MATH5007 2022 Semester 1: Assessment 2: Optimisation
Name: ___________ Student ID: _____________
Question 1: Verbal Training (30 Marks)
This part is about the capability to express optimisation problems and their solutions verbally. Consider the given model (concrete.mod) and data file (concrete.dat), explain all components in the model including the purpose of the variables and the constraint(s). The explanation does not have to be long but cover the main aspects of each component.
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• The problem is an existing one from the class, thus the focus is not so much on the novelty of the model but the capability of explaining it. If you need to include the data for your explanation, please do so. However, it is not expected that the data is explained and used in the explanation.
• DO NOT READ a prepared text. You should prepare but I do not want to see your capability of reading but explaining live as it is the case in the oral exam.
• Please use a software of your choice to do screen recording with voice. If possible, include a video stream from your camera. As a digital native generation, I expect that you are having the skill set to do this. HOWEVER, I will prepare some options for you to choose but please let me know as soon as possible when you need help with the recording.
• The video can be provided to me in a format of your choice. That includes links to platforms like Dropbox or YouTube (set the video setting to private when uploading) or a copy on a USB stick (I can copy the video during class). This is assuming that the video is too large for an email.
• Marks will be given on coverage all aspects (5 marks for each part: set/param/var, objective function, constraints, solving process, and solution presentation) as well as the problem description (5 marks). Note: Regarding the three special constraints for the companies, choose one of your choice rather than doing all three.
• The problem to consider is concrete.mod and the corresponding data file; both attached to the assessment.
Question 2: AMPL Problem (45 Marks)
SensoTech is planning new assembly plants in Western Australia. To successfully operate on the expected market, the plans consider a combined production capacity of at least 750,000 units per year with a combined maximum operating cost of 17,5 million per year. A preselection identified site options in 4 different cities. While the first city is able to host a facility of any of the suggested capacity, the others have restricted capacity options. The available investment in the construction is limited to $125 million, the strategic objective is a maximisation of the yearly profit. The table shows the relevant data.
Plant Location
Capacity (in tsd)
Cost (in tsd)
Profit (in tsd)
Investment (in tsd)
High Capacity
Mid Capacity
Low Capacity Site 2
Low Capacity Site 3
Mid Capacity
Low Capacity Site 4
High Capacity Mid Capacity
250 4,000 400 225 3,500 350 200 3,000 300
200 3,000 325
225 3,200 340 200 2,500 325
250 3,300 300 225 3,000 275
25,000 22,000 19,000
21,000 20.000
25,000 23,000
a. The manager asks for a solution to maximise the profit under the given investment, cost, and capacity constraints. Calculate the optimal solution under the assumption that multiple plants can be built at each site; report the objective function value and the plants to be opened. Use the provided data set plant_location_capacity.dat.
b. The manager decide that each site can only have a maximum of one plant. Change the model accordingly with additional constraint(s). Report the objective function value and the plants to be opened.
c. A further decision is made regarding the cost with no inclusion of plants with more than 3,800,000. Add a constraint to exclude those plants and report the new objective function value and the plants to be opened.
d. One option to report further results (and we explore others later) is the “display” in the console using the same construct as for the constraints. For example, “display sum{i in PRODUCTS} price[i] * x[i] ;” would report the total price for all ordered products. [Note this example is used to not reveal the solution for the given problem. In short, you use display and the left-hand-side of the constraint. Do not forget the ; at the end]. Report for the final model the remaining investment funds, the total cost and capacity.
Question 3: Optimisation Understanding (15 Marks)
Briefly answer the following questions:
– why is solving integer problems is more time consuming? A short explanation, it is
not required to explain the whole procedure.
– given the different network flow problems, explain the flow (through) constraint in your words
– binary variables can be used for counting. Explain how this is done using an example.
The final submission is done via email-attachments to or respectively. Use your Curtin email account. Attached in the submission should be a word document with all of your answers to the questions (You can use this file and insert your answer in a different color) as well as a .mod and .dat files based on the questions. Use for the filenames the following structure: as2_YOURID_Q[number of question this file relates to].mod/.dat. Please ensure the right name as it simplifies my work significantly.
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