Bachelor of Business Studies 59 Part Time, Singapore

MIS3010S: Analytics Modelling

Problem Assignment

Due date: 8th October, 2022.

Assessment weight: 40%.

Teams of three students: do problems 1, 2 and 3.

Teams of four students: do problems 1, 2, 3 and 4.

1. Introduction

1.1. Overall form of assignment. This is a team assignment, worth 40% of the course mark.

Teams of 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 righthand margin. Teams of 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 links.

## ORDER A PLAGIARISM – FREE PAPER NOW

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 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

below, 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.

To find the digits to use, work as follows, using the relevant student number for the relevant

problem:

1

Analytics Modelling: Problem Assignment 2

• 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.

1.3. Deliverable. Provide as your deliverable a single document, with word limit 3000 words, in

the form:

(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.

The cover page, individual statements, diagrams (and bibliography/references, if any) do not count

towards the word limit. This deliverable may be in Word, Openoffice.org or pdf format.

Name the deliverable according to the convention

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

where Surname List means one of

• Surname1 Surname2 Surname3 or

• Surname1 Surname2 Surname3 Surname4

as appropriate to the team size. Each model file developed (e. g., in Mosel) must also be named

with a similar convention, replacing problems by Q2 etc., as appropriate, e. g., you would submit

AM Surname List Q2.mos as the Mosel file for Problem 2.

Submit your deliverables through Brightspace. This must be done by 8th October, 2022; after

this time, it will lose marks for being late according to the UCD Late Submission of Coursework

policy.

Analytics Modelling: Problem Assignment 3

2. Problems

1. You will address a Decision Analysis problem as described below using the tools discussed in [30 ]

class, and make a recommendation to the decision maker. In this problem, you will notice

that “the chance that the antidumping tax will be imposed is p, where p is derived from the

third and eighth digits of your student number”. To find the p to use in your submission,

work as follows:

• 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 government, 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.

AAA believes that the chance that the antidumping tax will be imposed is p, where p is

derived from the third and eighth digits of your student number as described above. If it is

imposed, then it is equally likely that the tax will be 50%, 100%, or 200% of the sale price for

each HSN chip.

(i) Draw a decision tree for this decision.

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

2. It is the end of the financial year (the winter quarter). Floggit Ltd, a new startup, produces [30 ]

one product, for which the demand in units for the next four quarters is predicted to be as

given in Table 1.

Quarter Spring Summer Autumn Winter

Demand 70 100 150 180

Table 1. Floggit demand levels for the next four quarters

Assuming all the demand is to be met, there are various production policies that might be

followed:

One extreme: Track demand with production and carry no inventory;

The other extreme: Produce at a constant rate of 125 units per quarter (i. e., the average

demand) and allow inventory to absorb the fluctuations in demand;

Intermediate policy: Allow some variation (but not too much: how much is best?) in

production, and absorb the remaining fluctuations in demand by (a smaller) inventory.

Analytics Modelling: Problem Assignment 4

Floggit’s factory is limited to 100 units per quarter normal production. Above that production

level, overtime rates must be paid, which increases production costs.

There are costs associated with

• Holding inventory: Floggit estimates an inventory holding cost of S$40 for each unit of

inventory at the end of each period

• Varying the production level: Floggit estimates that changing the production level from

one period to the next costs S$30 per unit. [For example, if 140 were made in one period

and 120 in the next, then the cost of changing would be S$30×(140−120) = 30×20 = 600.]

• Normal production: up to 100 units per quarter, at a cost per unit of S$100

• Overtime production: this is seasonal, both in quantity that can be produced and in cost

per unit:

Quarter Spring Summer Autumn Winter

Production capacity (units) 40 60 90 80

Production cost/unit (S$) 12s1 13s2 14s3 13s4

There is an inventory capacity of at most 60 units.

The initial inventory is zero and the current production level is 100 units in this (winter)

quarter. Floggit require that these same levels be returned to at the end of next year’s winter

quarter. All costs, including the cost of returning to these same levels, must be considered.

