Reference no: EM132675764
UFMFY7-30-3 Decision Modelling - University of the West of England
A company that specialises in property developments on "brownfield" sites is trying to decide how to allocate its resources over the next three years among five possible projects. Each project will require different levels of investment over the three years and will give different returns over the period. The company has limited amounts of money available for investment in each of the three years. The investments needed and returns offered (which are net of investments needed) are given in the following table:
|
|
Investment needed
|
Estimated profits
|
|
Project
|
Year 1
|
Year 2
|
Year 3
|
Year 1
|
Year 2
|
Year 3
|
|
Project 1 Project 2 Project 3 Project 4 Project 5
|
3
4
9
8
2
|
3 2 2 1
4
|
3
1
2
3
6
|
0
1
2
0
0
|
0
2
0
3
4
|
5
2
8
7
6
|
All the values above are in £millions. The investment capital available in each year is fixed at a, b and c £million in years 1 to 3 respectively. The values of a, b and c you will use are determined by your student registration number as follows: Take your last three digits x, y and z of your student registration number. Then your values of a, b and c are calculated as follows: a = 5 + x mod 5, b= 5 +y mod 5, and c = 5 + z mod 5. For example, student number 12345628 has x = 6, y = 2 and z = 8, so that a= 5 + 6 mod 5 = 5 + 1 =6, followed by b =7 + 2 mod 5 = 5 + 2 = 7, and c = 5 + 8 mod 5 = 5 + 3 = 8.
The company wishes to choose the mix of projects to maximise the net present value (NPV) of the profits available over the three years. The annual interest rate the company uses for NPV calculations is 5% so that, for example, £100 received in a year's time is worth £100/(1.05) = £95.24 now (to 2dp). For reasons to do with the company's concern over its cash flow, you may assume that the company is not able to re-invest the profits made in one year in order to fund next year's investments. The company's accountants recommend that investments are taken as going out at the beginning of the year and that profits are regarded as arriving at the end of the year.
The company is part of a consortium of developers and so the option exists of partially investing in a project. Partially investing will mean that the costs and the profits are shared out in proportion to the amount invested.
To support your answers to Tasks 2 to 5 below, you should paste your AMPL model ( mod), data (.dat), run (. run), and output ( . out) files, using the I Courier New I font in the body of your answer (i.e., not in an appendix). Your answers to the tasks should be presented in language that a non-technical person can understand and implement (i.e., do not simply present your AMPL output).
Tasks for Element I
1) Formulate as a mathematical programming model the task of maximising the net present value of the projects for the company given the limitations on investment capital each year. Do not use AMPL notation (yet), but do use algebraic notation rather than actual data values in your formulation, so as to facilitate the specification of the model in AMPL in Task 2.
2) First, clearly state your student registration number and calculate your values for a, b and c. Then, use your answer to Task 1 along with AMPL to determine the best course of action for the company to adopt in this situation.
3) The consortium to which the company belongs worry that too many members might opt in to peculiar fractional values of projects and so they only allow members to opt for multiples of 10% of a project. How will you adjust your model to cope with this new situation, what will the optimum policy be now for the company, and how much money will this new policy affect the company investment?