MIS3010S: Analytics Modelling
Problem Assignment

1. Introduction

1.1. Overall form of assignment. This is a team assignment, worth 40% of the course mark. Teams of two or three students must attempt questions 1–3. Teams of four must attempt all four questions. The mark for each question or part of a question is given in brackets [ ] in the right-hand margin. Teams of two or three are marked out of 100. Teams of four are marked out of 133.

This is an open book assessment. You may use a calculator throughout, and software packages where stated; but otherwise you must show all of the details of your work, including when using algorithms.

Standard UCD policies on late submission, plagiarism etc., apply. See 

https://www.ucd.ie/governance/policypages/policypage-academicregulations 

and follow the relevant links.

1.2. Randomisation of problem data. In the problems, you will notice that I have used digits from student numbers. This is in order to make the problems differ from one student to another, and so enhance integrity of the assessment. Your student number is largely random and so allows for some randomisation of problem data.

Teams of two: choose one team member to be Student 1 and the other team member to be Student 2. Follow the instructions below, using the digits of Student 1’s student number for Question 1, and the digits of Student 2’s student number for both of Questions 2 and 3.

Teams of three: choose one team member to be Student 1, a different team member to be Student 2, and the third different team member to be Student 3. Follow the instructions mbelow, using the digits of Student 1’s student number for Question 1, the digits of Student 2’s student number for Question 2 and the digits of Student 3’s student number for Question 3.

Teams of four: choose one team member to be Student 1, a different team member to be Student 2, a third different team member to be Student 3 and the fourth different team member to be Student 4. Follow the instructions below, using the digits of Student 1’s student number for Question 1, the digits of Student 2’s student number for Question 2, the digits of Student 3’s student number for Question 3 and the digits of Student 4’s student number for Question 4.

• Let s1, s2, . . . , s8 be the first, second, . . . , eighth digits, respectively, of your student number, with the extra condition that if a digit is 0, you should change it to 5. For example, if your student number is 18473025, then s1 = 1, s2 = 8, s3 = 4, s4 = 7, s5 = 3, s6 = 5 (not 0), s7 = 2 and s8 = 5. This si notation refers exclusively to student number digits, and will not be used for any other purpose in this assignment.
• If two digits occur consecutively in a question, treat them as the 10s digit and units digit of a two digit number. For example, if your student number is 18473025 as above, then s3s8 = 45 as a decimal number. Similarly for three or more digits, or digits after a decimal point: for this example student number, s1s6s8 = 155, and if p = 0.s4s7, then you would get p = 0.72.
• Similarly if a student number digit comes after another digit, it does not mean multiplication, e. g., for student number 18473025, 3s3 = 34.
• −si means the negative of si , e. g., for student number 18473025, −s3 = −4.
• In certain questions, you may need to make other adjustments to some digits.

(i) A standard signed cover page (see Appendix 3 of Study Guide), containing

• title and handup date of assignment,
• full name and student number of each student, identifying which student’s student number was used in which question,
• a statement that this assignment is all your own work;

(ii) an individual statement by each student saying what that student contributed to the assignment: what they did for each question and the approximate percentage they did of the total work for the assignment. This may be used if differential grading is required.Each student may also give a personal reflection on the assignment;

(iii) your answers to the set problems:

• text must be typed, no smaller than 10 point font;
• diagrams e. g., of graphs/trees should be produced with a graphics tool if possible but may be hand-drawn if you cannot achieve this.

Name the document deliverable according to the convention

AM Surname List problems.pdf (or .docx, .odt, etc.)

2. Problems

• Let s3 and s8 be the third and eighth digits, respectively, of your student number. For example, if your student number is 18473925, then s3 = 4 and s8 = 5.
• If s3 ≤ 3, then set s3 := s3 + 3. For example, if s3 = 1, then set s3 to 4.
• If s3 ≥ 8, then set s3 := s3 − 2. For example, if s3 = 9, then set s3 to 7.
• Let p = 0.s3s8 as a decimal number. For example, if s3 = 5 and s8 = 9, then you would get p = 0.59.

AAA Electronics has contracted to supply half a million TabletPC systems to CostCo Stores in 90 days at a fixed price. Each TabletPC system requires a High Speed Northbridge chip (“HSN chip”) in order to function. In the past, AAA has bought these chips from a Korean chip manufacturer, Recce Chips. However, AAA has been approached by a Chinese manufacturer, CAC Electronics, which is offering a lower price on the chips. This offer is open for only 10 days, and AAA must decide by then whether to buy some or all of the HSN chips from CAC.

Any chips that AAA does not buy from CAC will be bought from Recce. Recce will sell HSN chips to AAA for S$3.00 per chip in any quantity. CAC will accept orders only in multiples of 250,000 HSN chips, and is offering to sell the chips for S$2.00 per chip for 250,000 chips, and for S$1.50 per chip in quantities of 500,000 or more chips.

However, the situation is complicated by a dumping charge that has been filed by Recce against CAC. If this charge is upheld by the Singapore courts, then the CAC chips will be subject to an antidumping tax. The judgement in this case will be delivered exactly two weeks from now and, if the charge is upheld, the antidumping tax will go into effect immediately. If AAA buys the CAC chips, these will not be shipped until 30 days from now, meaning the chips would be subject to the tax if the charge is upheld. Under the terms proposed by CAC, AAA would have to pay any antidumping tax that is imposed.

(i) Draw a decision tree for this decision.

(ii) Using expected value as the decision criterion, determine AAA’s preferred ordering alter native for the HSN chips.

Into which investments should you place your money so as to maximise your total present value?

Solve this problem using Branch and Bound, showing the full tree you develop, and clearly explaining why certain subproblems are fathomed. For each intermediate subproblem, solve the LP associated to that problem using Xpress. Include in your submission the Xpress model formulation and Xpress output for each subproblem investigated. Name the model files AM Surname List Q3a.mos, AM Surname List Q3b.mos, etc.

3. [35]In the following, s1, . . . , s8 are the digits of the relevant student number for this question. They are used for some edge weights in Figure 1 below. If any si = 0, then set that si := 5. For example, if s3 = 0, then set s3 to 5, meaning that the edge 4-5 in Figure 1 will have length 5.

Figure 1 represents the road system in the town Marawatna, with streets being edges and street junctions being vertices. The number on each street is the length of the street in hundreds of metres. Traffic can travel in either direction along any street. The Hospital is located at the junction marked 1.

(a) To improve ambulance service quality, you are asked to find a shortest path from the Hospital to vertex 11, and its length. Solve this problem, using an appropriate algorithm. Show all of your work, including the resulting shortest path spanning tree rooted at the Hospital.

From your work, what — if anything — can you say about the shortest path from vertex 3 to vertex 11; or the shortest path from vertex 3 to vertex 7? Explain your thinking.

HAL wishes to identify a policy to achieve these numbers, in terms of (a) hiring, (b) firing and (c) training.

A complicating factor is that there is a normal turnover of staff (that is, staff leaving HAL). HAL’s experience is that staff are more likely to leave during their first year. HAL have forecast the staff turnover percentage rates as in Table 2. Currently, all staff have been

Table 3. Expected staff availability for hiring, by category

Firing: The costs of making staff redundant are as in Table 4:

For simplicity, it is assumed that all of the events, namely, hiring, firing, training and staff turnover, occur once each year, on the first day of the year.

HAL’s objective is to meet these staffing requirements while minimising the amount of staff redundancy (firing) required. Formulate this as a mathematical programme and solve.

If their objective were changed to minimising costs, how much extra money could they save?