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QBUS2310 – Semester 2 2023 [Total maximum marks: 40]

Assignment 1 – Details

Due Wed 18^th October at 11:59pm

For this assignment, you are provided details of a scenario (below). You will use a combination of scenario details and real-world data to formulate and solve the problem detailed using Gurobi (Python), as well as answer a series of discussion questions relating to your findings.

You will need to compile all code, results, and write-ups into:

· A clean and formatted jupyter notebook with appropriate code comments, and

· A pdf export of the same jupyter notebook file.

There is no upper word limit as you need to submit your entire jupyter notebook file including code. Please provide explanations, discussions etc. as relevant, but be concise in your writing. You may use your own discretion to determine how long is appropriate.

Problem context:

You have been hired by the NSW state government to consult on a project in which they are proposing to develop several new milk distribution centres to service all LGAs of NSW. Some context for the problem is given below.

Your task is to provide advice for the government to inform its decision to build up to three milk distribution centres.

· The cost of distributing n litres of milk from LGA A to LGA B is a function of the distance between A and B. The cost can be calculated as being d x n x $0.10 where d = distance between A and B (in km) and n = number of litres.

· The cost of establishing a distribution centre is dependent on the proposed maximum capacity of the distribution centre. You can assume that the cost of creating a centre with processing capacity of n litres is n x $1000.

· There is sufficient budget to establish up to 3 distribution centres. To distribute external risk, no single distribution centre should be allowed to have more production capacity than 50% of the entire state’s demand.

· The RDI data for different population groups is as shown below:

Note: you may find that age breakdowns in the RDI data do not match the census (or other) data exactly. When this occurs, you may use an appropriate method to approximate the RDI for the given group or otherwise match the data.

· Additionally, you will require LGA distance data to determine distribution costs. For this assignment, you should use a random number generator (such as excel’s RANDBETWEEN() or python’s randint() functions) to generate a reasonable pseudo-dataset containing LGA distances to use.

Part 1: Suppose it is 2001. Formulate and solve a problem to determine the sites of the three distribution centres to minimise expected distribution costs while considering all other requirements. Provide a short description (as relevant) of your formulation.

Part 2: An additional consideration for the government is that Australia’s population is forecasted to grow over the coming years. They forecast 10% growth per annum over the next three years. Run a sensitivity analysis of your model to accommodate for potential population growth in the next three years. The government is planning for each facility to have a lifespan of at least 20 years. Please provide a discussion of how you would take this into account (no need to re-formulate).

Part 3: Aside from population change, what other factors might be important for the government to consider across a twenty-year lifespan? Consider factors both discussed and not discussed in the scenario provided. Provide a short discussion.

Part 4: Suppose it is now 2006 and five years have passed since the construction and opening of the distribution centres. Re-run your model with data from 2006 and compare your findings with those discussed in part 2. How do they compare? Provide a discussion of any insights gained. [Note: you can assume that all parameters aside from population size/demand remain unchanged].

Part 5: Repeat part 4 now with data from 2021 (20 years since the opening of the centres). This time, account for both population change, and inflation (55.6% between 2001 and 2021). Again, provide a discussion of any insights you have gained.

Useful links: [These are intended as a guide ONLY. You are not required to use these sources]

· You may find historical NSW Census data archives useful for understanding the breakdown of population groups by age and gender in 2001, 2006 and 2021. Note: you are not expected to find specific age breakdowns for each LGA. You can simply take age breakdowns at a state level and generalise these across all LGAs.

· You may find that the Australian Bureau of Statistics useful to understand populations of each LGA.

· For more details on recommended intake of calcium in Australia, see Eat for Health and Better Health