Reference no: EM132223537

Exercise 1. The Net Present Value (NPV) Model

Shambles, a large toy retailer, are looking at bringing out a new range of soft toys. The range under consideration is "Mythical Beasts." The "Mythical Beasts" range will cost £50,000 to setup and has running costs of £12,000 per year after that for five years. The predicted return from this range is:

1. Assume a discount rate of 10%. Use Excel to set up a discounted cash flow analysis of the above information, calculating the net present value (NPV) for the investment. Remember that the initial expenditure takes place in 2011.

Your spreadsheet must be constructed in such a way that it can accom- modate different values of the discount rate, and must be as efficient as possible. This means that formulas and fixed cell referencing must be used where appropriate. Also, the entire analysis must be contained in a single table. Include a print-out of cell values as well as a print-out of cell for- mulas.

2. From the information in the spreadsheet only, decide whether or not this is a worthwhile investment, giving your reasons.

3. Calculate the NPV for discount rates of 20%, 30%, 40% and 50%, giving your answers to two decimal places.

4. Using Excel and the data generated from part (c), plot NPV against the discount rate in the range 10% to 50%.

5. Use your graph to estimate the discount rate that would give an NPV of zero. What is the significance of this discount rate? (Hint: What happens at discount rates lower and higher than this figure?)

Exercise 2. The Linear Programming (Optimization) Model

Shambles have selected the "Mythical Beasts" range and decided to con- centrate on "Pegasus" and "Phoenix." They would now like to find the right mix of these two products in order to maximize profit. Each toy has to go through two processes during manufacture: sewing and stuffing.

Each toy (Pegasus or Phoenix) takes 12 minutes to sew; there are 10 hours (600 minutes) available for sewing each day. Each Pegasus toy takes 6 min- utes to stuff, whereas each Phoenix toy takes 18 minutes to stuff; there are 10 hours (600 minutes) available for stuffing each day. Pegasus generates £8 profit per toy whilst Phoenix generates £16 profit per toy.

It is also required that at least 10 Pegasus toys and at least 20 Phoenix toys are produced each day. What is the maximum possible daily profit, and how many of each product should be produced in order to achieve this?

1. Determine the maximum by pen-and-paper mathematical calculations and drawing. More precisely:
(a) Write the constraints of the problem and the objective function
(b) Compute mathematically the coordinates of the feasible region

(c)Draw the feasible region
(d)Compute the final solution [2 marks] (e)Draw the isoprofit line and use it to compute the solution graphically
(f)Change the numbers of the per-toy profit so that the maximum profit is achieved at a different corner of the feasible region.

2. Use the Microsoft Excel solver to solve this problem. Include:
(a)a print-out of cell values
(b)a print-out of cell formulae

(c)a print-out of the Solver dialogue box with optimization conditions and constraints
(d)an answer report from the solver
(e)a statement of the answer in words

Exercise 3. GPSS Simulation Model

(Remember that you can download the free Windows version of GPSS (i.e. GPSS World student version)

The sales counter next to the soft toy display in Shambles receives a cus-tomer every 6-10 minutes. Most of these customers (80%) are buying toys and are dealt with by the cashier in 5-15 minutes. The remaining 20% of customers come to open accounts that require an account manager. These customers wait for the account manager, who spends 20-40 minutes in serv- ing them. You are required to simulate an 8-hour day in this department using GPSS.

1. To begin with, construct a flowchart describing the above events using suitable GPSS blocks.

2. Now carry out the simulation in GPSS, showing your program code and simulation report.

3. Describe the results of your simulation using the simulation report, giving as much detail as possible.

4. Modify the simulation so that you factor in not one, but two cashiers. Show your modified program code and the simulation report and discuss what were the observable changes in the simulation.

Exercise 4. Association Rule Mining

A simple TDB is given below:

TID    Items bought
10    a, b, c
20    a, c
30    c, b

Please mine all the association rules with minimum support 66% (that is, 0.66). More precisely, you are required to do the following:

1. Determine, using the Apriori algorithm, all the item sets that have support equal to or higher than 66%. You must clearly show the steps of applying this algorithm.

2. For each item set selected in the above process, determine all the rules formed using that item set and compute the confidence for each such rule.

3. Please explain in one paragraph what is the difference between support and confidence.

Exercise 5. Artificial Neural Networks

There are four training input/target pairs for a two-class problem:

A two-input perceptron with hard limit activation function is used to solve this classification problem. Write down the step-by-step solution to train the classifier by the basic perceptron learning algorithm, starting with the initial weight vector [2, 1, 4] . Namely, you are required to do the following:

1. Describe the modified problem (by augmenting with 1 the vectors eⁱ).

2. Solve the modified problem by running the perceptron algorithm, showing the step-by-step evolution of the variables manipulated by the algorithm.

3. Construct the solution of the original problem from that of the modified problem.

4. Interpret graphically the problem and your solution, explaining, in graph- ical terms, what is the meaning of the values 0 and 1 for di and why does your solution satisfy these constraints.

Exercise 6. DSS Case Study

Design a DSS to help decision-makers run the 2020 Tokyo Olympics.

Your proposal (including diagrams and write-up) may use any combina- tion of DSS types, technology, architectures, frameworks, etc. that have been covered in the course. You may also apply them to any aspects of the case study mentioned above.

Credit will be given for the following areas:

1. Good description of the different stages in your decision making process.

2. Identification of the suitable DSS types relevant for this problem.

3. Good overall design with appropriate choice of the models that are useful for solving the problem.

4. Creativity, practicality and innovative thinking.