSE = 3.32.

B) Exponentially weighted moving average: MAD = 2.63, RMSE = 3.23, Holt’s method: MAD = 2.55, RMSE = 3.32.

C) Exponentially weighted moving average: MAD = 2.97, RMSE = 3.52, Holt’s method: MAD = 5.15, RMSE = 5.64.

D) Exponentially weighted moving average: MAD = 2.97, RMSE = 3.52, Holt’s method: MAD = 2.55, RMSE = 3.32.

f) Which forecasting method produces the more accurate forecasts? Is it the most appropriate method, and why?

(5 marks)