Question 1

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

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

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.

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.

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?

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.

Question 2

A motorcycle manufacturing company plans to launch a new motorcycle model in the ASEAN market. The company is considering setting 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 a standard deviation of 3,000 motorcycles. The demand for 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 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.

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. Analyze whether the optimal solution obtained in Question 2a will change.