$60 expert in linear programming, R code and CPLEX code

SIT718 Real world Analytics Assignment

Total Marks = 100, Weighting - 30% Due date: 3 May 2018 by 11.30 PM

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.

ULO6: Obtain optimal solutions for quantities that are either continuous or dis-

crete.

This assignment consists of two parts: Part A and Part B. Each part is allocated 50 marks

and contributes with 15% to the final mark.

1

SIT718 Assignment 2018 – T1 2 of 7

Part A: Analysis of Energy Efficiency Dataset for Buildings

Description:

In order to design energy efficient buildings, the computation of the Heating Load (HL) and

the Cooling Load (CL) is required to determine the specifications of the heating and cooling

equipment needed to maintain comfortable indoor air conditions. Energy simulation tools are

widely used to analyse or forecast building energy consumption. The Dataset provides energy

analysis of Heating Load (denoted as Y1) and the Cooling Load (denoted as Y2) using 768

building shapes that are simulated using a building simulator. Select one of Y1 or Y2 as your

variable of interest and focus the analysis on this variable. The dataset comprises 5 features

(variables), which are denoted as X1, X2, X3,X4,X5. The description of the variables is given

below:

X1: Relative compactness in percentage (expressed in decimals) - A measure of building

compactness. A high value means highly compact.

X2: Surface area in square metres

X3: Wall area in square metres

X4: Roof area in square metres

X5: Overall height in metres

Y1: Heating load in kWh.m−2 per annum

Y2: Cooling load in kWh.m−2 per annum

Tasks:

1. Understand the data [10 marks]

(i) Download the txt file (ENB18data.txt) from CloudDeakin and save it to your R work-

ing directory.

(ii) Assign the data to a matrix, e.g. using

the.data <- as.matrix(read.table("ENB18data.txt"))

(iii) Decide whether you would like to investigate Heating Load (Y1) or Cooling Load

(Y2). This is your variable of interest. Generate a subset of 300 data, e.g. using:

To investigate Heating Load Y1:

my.data <- the.data[sample(1:768,300),c(1:5,6)]

To investigate Cooling Load Y2:

SIT718 Assignment 2018 – T1 3 of 7

my.data <- the.data[sample(1:768,300),c(1:5,7)]

(iv) Using scatterplots and histograms, report on the general relationship between each

of the variables X1,X2, X3, X4 and X5 and your variable of interest Y1 (heating load)

or Y2 (cooling load). Include a scatter plot for each of the variables X1, X2, X3, X4, X5

and your variable of interest Y1 or Y2. Include a histogram for X1,X2,...,X5, and Y1 or

Y2. Include 1 or 2 sentences about the relationships and distributions.

2. Transform the data [15 marks]

(i) Choose any four from the first five variables X1,X2,X3,X4,X5.

Make appropriate transformations to the variables (including Y1 or Y2) so that the val-

ues can be aggregated in order to predict the variable of interest (your selected Heating

Load Y1, or cooling load Y2). The transformations should reflect the general relationship

between each of the four variables and the variable of interest. Assign your transformed

data along with your transformed variable of interest to an array (it should be 300 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 each transformation for your selected variables and the variable of

interest Y1 or Y2. (1- 2 sentences each).

3. Build models and investigate the importance of each variable. [15 marks]

(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 (RMSE, Av.abs error,

Pearson correlation, Spearman correlation) and one summarising the weights/parameters

that were learned for your data.

SIT718 Assignment 2018 – T1 4 of 7

(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 (the four variables that you have selected),

(c) Any interaction between any of those variables (are they complementary or redun-

dant?)

(d) better models favour higher or lower inputs (1-2 paragraphs for part (iv)).

4. Use your model for prediction. [10 marks]

(i) Using your best fitting model, predict the Heating Load Y1 or the Cooling Load Y2

for the following input:

X1=0.82, X2=612.5, X3=318.5, X4=147, X5=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 low heating or cooling load will occur. (1-2 sentences)

For this part, your submission should include:

1. A report (created in any word processor), covering all of the items in above. With plots

and tables it should only be 2 - 3 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 us distinguish them!).

3. R code file, (that you have written to produce your results) named ”name-code.R”, where

name is your name;

SIT718 Assignment 2018 – T1 5 of 7

Part B: Optimisation

1. A food factory is making a special Juice for a customer from mixing two different existing

products JA and JB. The compositions of JA and JB and prices ($/l) are given as follows,

Amount (l) in /100 l of JA and JB Carrot Orange Apple Cost ($/l)

JA 4 6 3 6 JB 8 3 6 5

The customer requires that there must be at least 3.5 litres Orange and at least 4 litres

of Apple concentrate per 100 litres of the Juice respectively, but no more than 6 litres of

Carrot concentrate per 100 litres of Juice. The customer needs at least 50 litres of Juice

per week.

a) Formulate a Linear Programming (LP) model for the factory that minimises the total

cost of producing the Juice while satisfying all constraints.

b) Use the graphical method to find the optimal solution. Show the feasible region and

the optimal solution on the graph. Annotate all lines on your graph. What is the mini-

mal cost for the product?

[25 marks]

SIT718 Assignment 2018 – T1 6 of 7

2. A factory makes three products (fabrics): Summer, Autumn, and Winter from three

materials containing: Cotton, Wool and Viscose. The following table provides details

on the sales price, production cost and purchase cost per ton of products and materials

respectively.

Sales price Production cost Purchase price Summer $50 $4 Cotton $30 Autumn $55 $4 Wool $45 Winter $60 $5 Viscose $40

The maximal demand (in tons) for each product, the minimum cotton and wool propor-

tion in each product is as follows.

Demand min Cotton proportion min Wool proportion Summer 4500 60% 30% Autumn 4000 60 % 30% Winter 3800 40% 50%

Formulate a LP model for the factory that maximises the profit, while satisfying the

demand and the cotton and wool proportion constraints.

Solve the model using IBM ILOG CPLEX. What are the optimal profit and optimal

values of the decision variables?

Hints:

1. Let xij ≥ 0 be a decision variable that denotes the number of tons of products j for j ∈ {1 = Summer, 2 = Autumn, 3 = Winter} to be produced from Materials i ∈{C=Cotton, W=Wool, V=Viscose}.

2. The proportion of a particular type of Material in a particular type of Product can be

calculated as:

e.g., the proportion of Cotton in product Summer is given by: xC,1

xC,1 + xW,1 + xV,1 .

[25 marks]

Submission

Submit to the SIT718 Clouddeakin Dropbox.

Combine the report from part A and the Solutions from part B in ONE pdf file. Copy and

paste your CLEX code to Solutions for Part B. Label the file with name.pdf, where ‘name’ is

replaced with your name - you can use your surname or first name - to help distinguish them!).

Your final submission should consist of no more than 4 files:

SIT718 Assignment 2018 – T1 7 of 7

1. One pdf file (created in any word processor), containing the report of Part A, the Solutions

of the two questions of Part B, including CPLEX code, labelled with your name. This

file should be no more than 5-6 pages.;

2. A data file named “name-transformed.txt” (where ‘name’ is replaced with your name;

3. A code with your R file, labelled with your name.R;

4. A code with your CPLEX file, labelled with your name.mod, also copy the code in your

solution document.