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MGRC30003: Decision Analysis & Simulation – Summative Individual Coursework

Administration

This is the summative individual assessment for this unit. It accounts for 70% of the overall unit mark. You must answer all of the questions from both cases attached. Please submit your work, presented either in a single Word or PDF format document. The assessment is to be completed individually and independently.

1^st Case: AquaLux Bath Soaps

The leadership team at AquaLux, a prominent bath soap manufacturer, is aiming to optimize their inventory expenses. The cost incurred weekly for holding a single unit of soap in stock amounts to £30 (where one unit equates to 1000 soap cases). The marketing division has projected a weekly demand with an average of 120 units and a standard deviation of 15 units. This demand follows a relatively accurate normal distribution pattern. Sales exceeding the available soap quantity result in lost sales; in other words, there's no backlog for unmet demand.

The manufacturing department can operate at one of three production capacities: 110, 120, or 130 units per week. A production level shift incurs a £3000 cost. The management intends to assess the following production strategy: When the existing inventory falls below L = 30 units, they will manufacture 130 units in the subsequent week. If the current inventory surpasses U = 80 units, they will produce 110 units in the upcoming week. In all other cases, AquaLux will maintain the previous week's production level. At present, AquaLux maintains an inventory of 60 units. The production level from the prior week was set at 120 units.

(A) Construct a simulation model to cover 52 weeks of operational activity at AquaLux. Plot the soap inventory against time. Determine the overall expenses, including inventory costs and production change costs, for the entire 52-week period. (20 points)

(B) Execute the simulation for 500 iterations to approximate the mean cost over 52 weeks. Vary the value of U within the range of 30 to 80, increasing it by intervals of 10. Maintain L at a constant value of 30 (15 points)

(C) Provide the average and standard deviation of the 52-week cost for each policy based on the simulated outcomes. Utilize these simulated results to potentially create 95% confidence intervals for the mean 52-week cost associated with each U value. Irrespective of this, plot the relationship between the average 52-week cost and different U values. Identify the optimal U value when L is set at 30. (10 points)

(D) Instead of a normal distribution, suppose the demand for soap follows a Poisson distribution. How might this change in the demand distribution affect the optimal production policy and the resulting costs? (10 points)

(E) AquaLux is considering partnering with a third-party logistics provider to handle their inventory management. How might this outsourcing decision influence their production policies and costs. (15 points)

2^nd Case: Meadow Farms and Sunny Orchard Sales in Greenvale

In a small town called Greenvale, two major farms, Meadow Farms and Sunny Orchard, stand as the most significant food suppliers of the region. Meadow Farms mainly produces grains like wheat and barley, whereas Sunny Orchard specializes in fruit trees, such as apples and oranges.

Every month, both farms record their sales value (check the TS_data.csv file for reference), reflecting their production efficiency and the market's demand. Over recent years, monthly sales figures have fluctuated for both farms due to the impacts of climate change and advancements in technology. To better understand their sales trends and make decisions for future planting and market strategies, they have decided to undertake a time series analysis of their data.

(F) Suppose both farms want to forecast the 6 monthly sales based on the historical data with Smoothing, which method should be chosen respectively and what are the predicted values? Please write down your analysis with R. (15 points)

(G) Suppose both farms want to forecast the 6 monthly sales based on the historical data with ARIMA, which ARIMA models (indicate p,d and q) should be chosen and how to interpret the parameters? Please write down your analysis with R. (15 points)

Reading beyond the course materials and text could be vital. You are expected to provide a comprehensive managerial report on formulation, solution, and the discussion of the interpretation of the output. Use of graphs and diagrams to illustrate your analysis is certainly encouraged. Use of screenshots of the Excel spreadsheet or R model for each of the various scenarios is also recommended for your own convenience. You should also include the discussion of any assumptions made in applying your techniques to this reassessment case study. You are reminded that this assignment should be handled as an academic report and therefore, the justification of your answers is considered essential. You should consider integrating any technical details and/or mathematical justification in the appendix. Finally, it is important to involve an extended analysis followed by more general suggestions of how this project could be extended, including a statement of requirements to carry out the proposed extension. (ILOs 1-5)

Intended Learning Outcomes (ILOs):

1) define and identify the problematic area through developing your logical reasoning and creativity,

2) transform a conceptual framework or verbal statement into its equivalent mathematical model,

3) develop and apply fundamental optimization, simulation, and (multi-criteria) decision analysis models towards the effective decision-making in practice,

4) demonstrate a sound knowledge of a range of available tools and methodologies for the solution of problems and the robust analysis and interpretation of their outputs,

5) utilise computer-based softwares which, along with appropriate data, can facilitate the formulation and execution of various models.

Submission Requirements:

a. This type of individual summative assessment is weighing 70% of the overall unit mark and is related to covering all intended learning outcomes of weeks 8, 9, 10, and 11 of the unit.

b. The report should be uploaded to Turnitin either in a Microsoft Word or a PDF format. You should use a 12-point font size and line-spacing of 1.5 with blank line between paragraphs. Margins should be set to “Normal”.

c. 1500 words is suggested as a guideline for length. It may be longer or shorter than this, but if shorter, it will be assessed as to whether it has covered the salient issues in sufficient depth. If longer, it will be assessed from the perspective of whether unnecessary material has been included. Hence, the word length is an element of academic judgement in marking, not a penalty for failing to meet a word count.

d. An outline marking scheme is shown in brackets to the right of each question.

e. Use Harvard System for referencing.

f. There is no expected absolute number of sources, as the quality of sources is more important than the quantity. Students are expected to read widely and should consult the recommended journal list in the Unit Handbook for guidance on high-quality sources.

g. Ensure that you take frequent and multiple backups of your work, since excuses concerning lost or corrupted files will not be treated sympathetically.

h. You must submit an electronic copy of the assignment to the Turnitin through Blackboard. Regarding the similarity index, you might consult Undergraduate Studies Office for more information about academic plagiarism policy. In addition, full submission details can be found in your BSc program Handbook. 

i. The individual assessment submission date is at 13:00pm on Monday 8 January 2024.