MATH5007 2024 Tri3a: Assignment 3 (Singapore)
Question 1: General (30 Marks); max 300 words
The unit provided you with knowledge and skill sets on optimisation (and later simulation) and introduced you to models implemented with AMPL.
1. Why is the optimisation knowledge valuable for providing decision support even if you are not in charge of creating and solving optimisation models? Should managers have at least an introduction to optimisation? 8M
2. Explain IN YOUR WORDS the difference between prescriptive and predictive modelling to someone unfamiliar with the subject. 8M
3. Why is modelling a process with toy car models a possible option? Describe a scenario where you could see Lego being used (at least in an early planning stage). 8M
4. Consider removing a constraint from a model; what are the expected changes to the objective function value for the optimal solution in case of a minimisation problem? Provide a short argumentation. 6M
Question 2: Network Flow (85 Marks)
Answer the following questions about network flow problems.
1. We used a BigM constraint in the MST-problem. Explain the BigM constraint (5M) and why it was required to find the solution (5M). Include in your answer why solving the problem without the BigM constraint results in a wrong answer (5M).
Answer the following questions about network flow problems.
1. Map the differences between the four variations discussed in the classroom (Transhipment, Routing, Max-Flow, MST). Consider the data as well as the model. 10M
2. How would you model for the routing problem a toll (that is a fee being paid if the connection is used) and a blocked connection? As there is no specific model given, provide enough details to explain your answer. 10M
3. Solve the following problem using a network flow approach. (overall 50M)
A producer of outdoor BBQ-sets has a production period from January to June, with the product being on the shelves at dedicated retail stores from March to August. The capacity and demand (in 1000s) are shown in the table below. The manufacturing cost as well as the carrying cost varies in the considered time periods (cost per 1000).
a. Draw the network representation you are using. 10M
b. Write the data and model files solving the problem. 35M
c. What is the optimal solution? Do not limit the answer to the objective function value but visualise the decision variables as well. 5M
Use comments in your model/data files to explain the elements of the model.
|
Month
|
Capacity (in 1000s)
|
Demand (in 1000s)
|
Cost per 1000
|
Carrying Cost First Month
|
Carrying Cost Other Months
|
|
January
|
16
|
|
7100
|
110
|
55
|
|
February
|
18
|
|
7700
|
110
|
55
|
|
March
|
20
|
14
|
7600
|
120
|
55
|
|
April
|
28
|
20
|
7800
|
135
|
55
|
|
May
|
29
|
26
|
7900
|
150
|
55
|
|
June
|
36
|
33
|
7400
|
155
|
55
|
|
July
|
|
28
|
|
|
|
|
August
|
|
10
|
|
|
|
Question 3: Multi-Objective Optimisation (10 Marks)
The question has the following tasks:
1. Explain in YOUR words MOO with 100 words max. (10M)
2. Follow the instructions below to modify the given problem.
Given is the shopping_moo.mod model. The model itself describes a knapsack problem, where items with a value and a weight have to be packed in a given number of bags. The optimisation target here is either the maximisation of value (zv) or the maximisation of the number of items in the bags (zi).
The problem has two constraints.
1. Weight constraint ensure that the weight restrictions of the bags are kept
2. The number of items of each product in all bags is restricted
Running the model, you get either a value of 328 with 15 items (zv) or 307 with 19 items (zi). Use Multi-Objective optimisation to see if there is a solution that maximises both objectives. In the data file, there is already a declaration of targets and weights. Your task is to
1. Write the MOO-Objective function (10M)
2. Write the constraint for restricting the deviation to Q (15M)
3. Find the weights (param weights) for the deviation constraint that results in a solution with 16 items. How do you approach a solution for the weights? (15M)
Note: Follow the example we had in class.
IMPORTANT: It is a maximisation and NOT a minimisation problem. What impact does this have on the deviation constraint?
Include in the word document the results and submit the updated shopping_moo.mod
Total: 107 Marks (representing 10% of the final mark)
The final submission is via email attachments to the lecturer (Adrian). Use your Curtin email account. Attached to the submission should be a Word document with all your answers to the questions (You can use this file and insert your answer in a different colour) and .mod and .dat files based on the questions. You can use a compressed folder or zip file. Use for the filenames the following structure: a3_YOURID_answers.docx for the answer to the questions, a3_YOURID_answers.zip in case you submit all in a compressed file, and a3_YOURID_Q[number of question this file relates to].mod/.dat. Using given formats and naming conventions is crucial in organisations, so we deduct up to 5M if the filenames are not as specified.