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Decision Making Examples and Linear Programming Problem

## Problem description for PDC's construction project

The PDC is a government agency tasked with supporting the development of the Oman economy. One of PDC`s key strategies is to support the diversification of the economy away from a reliance on oil. One of the initiatives under considerations is the construction of a new business complex. The complex will be located near the international airport and will consist of a number of purpose built business units. PDC is also expected to maximize the financial return on the project. However, PDC is facing some uncertainty particularly in relation to the expected demand for units in the complex. PDC president gave two possible chance event outcomes: a strong demand and a weak demand.

S1 = strong demand for the units

S2 = weak demand for the units

As a result of this uncertainty, PDC has commissioned three alternative plans for the complex:

D1 = to build a small complex of 30 business units

D2= to build a medium sized complex of 60 units

D3=to build a large complex of 90 units.

State of nature

Decision Alternative Strong Demand S1 Weak Demand

S2

Small complex,D1 8 7

Medium Complex,D2 14 5

Large Complex,D3 20 -9

Table show, payoff table for the PDC project (in million Rials)

Draw a decision tree. PDC is optimistic about the potential for the complex, Suppose that this optimism leads to an initial subjective probability assessment of 0.8 that demand will be strong(S1) and corresponding probability of 0.2 that demands will be weak (S2), Calculate the expected value for each of the three decision alternatives and draw a decision dree. What is the recommended decision using the decision tree with expected value? and why? Now, PDC to make the best possible decision, they want to see additional information about the states of nature. So PDC is considering market research study designed to learn more about potential market acceptance of the PDC project. Management anticipated that the market research study will provide one of the following two results:

1.Favourable report: A significant number of the individuals contacted express interest in purchasing or leasing a PDC unit.

2.Unfavourable report: Very few of the individuals’ contacted express interest in purchasing or leasing a PDC unit.

Draw a Decision tree using the market research study. Now, PDC have anticipated below probabilities,

If the market research study is undertaken:

P(Favourable report)=0.77

P(Unfavourable report)=0.23

If the market research report is favourable:

P(Strong demand given a favourable report)=0.94

## Generating decision tree and choosing the recommended decision for PDC

P(Weak demand given a favourable report)=0.06

If the market research report is unfavourable:

P(Strong demand given a unfavourable report)=0.35

P(Weak demand given a unfavourable report)=0.65

If the market research report is not undertaken, the prior probabilities are applied. Calculate the expected value for each of the three decision alternatives and draw a decision dree. What is the recommended decision using the decision tree with expected value and why?

Bayes` Rule: A printer manufacturer obtained the following probabilities from a database of test results. Printer failures are associated with three types of problems: hardware, software, and other (such as connectors) with probabilities of 0.1, 0.6, and 0.3 respectively. The probability of a printer failure given a hardware problem is 0.9, given a software problem is 0.2 and given any other type of problem is 0.5. If a customer enters the manufacturer`s website to diagnose a printer failure, what is the most likely cause of the problem?

Introduction to problem

Decisions Tree without EMV

EMV with Decision Tree and Discussion

Decision Tree, EMV and  Final Decision and Discussion

Byes Rule problem

Byes Rule two outcomes and discussion

In Week 5 and 6(using the Decision Making Examples manual), you developed a breakeven analysis  for Quality Sweaters company, sells hand-knitted sweaters The company is planning to print a catalogue of its products and undertake a direct mail campaign. The objective of the model is to determine the company’s profit and to see how sensitive the profit is to the response rate from the mailing. Now, use the fully developed spreadsheet (after completing the manual) and perform below changes on the model,

1.Export all the results and discussions to below questions

How does a change in the response rate affect profit?

For what response does the company break even?

If the company estimates a response rate of 3%, should it proceed with the mailing?

2.Continuing the previous problem use goal seek for each value of number mailed (once for 80000, once for 90000 and so on). For each, find the response rate that allows the company to break even.

3.In the quality sweaters model, the range E9:E11 does not have a range name. Open your completed Excel file and name this range Costs. Then look at the formula in cell E12. It does not automatically use the new range name. Modify the formula so that it does. Then click on cell G4 and paste the new list of range names over the previous list.

## Bayes' Rule problem for printer manufacturer

As the quality sweaters problem is now modelled, if all inputs remain fixed except for the number mailed, profit will increase indefinitely as the number mailed increased. This hardly seems relative- the company could become infinitely rich. Discuss realistic ways to modify the model so that this unrealistic behaviour is eliminated

RMC,inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products; a fuel additive and a solvent base. Each kilo of fuel additive is a mixture of 0.4 kilos of material 1 and 0.6kilos of material 3. A kilo of solvent base is a mixture of 0.5kilos of materials 1, 0.2 kilos of materials 2 and 0.3kilos of material 3. After deducting relevant costs, the profit contribution is £40 for every kilo of fuel additive produced and £30 for every kilo of solvent base produced. RMC`s production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:

Raw Material Amount Available for production

Material 1 20 kilos

Material 2 5 Kilos

Material 3 21 Kilos

Assuming that RMC is interested in maximising the total profit contribution,

(a)What is the linear programming model for this problem?

(b)Find the optimal solutions using the graphical solutions procedure. How much kilos of each product should be produced, and what is the projected total profit contribution?

(c)Is there any unused material? If so, how much?

(d)Are there any redundant constraints? If so, which ones?

2.Produce an Excel model and use Solver to replicate the hand calculation.

Read the attached paper (specially paper 2) carefully and develop the following:

1.Project network of the example given in the paper using spread sheet. You can show it in table format or network diagram view.

2.Incorporate the methodologies of risk factor discussed in the paper, in your project model (using spreadsheet). Explain the procedure of developing the project model and discuss on the risk methodologies used in the paper.

3.Compare the results of your model with results in the paper and provide comments.

4.If distribution of the weather risk factor is modelled using uniform distribution, discuss and critically comment on the new results as compared to Point 3.

5.Conduct sensitivity analysis to identify the influence of different risks on project durations and critical review the outcome.