Assignment 1:

Nganunu Corporation (NC) purchased land that will be the site of a new luxury double-storey complex. The location provides a spectacular view of the surrounding countryside, including mountains and rivers. NC plans to price the individual units between R300 000 and R1 400 000. NC commissioned preliminary architectural drawings for three different projects: one with 30 units, one with 60 units and one with 90 units. The financial success of the project depends upon the size of the complex and the chance event of demand for the units.

The decision problem is to select the size of the new complex that will generate the largest profit, given the uncertainty about the demand of for the units. The information on the NC case (in terms of action and states of nature), including the corresponding payoffs, can be summarised as follows:

The management of NC is considering a six-month market research study to learn more about the potential market’s acceptance of the NC project. Suppose that the company asks economic experts for their opinion on the potential market’s acceptance of the NC project. Historically, their upside predictions have been 90% accurate, while their downside predictions have been 60% accurate.

a) Using decision trees, determine the best strategy
i. if Nganunu does not use experts (15)
ii. if Nganunu uses experts (45)

b) What is the expected value of sample information (EVSI)? (5)
c) What is expected value of perfect information (EVPI)? (5)
d) Based on your analysis and using only the part of the decision tree where NC used experts, provide a corresponding risk profile for the optimal decision strategy. (10)

Your answers will be assessed in terms of the level of communication displayed, the insights and inferences drawn, and your ability to show the implications of the factors that you have assessed and discussed. An answer that merely gives a list of events that have happened or a synopsis of a situation, without showing insight into the reasons and results, will not earn good marks. Your referencing must consistently follow the augmented Harvard method.

Assignment 2:

A foundry that specialises in custom blended alloys has received an order for 1 000 kg of an alloy containing at least 5% chromium and not more than 50% iron. Four types of scrap that can be easily acquired can be blended to produce the order. The cost and metal characteristics of the four scrap types are given below:

a) Define your decision variables explicitly. (10)
b) Formulate this optimisation problem as a linear program. (20)
c) Solve this model using Solver. (20)
d) Write down the optimal solution and the associated total costs. (5)

Use only the initial printout of the optimal solution to answer the following questions. (This means that you may not change the relevant parameters in the model and do re-runs.) Explain how you arrive at your answers.

e) How good a deal would the purchasing manager need to get on scrap type 1 before he would be willing to buy it for this order? (5)
f) Upon further investigation, the purchasing manager finds that scrap type 2 is now being sold at R5,40 per kg. Will the purchasing plan change? By how much will the cost of purchasing the metals increase? (8)
g) The customer is willing to raise the ceiling on the iron content to negotiate a reduction in price he pays. How should the purchasing manager react to this? (7)
h) The customer now specifies that the alloy must contain at least 6% chromium. Can the purchasing manager comply with this new specification? Will the price charged for the order change? (5)
Your answers to the above will be assessed in terms of the level of communication displayed, the insights and inferences drawn, and your ability to show the implications of the factors that

you have assessed and discussed. An answer that merely gives a list of events that have happened or a synopsis of a situation, without showing insight into the reasons and results, will not earn good marks. Your method of referencing must consistently follow the Augmented Harvard method. Annexures can be used to attach additional information.

Answers to Above Questions on Decision Support Systems

Answer 1: A decision tree is the best way to determine the appropriate strategy in the given case scenario which comprises different decision alternatives. With the help of a decision tree, it is possible to visualise different decision alternatives such as states of nature, probabilities and payoffs as associated with each of the combinations. This will help in calculating the expected payoffs with respect to each of the alternatives and it is possible to select the best possible one which provides the highest payoffs.

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