DECISION SUPPORT MODELS 2012/2013

Transcription

1 DECISION SUPPORT MODELS 2012/2013 Rules for the 1 st groupwork assignment Instructions This work consists of solving four exercises while using, whenever appropriate, software tools learned in the course. Each group will need to prepare and submit: A word file with the solution of the exercises, presenting clearly the information used to solve the exercise, the assumptions in use, as well as the main outputs produced while using the software to solve the problem. This file should have, at most, 20 pages; A very brief assessment on the weaknesses and strengths of the software in use; A copy of the software files used to solve the exercises. These files will need to be sent electronically to monica.oliveira@ist.utl.pt by the 5 th of April. Note that you will need to install the Palisade Decision Tools software available at (free trial available for 15 days): bin/trialversion_info.pl?product=1400 I 6000 EN&FormRegion=PE. 1

2 Exercise 1 (3/20 values) On March 23, 1989, Stanley Pons and Martin Fleischmann announced in a press conference at the University of Utah that they had succeeded in creating a small scale nuclear fusion reaction in a simple apparatus at room temperature. They called the process cold fusion. Although many details were missing from their description of the experiment, their claim inspired thoughts of a cheap and limitless energy supply, the raw material for which would be ocean water. The entire structure of the world economy potentially would change. For a variety of reasons, Pons and Fleischmann were reluctant to reveal all of the details of their experiment. If their process really was producing energy from a fusion reaction, and any commercial potential existed, then they could become quite wealthy. The state of Utah also considered the economic possibilities and even went so far as to approve $5 million to support cold fusion research. Congressman Wayne Owens from Utah introduced a bill in the US House of Representatives requesting $100 million to develop a national cold fusion research centre at the University of Utah campus. But were the results correct? Experimentalists around the world attempted to replicate Pons and Fleischmann s results. Some reported success, while many others did not. A team at Texas A&M claimed to have detected neutrons, the telltale sign of fusion. Other teams detected excess heat as had Pons and Fleischmann. However, many experiments failed to confirm a fusion reaction and several physicists claimed that the Utah pair simply had mistakes in their measurements. a) Consider the problem that a member of the US Congress would have in deciding whether to vote for Congressmen Owens s bill. What alternatives are available? What are the key uncertainties? What objectives might the Congress member consider? Structure the decision problem using an influence diagram and a decision tree. b) A key part of the experimental apparatus was a core of palladium, a rare metal. Consider a speculator who is thinking of investing in palladium in response to the announcement. Structure the investor s decision. How does it compare to the decision problem in a)? Exercise 2 (7/20 values) The executives of PharmaEthics (PE) have to decide which of the three products introduce, A, B or C. Product C is essentially a risk free product, from which the company will obtain a net profit of 1 million. Product B is considerably more risky. Sales may be high, with resulting net profit of 8 million, medium with net profit of 4 million, or low, in which case the company just breaks even. The probabilities for these outcomes are: P(Sales High for B)=0.38 P(Sales Medium for B)=0.12 P(Sales Low for B)=0.50 Product A poses something of a difficulty: a problem with the production system has not yet been solved. The engineering division has indicated its confidence in solving the problem, but there is a slight (5%) chance that devising a workable solution may take a long time. In this event, there will be a delay in introducing the product, and that delay will result in lower sales and profits. Another issue is the price for Product A. The options are to introduce it at either high or low price; the price would not be set until just before the product is to be introduced. Both of these issues have an impact on the ultimate net profit. 2