You must find the production and inventory policy that gives the least total cost while

meeting these requirements. Formulate and solve this problem, assuming:

(a) the production and inventory variables are continuous (e. g., the product is petrol);

(b) the production and inventory variables are integer (e. g., the product is fridges).

Where appropriate, carry out sensitivity analysis to determine for which constraints the objective function value is most sensitive.

3. In the following, s1, . . . , s8 are the digits of the relevant student number for this question. [40 ]

You wish to invest S$50,000. You have identified five investment opportunities. Each is an

“all-or-nothing” investment: you must invest the full amount or not invest at all.

• Investment 1 requires an investment of S$16,000 and has a present value (a time-discounted

value) of S$23,000;

• Investment 2 requires S$14,000 and has a present value of S$s1s2,000;

• Investment 3 requires S$22,000 and has a present value of S$s38,000;

• Investment 4 requires S$12,000 and has a present value of S$14,000; and

• Investment 5 requires S$38,000 and has a present value of S$4s8,000.

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 (omitting

pruned branches), and clearly explaining why certain subproblems are fathomed. For each

intermediate subproblem, solve the LP associated to that problem using Xpress or another

solver. Include in your submission the Xpress formulation and Xpress output for each subproblem investigated.

4. A large engineering firm, Heavy Automation Logistics (HAL), is changing its focus to become [33 ]

a services firm, and seeks an efficient way to do this. HAL has identified three categories of

customer-facing staff: Engineers, IT Consultants and Business Consultants. It is embarked

on a workforce repositioning effort, wherein it wishes to decrease the number of engineers and

increase the numbers of business consultants and IT consultants. Its approach to achieving

this will be a combination of hiring, firing and training (new skills development). Coupled

with this workforce repositioning, the current economic climate is expected to mean a short

term reduction in the total number of staff required. Table 2 gives the expected number of

staff of each category required over each of the next three years.

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

and (c) training.

Analytics Modelling: Problem Assignment 5

Engineer IT Consultant Business Consultant

Current (2022) 3000 500 1000

Required 2023 2000 600 1100

Required 2024 1200 1200 1900

Required 2025 500 2000 2500

Table 2. Current and expected required staff levels by category, up to 2025

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 3. Currently, all staff have been

Engineer IT Consultant Business Consultant

≤ 1 year service 12% 15% 10%

> 1 year service 7% 10% 5%

Table 3. Expected staff turnover rates, by category

working for HAL for more than one year.

The information to hand regarding possibilities of hiring, firing and training is as follows.

Hiring: It is possible to recruit from outside a limited number of people with the appropriate skill sets for HAL. It is expected that in each of the years from now to 2025, the

availabilities of the three categories will be as in Table 4:

Engineer IT Consultant Business Consultant

Number available 400 900 800

Table 4. Expected staff availability for hiring, by category

Firing: The costs of making staff redundant are as in Table 5:

Engineer IT Consultant Business Consultant

Redundancy cost 1s3s4 1s5s6 1s7s8

Table 5. Cost in thousands of S$ of making staff redundant, by category

Training: Certain categories of staff may be retrained to other categories, as given below.

However, it is considered too expensive to retrain Engineers to be Business Consultants,

or vice versa, since their skillsets are so different.

• Up to 400 Engineers may be retrained to be IT Consultants each year, at a cost of

S$5000 each, by sending them on external courses.

• IT Consultants may be retrained to be Business Consultants, at a cost of S$7000

each; however, some of this training is done on the job by existing HAL Business

Consultants, which means that the number trained in this way each year is limited

to at most one third of that year’s Business Consultant population.

• Up to 300 Business Consultants may be retrained to be IT Consultants each year,

at a cost of S$6000 each, again by sending them on external courses.

• Up to 200 IT Consultants may be retrained to be Engineers each year, at a cost of

S$4000 each, also by sending them on external courses.

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?

Modify your mathematical programme to answer this revised question