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ETF5650: Business Optimisation Skills

Assignment 1, 2024

(Forecasting and quality control)

Instructions

· This is an individual assignment.

· Answer all questions showing all working.

· Submit answers in ONE EXCEL file.

· Provide worded answers in a text box within the spreadsheet.  

· Label each sheet with question number and part of the answer. For example; Question 1 Part (a), Question 1 Part (b).

· Submit the .xlsx file via “Assignment 1 submission” link in the Moodle site. Submission is not allowed until one week before the deadline.

· Submit the .xlsx file before 11.55pm, 9 April 2024. Late submission incurs penalties.

· VERY IMPORTANT: Copy and paste the declaration given in page 2 in a text box on a separate sheet in the .xlsx file and sign or print your name with date.

· VERY IMPORTANT: You must not use generative artificial intelligence (AI) to generate any materials or content in relation to this assessment task.

Format of the file for submission in Moodle:

Your surname_initials_(ID number).xlsx

E.g. Tan_A_(12345678).xlsx  

Upload your .xlsx file to Moodle as follows;

Click on the “Assignment 1 Submission” link and upload your file. 

You have to accept the Submission Statement before clicking the Submit button. Once you upload the file, the following message will appear “File uploaded successfully.” To confirm that your upload was successful, click on the “Assignment Submission” uploading link.  You can then see the uploaded file name.

The aim of this assignment is to give you more insights on some analytical concepts and for you to get hands on experience in the application of the techniques that fall within the areas examined.  

NOTE: You are allowed to submit only once. So, submit only the final version. 

Total mark is 55

Question 1                                                                                                       4+(4+1+2)+4 = 15 marks

(a) Moving averages and exponential smoothing are two forecasting methods. When are they most appropriate as forecasting methods and why are they referred to as smoothing methods?

(b) Table 1 gives weekly Unleaded91 petrol sales at a small petrol station in Waverley Glen.

(i) Forecast week 9 Unleaded91 petrol sales using the method of exponential smoothing with .

(ii) Forecast week 10 Unleaded91 petrol sales using the method of exponential smoothing with .

(iii) Show that the forecast for week 4 is actually a weighted average of all previous observed values. Your answer should show all the weights. 

(c) Suppose exponential smoothing is an appropriate forecasting method for time series; Series A and Series B. Series A contains substantial random variability and Series B contains relatively little random variation. An analyst intends to determine forecasts for the next period in both series. What is your recommendation on smoothing constant selection for Series A and Series B? Give reasons for your answer. 

Question 2                                                                                                              5+4+7+4 = 20 marks

In recent years, the United States has consumed over 30 trillion cubic feet of natural gas annually. Natural gas is commonly used for heating homes, cooking, and other residential and commercial purposes. The winter months typically see increased demand for natural gas due to heating needs. Many industries use natural gas as a fuel for various processes. Industries such as manufacturing, chemicals, and refining are major consumers. Natural gas is a significant source of energy for electricity generation in the U.S. Power plants use natural gas to produce electricity, and its share in the energy mix has increased in recent years due to its relatively lower carbon emissions compared to other fossil fuels. While natural gas is not as widely used in transportation as gasoline or diesel, there are some applications, such as buses and trucks, that run on compressed natural gas (CNG) or liquefied natural gas (LNG). The U.S. imports and exports natural gas. Imports typically come from Canada, while exports have increased with the growth of liquefied natural gas (LNG) exports to various countries.

Let us see if we can do a good job of forecasting total natural gas consumption in the United States. The following website gives historical consumption.

http://www.eia.gov/oil_gas/natural_gas/data_publications/natural_gas_monthly/ngm.html

Select Table 2 (Natural gas consumption in the United States, 2018-2023) given under the Table of Contents.

Access the worksheet labelled "Data 1" and choose the dataset corresponding to the series N9140US1, denoting U.S. Natural Gas Total Consumption in billion cubic feet (Bcf). Consider the historical monthly data spanning from January 2018 to December 2022, encompassing a total of 60 months. Additionally, the worksheet provides the real consumption figures for the period extending from January 2023 to September 2023. This allows for a verification of the accuracy of our forecasts for this period from historical data. 

2.1 Forecast total natural gas consumption from January 2023 to September 2023 assuming there is only a linear trend and no seasonal variation.

2.2 Compute the residuals when only a linear trend and no seasonal variation is assumed. Draw a plot of the residuals. Utilising visual scrutiny of the residual plot, discuss the potential time series components inherent in the observed data.

2.3 Now, forecast total gas consumption from January 2023 to September 2023 assuming the series demonstrates a linear trend and seasonal variation.

2.4 Which forecasting method would you endorse? Provide numerical evidence to substantiate your recommendation.

Question 3                                                                                                          7+5+2+3+3 = 20 marks

In an application of the control chart for fraction non-conforming, the sample is the entire production over the inspection period. In one such case, the total number of units produced over the inspection period (entire production) may vary. This means, sample size may vary from one inspection period to another. Quality control literature suggests several methods of constructing control charts when sample size vary. We shall consider the following two methods.

Method 1: A control chart with variable-width control limits

The upper and the lower control limits are constructed using  where  is the number of non-conforming units in the ith sample and  is the size of the ith sample.

Method 2: A control chart with fixed-width control limits  

The upper and the lower control limits are constructed using  where  is the number of non-conforming units in the ith sample, N is the size of the ith sample and N is the total number of samples inspected. 

APPLICATION

Number of purchase orders issued each week by the purchasing department of a large scale manufacturer is given in Table 1.

Table 1

3.1 Construct a p-chart adopting Method 1 and discuss your finding.

3.2 Construct a p-chart adopting Method 2 and discuss your finding.

3.3 In Method 1, when does the difference between UCL and LCL becomes relatively wider? Explain.

3.4 In some weeks you might observe that Method 2 signals an out-of-control process, whereas Method 1 does not exhibit the same indication. Pick one week that has this conclusion and explain the reason for the disparity?

3.5 Assume that, in Method 2, the process is identified as being in an out of control state with week 20 observation exceeding the UCL. Assume that all other observations are within the control limits. Assume further that week 20 observation is due at an assignable cause. Explain how you would proceed with the quality control inspection procedure beyond week 20.