Question 1

At your company or any organization that you are interested in, identify a business problem that Linear Programming (LP) can/could be applied to help managers to make a better decision. (1) Describe the business problem. (2) Recognize potential concerns in formulating it as an LP problem. (3) Finally, discuss how to address the concerns.

(Note: Please do NOT write a textbook-definition description. You have to explain the application process of LP in your own words so that someone like your grand-parents or your nephew of 12 years old who have not heard anything about operations research would understand.)

Question 2

Our neighboring country, Indonesia, has opened up its crude oil refinery industry by inviting private investors to start a private oil refinery business. Your company, Sing O&G, which has oil refinery operations experience in other countries, has tasked you with the task of analyzing the refinery operations in view of the different constraints and profits.

Sing O&G received its crude oil in four different grades (Grade 1, 2, 3 and 4, where Grade 1 is the highest and most valuable grade) where each grade differs from each other in terms of its physical characteristics and chemical compositions. Sing O&G purchased its supply of crude oil from the Indonesian government where the maximum allowable monthly supply of Grade 1, Grade 2, Grade 3 and Grade 4 crude oil is 5,000, 7,000, 8,000 and 10,000 barrels, respectively.

Crude oil needs to be processed before it can be used. Three major types of operations are performed to refine the crude oil into finished products (i.e., oil products): Separation, Conversion, and Treating. Sing O&G can sell the refined oil products at any of the 3 stages, where the profit is dependent on the grade of the raw (or unrefined) crude oil and refining stage at which it is sold. Crude oil of a higher grade would require lesser energy to be refined, hence this translates into a higher net profit which is shown in Table 2-1.

Table 2-1: Net Profit ($/barrel) of Refined Oil Products Sold at Each Refining Stage by Grade

Due to contractual commitment, Sing O&G is required to supply at least 4,000 barrels of refined oil per month after the Separation stage. Also, the management has adopted a policy where the amount of refined oil sold (in barrels) after the Separation stage is limited to a quarter of the total amount of crude oil purchased for that month.

(a) Determine an LP model to maximize your profit. Discuss any two (2) assumptions, pertaining to the case, to be made prior to analyzing the business case.

(b) Solve the LP problem by using Microsoft Excel.

(c) Due to climate change, countries around the world are increasing their effort in reducing carbon footprint through various measures. Comment on how the possible measures are undertaken by the government to reduce the consumption of treated refined oil (final refine stage of crude oil after undergoing the three stages) could affect your original solutions based on Excel Sensitivity Report.

Question 3

Widely recognized as one of the best airports in the world, Changi Airport provides excellent connectivity to the Asia Pacific region, making Singapore a vibrant aviation hub of choice.

Changi Airport is served by many leading airlines and is an important hub for airline alliances such as Star Alliance and Oneworld, providing an important connection from ASEAN cities to ones in Europe and the United States.

There are currently 4 terminals in operations at Changi Airport and with the addition of the fifth terminal that is scheduled to be operational in 2030, Changi Airport will be able to cater to more than 135 million passengers per year.

As an intern at the airport, you have been provided with a set of aircraft traffic data (from January 1991 to December 2019) that shows the number of aircraft arrival and departure for each month and are required to analyze and do a projection of the aircraft traffic up to December 2021. This information will help the authority to decide if the pace of constructing Terminal 5 needs to be accelerated for completion ahead of 2030.

(a) Discuss which time period of the record should be used for this forecasting. Recommend an appropriate time series model to forecast the monthly aircraft traffic up to December 2021 with justifications.

(b) From Question 3(a)’s conclusion, determine the monthly forecast for aircraft traffic up to December 2021. Show the steps in calculating the forecast.