Part B Simulation Question 4, 5 and 6
University of Westminster Department of Computer Science 5BUIS002W Coursework (2019/20) Module leader Salma Chahed Unit Individual Coursework Weighting: 50% Qualifying mark 30% Description Forecasting and Simulation modelling Learning Outcomes Covered in this Assignment: The coursework rationale is to model and solve problems with appropriate forecasting and simulation techniques and analyse and discuss their solutions. It relates to learning outcomes (LO3 – LO6 and LO8). Handed Out: 3 February 2020 Due Date 11 March 2020, 13:00 Expected deliverables Electronic file Method of Submission: online via Blackboard Type of Feedback and Due Date: Written feedback and marks 15 working days (3 weeks) after the submission deadline, on Wednesday 1 April 2020 All marks will remain provisional until formally agreed by an Assessment Board. Assessment regulations Refer to section 4 of the “How you study” guide for undergraduate students for a clarification of how you are assessed, penalties and late submissions, what constitutes plagiarism etc. Penalty for Late Submission If you submit your coursework late but within 24 hours or one working day of the specified deadline, 10 marks will be deducted from the final mark, as a penalty for late submission, except for work which obtains a mark in the range 40 – 49%, in which case the mark will be capped at the pass mark (40%). If you submit your coursework more than 24 hours or more than one working day after the specified deadline you will be given a mark of zero for the work in question unless a claim of Mitigating Circumstances has been submitted and accepted as valid. It is recognised that on occasion, illness or a personal crisis can mean that you fail to submit a piece of work on time. In such cases you must inform the Campus Office in writing on a mitigating circumstances form, giving the reason for your late or non-submission. You must provide relevant documentary evidence with the form. This information will be reported to the relevant Assessment Board that will decide whether the mark of zero shall stand. For more detailed information regarding University Assessment Regulations, please refer to the following website:http://www.westminster.ac.uk/study/current-students/resources/academic-regulations http://www.westminster.ac.uk/study/current-students/resources/academic-regulations Coursework Description Part A: Forecasting [60 Marks] Digital subscription streaming services such as Netflix and Spotify have seen their popularity increasing over recent years. With improving consumer internet technologies facilitating high-quality streaming, these digital services proved to be for users a practical way of content delivery: they allow access to a broader catalogue of media without the commitment or cost associated with traditional physical media such as DVD and CD. Consequently the number of subscription services on the market is increasing providing consumers with a broader choice amongst those services which means that companies must make significant effort to grow but also to keep customers subscribed to their services through the sale of additional products and services. FamilyOnDemand is a digital subscription service that was launched in the UK few years ago. It offers a broad range of family-friendly media to stream and download, such as movies, television content, music, e-books and premium games. The service is available at a relatively low cost payable monthly after the completion of a free one-month trial. Data pertaining to subscribers including media consumption have been collected. You work as a data analyst within the FamilyOnDemand service team and as part of your responsibilities you have to derive a set of recommendations based on the analysis of the data. The service team is particularly interested in the consumption of family movies and kids e-books. The monthly time consumption of each product (in minutes) is available in the Excel file “FamilyOnDemand_Data.xlsx”. Although monthly time consumption for these two products is fairly stable from month to month, there is enough variation to concern the service team. There have been few attempts by your predecessor to forecast monthly consumption, but he has not been really successful. Sometimes media time consumption are lower than forecast, other times forecasts are too low. FamilyOnDemand requires accurate forecasts to improve the range of products and services offered meeting subscribers’ expectations, and to avoid losing them to competitors. 1. Plot both time series in the same graph. [4 Marks] 2. Assuming that a stationary model proved to be appropriate, the service team has selected a number of methods to forecast monthly time consumption. Determine, for each product (i.e. family movies and kids e-books), what forecast for time consumption would be for the next month by: [16 Marks] a. Using Naïve method; b. Using 3-month moving average. 