operational research

Couse work I-MTH203 (S2, AY201920)

Release Date: April 18 Submission deadline: 11:59pm April 26

Way of Submission: Online through ICE.

You could either type or hand-write the solutions, then upload it on ICE. .docx or

pdf files are preferred. It is OK to take pictures of your handwriting but make

sure the pictures are easy to read so that you do not loose marks.

Question 1. (Free Style) (1) Make up one question covering any two of the following knowledge points: decision tree, decisions under uncertainty, Markov decision process, utility function, Pareto-optimum (2) Solve the question you created in (1). Note that:

• Please do not make totally separate contexts to cover the two knowledge points, i.e., the background for the two should be connected.

• Have at least two sub questions. • Do not directly use the previous exam questions. • Make sure the needed information (e.g. parameters, probabilities) is provided in your

question. Question 2. Table 1 gives the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont over the past 12 weeks.

Week Sales (1000s of gallons)

1 17

2 21

3 19

4 23

5 18

6 16

7 20

8 18

9 22

10 20

11 15

12 22

Table 1. Gasoline Sales Data It is believed that the data points follow a constant level model. Suppose we apply Exponential Smoothing Method using Excel and Figures 1 and 2 show the input and output.

Figure 1. Exponential Smoothing_Excel Input

Figure 2. Exponential Smoothing_Excel Output

(1) According to the figures, what are the values of 𝐴0 and 𝛼? (2) Compute 𝐹13 (round your answer to 2 decimal places). (3) Suppose that comparing with the sales data in early weeks, we have a good reason to believe

that the recent weeks are more reliable but still want to apply exponential smoothing method, redo the exponential smoothing using Excel to employ this idea, show the snapshots of your input and output.

Question 3. Chris works at Welfare Insurance Call Center, where people call for consultation and decide what types of insurance to buy. Based on the past experience, Chris will receive between 0 and 5 calls per hour, according to the discrete probability distribution in Table 2:

Calls Probability

0 0.05

1 0.13

2 0.3

3 0.25

4 0.12

5 0.15

Table 2. Calls and probability

The call center classifies each call based on the insurance types: travel, business visit or private visit. The probability that a particular call will be each type is listed in Table 3.

Insurance Type Probability

Travel 0.4

Business visit 0.3

Private visit 0.3

Table 3. Insurance types and probability Then Chris would compute the time needed to prepare the detailed contracts he gained. Specifically, a travel insurance contract takes 𝑥 hours, a business visit insurance contract takes 𝑦 hours and a private visit insurance contract takes 𝑧 hours. (1) Simulate the calls received by Chris in one day (i.e. 8 hours). Generate random numbers

when you need. (2) Suppose that based on your simulation in (1), we try to make the contract preparation the

most efficient, suggest values of 𝑥, 𝑦 and 𝑧.