3 Finally, once the product is introduced, sales can be either high or low. If the company decides to set a low price, then low sales are just as likely as high sales. If the company sets a high price, the likelihood of low sales depends on whether the product was delayed by the production problem. If there was no delay and the company sets a high price, the probability is 0.4 that sales will be high. However, if there is a delay and the price is set high, the probability is only 0.3 that sales will be high. The following table shows the possible net profit figures (in millions) for product A: Price High sales ( million) Low sales ( million) Time delay No delay High Low High 8 0 Low a) Draw an influence diagram for PE s problem. Specify the possible outcomes and the probability distributions for each chance node. Specify the possible alternatives for each decision node. Write out the complete table for the consequence node. Use a software program to answer to this question. b) Draw a complete decision tree for PE. Solve the decision tree. What should PE do? Use a software program to help answering to this question. c) Create cumulative risk profiles for each of the three products in one graph. Calculate the EVPI for the uncertain events. Interpret the graph and the values. Which conclusions can be drawn? d) One of the executives of PE is considerably less optimistic about product B and assesses the probability of medium sales as 0.3 and the probability of low sales as 0.4. Based on the expected value, what decision would this executive make? Should this executive argue about the probabilities? Why or why not? e) Comment on the specification of chance outcomes and decision alternatives. Would this pass the clarity test? If not, what changes in the problem must be made in order to pass the clarity test? Exercise 3 (6/20 values) ENERGISE (ENE) is a manufacturing company that performs contract work for a wide variety of firms. It primarily manufactures and assembles metal items, and so most of the equipment is designed for precision machining tasks. The executives of ENE currently are trying to decide between two processes for manufacturing a product. Their main criterion for measuring the value of a manufacturing process is net present value (NPV). The contractor will pay ENE 8 per unit. ENE is using a three year horizon for its evaluation (the current year and the next two years). 3

4 Process 1 Under the first process, ENE s current machinery is used to make the product. The following inputs are used: Demand: Demand for each of the three years is unknown. These three quantities are modelled as discrete random variables denoted D 0, D 1 and D 2 with the following probability distributions: D 0 P(D 0 ) D 1 P(D 1 ) D 2 P(D 2 ) Variable Cost: Variable cost per unit changes each year, depending on the cost for material and labor. Let V 0, V 1 and V 2 represent the tree variable costs. The uncertainty surrounding each variable is represented by a normal distribution with mean 4 and standard deviation 0.4. Machine failure: Each year, ENE s machines fail occasionally, but obviously it is impossible to predict when or how many failures will occur during the year. Each time machine fails, it costs the firm Let Z 0, Z 1 and Z 2 represent the number of machines failures in each of the three years, and assume that each is a Poisson random variable with parameter =4. Fixed Cost: Each year a fixed cost of 12,000 is incurred. Process 2 The second process involves scrapping the current equipment (it has no salvage value) and purchasing new equipment to make the product at a cost of 60,000. Assume that the firm pays cash for the new machine, and ignore tax effects. Demand: Because of the new machine the final product is slightly altered and improved, and consequently the demands are likely to be higher than before, although more uncertain. The new demand distributions are: D 0 P(D 0 ) D 1 P(D 1 ) D 2 P(D 2 ) Variable cost: Variable costs still changes each year, but this time V 0, V 1 and V 2 are each judged to be normal with mean 3.5 and standard deviation 1. Machine failures: Equipment failures are less likely with the new equipment, occurring each year according to a Poisson distribution with parameters =3. They also tend to be less serious, costing only 6,000. Fixed cost: The fixed cost of 12,000 is unchanged. 4

5 a) Draw an influence diagram for this decision problem. b) Write out the formula for the NPV for both processes described above. Use the variables names as specified, and assume a 10% interest rate. c) For process 1, construct a model and perform 1000 simulations trials. Estimate the mean and the standard deviation of NPV for this process. Print a histogram of the results, and indicate which is the probability of a negative NPV occurring. d) Repeat Question c) for Process 2. e) Which process would be better for ENE? Explain why. Exercise 4 (4/20 values) Find a decision maker and assess the percentiles 0.05, 0.25, 0.50, 0.75 and 0.95 for the uncertain quantity: the value of the next jackpot of Euromillions. a) Explain which questions you have used to obtain these assessments and plot the assessments to create graphs of the subjective cumulative density functions. b) Compare the discrete approximation methods by doing the following: Use the extended Pearson Tukey method to create three point discrete approximations for the continuous distributions assessed in the previous point; Find a distribution that fits the values given by your decision maker; Compare your estimated expected values from the methods in use. 5