3. Develop an exponential smoothing forecast using a smoothing constant (α) that minimises the MAPE, and forecast the time consumption of each product for month 2 through 71. Conclude. [18 Marks] 4. Based on the results of questions 2 and 3 and by consulting the literature on time series forecasting, explain what forecasting technique you would recommend. [11 Marks] 5. The service team is wondering whether it is possible, when trying to forecast the time consumption of one product (e.g. family movies), to somehow incorporate time consumption of the other product (e.g. kids e-books) in the forecast model. The idea is there might be a relationship between the consumption of both products, meaning that these two products might be considered as substitute or complementary products. Use the methods of least squares to develop a straight –line approximation of the relationship between the two products. [11 Marks] Part B: Simulation [40 Marks] SportyPeople, is a small company that designs, produces and sells sportswear. The design team has created a new design of tracksuit. The company management has now to decide how many tracksuits to produce in the current production run. Because of the lead times involved, no other production runs will be possible during the season. Predicting tracksuit sales months in advance of the selling season can be quite tricky. SportyPeople has been in operation for only three years, and its tracksuit designs were quite successful in two of those years. Based on realised sales since the company was launched, current economic conditions, and expert judgement, SportyPeople management believes that in the coming year the following probability distribution for the unknown demand of tracksuits is a reasonable model: Demand Probability 5000 0.2 9000 0.3 13000 0.4 16000 0.1 To assist in the decision on the number of units for the production run, management has gathered the data in the following table: Monetary values Variable production cost per unit (C) £80 Selling price per unit (S) £100 Salvage value per unit (V) £30 Fixed production cost (F) £100,000 Note that S is the price SportyPeople charges retailers. Any tracksuits that do not sell during the season can be sold by SportyPeople to discounters for V per jacket. The fixed cost of plant and equipment is F. This cost is incurred regardless of the size of the production run. 1. Determine appropriate intervals for the random numbers that can be used to generate the demand for tracksuits. [2 Marks] 2. Use the following random numbers: 0.11164, 0.36318, 0.75061, 0.37674, 0.26320, 0.75100, 0.10431, 0.20418, 0.19228 and 0.91792 to simulate the demand of the first 10 iterations. [4 Marks] 3. Develop and explain the profit model. [4 Marks] 4. Using your answers for question 2, [12 Marks] a. Use a spreadsheet model to simulate 10 possible outcomes for the demand in the coming year, determine both the expected profit and the standard deviation of profit if SportyPeople produces Q = 7800 tracksuits (Scenario 1). b. Use a spreadsheet model to simulate 10 possible outcomes for the demand in the coming year, determine both the expected profit and the standard deviation of profit if SportyPeople produces Q = 12,000 tracksuits (Scenario 2). 5. After further investigation, SportyPeople management estimated that the demand for tracksuits follow a normal distribution with a mean 12,000 and a standard deviation of 3,497 is a reasonable model. [12 Marks] a. Use a spreadsheet model to simulate 10 possible outcomes for the demand in the coming year, determine both the expected profit and the standard deviation of profit if SportyPeople produces Q = 7800 tracksuits (Scenario 3). b. Use a spreadsheet model to simulate 10 possible outcomes for the demand in the coming year, determine both the expected profit and the standard deviation of profit if SportyPeople produces Q = 12,000 tracksuits (Scenario 4). 6. Compare all four scenarios. [6 Marks] a. Does the probability distribution of the demand have any impact on the model outputs? b. What are your recommendations in terms of production quantity? Instructions: 1) Your written report should not be more than a maximum of twenty A4 pages. Font size no less than 10pt. Margins all around should be no less than 2cm. 2) Do not copy and paste questions in your report. 3) Add algebraic formulas and equations used to answer the questions. Excel formulas should NOT be used to justify your answers in the report. 4) Upload a zipped folder containing evidence of your work (e.g. Excel files). A separate submission link will be created for this purpose. These files will not be marked but will be used to check you have done the work. Complete answers including formulas, graphs, results and discussion should be available in the report. It is your responsibility to show all the steps. Failing to do so you will be penalised.