Real world Analytics
Assignment (pdf or MS word doc and appropriate programme files with your codes) must be submitted via CloudDeakin's Assignment Dropbox. You can sub- mit an electronic version of your assignment (photos of written document are not accepted). No hard copy or email submissions are accepted.You should label all figures and tables.
This assignment assesses :
ULO1: Apply the concepts of multivariate functions to summarise datasets.
ULO2: Analyse datasets by interpreting model and function parameters of impor- tant families of multivariate functions.
ULO3: Transform a real-life problem into a mathematical model.
ULO4: Apply linear programming concepts to make optimal decisions.
ULO5: Obtain optimal solutions for quantities that are either continuous or dis- crete.
Tasks:
1. Understand the data
(i) Download the txt file from CloudDeakin and save it to your R working directory. You can also use the Excel file provided for further information about the data.
(ii) Assign the data to a matrix, e.g. using
the.data <- as.matrix(read.table("filename.txt"))
(iii) Your variable of interest is Y -Rank ID. Generate a subset of 100 data, e.g. using:
my.data <- the.data[sample(1:161,100), c(1,3:10,12,13)]
(iv) Using scatterplots and histograms, report on the general relationship between each of the variables and your variable of interest Y . Include a plot and 1 or 2 sentences for each of the variables including the variable Y .
Note: In case you need to transform your data into numeric values use the following command in R;
my.data <- mapply(my.data, FUN=as.numeric)
After this, you'll need to reconstruct your matrix with the same dimensions as the orig- inal matrix, using for example the command in R,
my.data <- matrix(data=my.data, ncol=11, nrow=100)
2. Transform the data
(i) Choose any four from the variables, for example Journal ID, Number of citations, Impact Factor, and Half-life, or another combination that you like.
Make appropriate transformations to the variables (including Y) so that the values can be aggregated in order to predict the variable of interest. Assign your transformed data along with your transformed variable of interest to an array (it should be 100 rows and 5 columns). Save it to a txt file titled "name-transformed.txt" using
write.table(your.data,"name-transformed.txt",)
(ii) Briefly explain the general relationship between each of your transformed variables and the variable of interest (1- 2 sentences each).
3. Build models and investigate the importance of each variable.
(i) Download the AggWaFit R file (from CloudDeakin) to your working directory and load into the R workspace using, source("AggWaFit718.R")
(ii) Use the fitting functions to learn the parameters for
- Weighted arithmetic mean (WAM),
- Weighted power means (PM) with p = 0.5, and p = 2,
- Ordered weighted averaging function (OWA), and
- Choquet integral.
(iii) Include two tables in your report - one with the error measures, and one summarising the weights/parameters that were learned for your data.
(iv) Compare and interpret the data in your tables. Be sure to comment on:
(a) How good the model is,
(b) The importance of each of the variables,
(c) Any interaction between any of the variables (are they complementary or redundant?)
(d) better models favour higher or lower inputs (1-3 paragraphs).
4. Use your model for prediction.
(i) Using your best fitting model, predict the Rank with the following values:
Journal ID=110, Number of citations=116, IF=0.694, 5 yrs IF= 0.762, ii=0.132, Arti- cles=38, Half-life=5, Art-i=0.00175, Eigenfactor=0.894, Number=0.7.
Give your result and comment on whether you think it is reasonable. (1-2 sentences)
(ii) Comment generally on the ideal conditions (in terms of your 4 variables) under which a high Rank will occur. (1-2 sentences)
For this part, your submission, which can be submitted to the SIT718 Clouddeakin Dropbox, should include two files.
1. A report (created in any word processor), covering all of the items in above (items coloured blue usually have explicit instructions about what should be included). With plots and tables it should only be 2 - 5 pages.
2. A data file named "name-transformed.txt" (where ‘name' is replaced with your name - you can use your surname or first name - just to help me distinguish them!).
Part B: Optimisation
Garment factory produces T-shirts and Shorts for Coles supermarket stores in Victoria. Coles will accept all the production supplied by the garment factory. The production process includes cutting, sewing and packaging. The factory employs 22 workers in the cutting department, 50 workers in the sewing department and 12 workers in the packaging department. The factory works 8 hours a day (these are productive hours). There is a daily demand for at least 100 T-shirts. The table below gives the time requirements (in minutes) and profit per unit for the two garments.
|
|
minutes
|
per
|
unit
|
|
|
|
Cutting
|
Sewing
|
Packaging
|
Unit profit
|
($)
|
|
T-shirts
|
20
|
20
|
10
|
6
|
|
Shorts
|
10
|
50
|
10
|
10
|
a) Formulate a Linear Programming model to help the CEO of the factory determine the optimal daily production schedule.
b) Use the graphical method to find the optimum solution. Show the feasible region and the optimal solution on the graph. Annotate your graph. What is the optimum profit?
c) Find a range for the profit ($) of a shirt that can be changed without affecting the optimum solution obtained above.
food factory makes three types of cereals A, B, and C from a mix of several ingredients Oates, Raisins, Coconuts and Almonds. The cereals are produced in 2kg boxes. The following table provides details of the sales price per box of cereals and the production cost per ton (1000 kg) of cereals respectively.
|
|
Sales price per box
|
Production cost per ton
|
|
Cereal A
|
$2.50
|
$4.00
|
|
Cereal B
|
$2.00
|
$2.80
|
|
Cereal C
|
$3.50
|
$3.00
|
The following table provides the purchase price per ton of ingredients and the maximum availability of the ingredients in tons respectively.
|
Ingredients
|
Purchase price per ton
|
Maximum availability in tons
|
|
Oates
|
$100
|
10
|
|
Raisins
|
$80
|
5
|
|
Coconut
|
$120
|
2
|
|
Almonds
|
$200
|
2
|
The minimum daily demand (in boxes) for each cereal and the proportion of the Oates, raisins, coconut and almonds in each cereal is detailed in the following table.
|
|
Minimum demand (boxes)
|
proportion of
|
|
Oates
|
Raisins
|
Coconut
|
Almonds
|
|
Cereal A
|
1000 |
0.8
|
0.1
|
0.05
|
0.05
|
|
Cereal B
|
700 |
0.65
|
0.2
|
0.05
|
0.1
|
|
Cereal C
|
750 |
0.5
|
0.1
|
0.1
|
0.3
|
a) Let xij ≥ 0 be a decision variable that denotes the kg of ingredient i ∈ {Oates, Raisins, Coconut, Almonds} used to produce the Cereal j ∈ {A, B, C} (in boxes). Formulate a linear programming (LP) model to determine the optimal production mix of cereals and the associated amounts of ingredients that maximizes the profit, while satisfying the constraints.
b) Find the optimal solution using the IBM CPLEX software.