A university plans to build a new computer lab for its students for data analysis and simulation modelling.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question 1

 

A university plans to build a new computer lab for its students for data analysis and simulation modelling. It has determined the number of computers needed each month for the next 12 months based on the student enrollment, as given in Table 1.

 

Table 1: Number of computers needed

 

Month 1 2 3 4 5 6

Requirements 60 60 60 80 80 20

Month 7 8 9 10 11 12

Requirements 20 60 70 70 80 80

 

The university is wondering whether to rent the computers or buy new computers. Computers can be rented for a period of one, two, or three months. Table 2 shows the cost of renting.

 

Table 2: Cost of renting

 

Duration of rent Cost

1 $250

2 $450

3 $650

The university does not have any computers at the start of the year.

 

Question 1a

 

Apply linear programming (LP) to formulate the problem to determine the number of computers the university should rent each month and for how long, so that the total cost of renting is minimum.

 

(5 marks)

 

Question 1b

 

Solve the LP model in Question 1a by developing a spreadsheet model.

 

How many computers should the university rent each month and for how long? What is the optimal cost of renting?

 

You can assume that fractional rental is possible. Present your solutions by rounding up or down the number.

 

(12 marks)

 

Question 1c

 

How does the model change if the university has 50 computers at the start of the year? Is there any change in the solution obtained in Question 1a?

 

(8 marks)

 

Question 1d

 

If the university wants the solution only in integer numbers, what amendments need to be done to the previous model?

 

Solve for the best solution in this case.

 

(5 marks)

 

Question 2

 

A motorcycle manufacturing company plans to launch a new motorcycle model in the ASEAN market. The company is considering to set up a manufacturing plant in Batam but is struggling to determine the capacity for the plant. Capacities of 10,000, 12,000, 14,000, 16,000, 18,000 and 20,000 units are being considered.

 

To build a unit of capacity, the company has to incur $5,000, but that cost can be divided equally for the next four years. There is also a fixed maintenance cost for keeping the capacity, given by $(X + 1)*50 per year, where X is the last digit of your PI number, e.g., if your PI number is B1234567, X = 7 and the maintenance cost = $(7 + 1)*50 =

$400 per year.

 

It is expected that the demand for the motorcycle for the next four years would be normally distributed, with a mean of 13,000 and standard deviation of 3,000 motorcycles. The demand of motorcycles each year does not impact the demand the next year. Each motorcycle will be sold at $10,000 with a production cost of $7,500. The profits generated are discounted at 4% annual interest.

 

The company does not want to keep inventory from one year to another and is planning only for the next four years.

 

 

Question 2a

 

Construct a simulation model to determine the net present value (NPV) for different potential capacities. Find the optimal capacity level of the plant, based on the mean NPV. Mention all the settings used for the simulation model.

 

(25 marks)

 

Question 2b

 

Using the result and output chart obtained in Question 2a, determine the value of the NPV that has 5% chance that the actual NPV will exceed it.

 

(5 marks)

 

Question 2c

 

Suppose the company is averse to risk, i.e., it does not want to go for a capacity with too much variability in the NPV. Analyse whether the optimal solution obtained in Question 2a will change.

 

(5 marks)

 

 

 

SECTION B (25 marks)

 

Prepare a video recording of the presentation of at least 3 minutes but not exceeding 6 minutes. There are two methods for ECA video assignment submission; either Record Media or Upload Media. For Upload Media, please note that your file size should be no more than 500MB and the format is in .mp4.

 

(25 marks)

 

SECTION C (10 marks)

 

Prepare a set of PowerPoint presentation slides upon which the video presentation is based. Please note that the PowerPoint must be converted to PDF before submission to Canvas.

 

Attachments:

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