Couse work I-MTH203 (S2, AY2021-22)

Release Date: April 11 Submission: 5:00pm April 17 via LMO

1. You are allowed to use computer programming and/or Excel, but codes and/or Excel worksheets and/or snapshots of computations should be provided to gain higher marks.

2. We only accept submissions in the format of pdf, docx, xlsx (i.e.,Excel).

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Question 1. [40 marks] A time series dataset is provided in the Excel file “data.xlsx” which contains 156 data points.

(1) Describe the dataset. Consider various aspects, for example the graph, the “pattern”, the trend, etc.

(2) Treat the data points as they follow a linear trend model. Generate 𝐹 ,𝐹 ,…,𝐹 by using Double Exponential Smoothing method with

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S0=30,B0=10,α=0.3,β=0.1 and present the forecasts and real

observations in one graph. Round your answers to 3 decimal places.

Conceptually do you think this is appropriate for this particular dataset? Why? (3) Use a different way to produce 𝐹 ,𝐹 ,…,𝐹 and make a comparison

with your result in (2), provide sufficient explanation/reasoning. Again present the forecasts and real observations in one graph. Round your answers to 3 decimal places.

Question 2. [30 marks] Caspar owns a Company which manufactures electronic chips and his business partner, Martin, would like to order 200,000 chips, which would make the whole company work full time for a week, each chip profits $5 but if Caspar couldn’t finish, he has no gain and needs to pay liquidated damage $500,000; or Martin orders 100,000 chips, each profit $4, in which case the company would work part-time, the liquidated damage is $150,000. Also Caspar could choose not to take any orders from Matin and let the company not work for now. Due to the recent spread of COVID-19 in the city, all the companies are monitored by the government. So there is a 50% chance that a company with full time operations will be urged to close temporarily and 20% for companies with part time operations. As an alternative, companies could conduct a nucleic acid testing (costing $10,000) before their productions, the ones with “all negative” would be allowed to work (regardless of full-time or part-time) with probability 0.65, if one or two positive cases were detected, companies working full-time will be stopped and the ones working part-time would keep working with probability 0.6. All the companies with more than two positive cases would be asked to close right away. Suppose that Caspar

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wishes to generate the optimal decisions using decision tree method.

(1) Draw the draft tree to present the logic of the problem.

(2) Solve the problem, make additional information if necessary.

Question 3 (DIY) [30 marks]. (1) Create a Markov Decision Process (MDP) question that contains 3 actions, each with a 3 by 3 probability transition matrix and a 3 by 3 cost matrix. Suppose we make decisions for 4 stages. Introduce the background of the problem (rather than just giving maths) and ensure that solution of the question is non-trivial, i.e., it would not always lead to the same action in all stages. (2) Solve the question you create in (1), show your work.

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