2020/21 EXAMINATIONS

MANAGEMENT SCIENCE

MSCI 502 Operational Research and Prescriptive Analytics

Online examination

Target duration: 2-5 hours

We anticipate that this task should take students between 2-5 hours to complete. As the time taken to complete the task does not form part of the assessment criteria, and to take into consideration of students with additional needs, all students will be given at least 24hrs to complete the assessment task.

Available from 12noon on Thursday 7th January 2021 and to be submitted by 12noon on Friday 8th January 2021.

You must answer ALL questions.

You must work independently on this exam. You are not allowed to consult or have discussions with other people. All work will be subject to plagiarism and malpractice checks.

The tasks are worth 70 marks.

The model design is worth 30 marks.

学生将有至少 24 小时的时间来完成评估任务。 从 2021 年 1 月 7 日星期四中午 12 点开始提供，并在 2021 年 1 月 8 日星期五中午 12 点之前提交。 您必须回答所有问题。 您必须独立完成此考试。不得与他人协商或讨论。所有作品都将接受抄袭和舞弊检查。 这些任务价值 70 分。 模型设计值 30 分。

- See your specific datafile on moodle for the values for $A, B, C, D, E, k_{1}, k_{2}, k_{3}, k_{4}, p_{1}, p_{2}$ and $p_{3} *$

Hindle Hifi make acoustic isolation hifi platforms out of a revolutionary mix of hi-tech polymers. They manufacture three different densities of the platforms, depending on the type of hifi equipment the platform will be placed underneath. The Extendex and Resistex platforms weigh $1 \mathrm{~kg}$ each but the Airtex is lighter at 500 grams. Note: $1 \mathrm{~kg}=1,000$ grams All the polymers, including the base polymer, are also produced in-house by Hindle Hifi.

$\begin{array}{ll}\text { Airtex } & \text { (a light platform for CD players, streamers and other digital source equipment) } \ \text { Fytendey } & \text { (a heavier nlatform for amnlifiers and solid_state equinment) }\end{array}$ Extendex (a heavier platform for amplifiers and solid-state equipment) Resistex $\quad$ (a harder platform for mono-blocks, speakers and subwoofers)

All three products require the same four ingredients – three special proprietary chemical polymers and a standard base. Everything is made on-site. The amounts of each ingredient are given in the table below

\begin{tabular}{lcccc}

& \multicolumn{3}{c}{ Ingredient (grams per kg of product) } \

\cline { 2 – 5 } Product & Polymer A & Polymer B & Polymer C & Base \

\hline Airtex & 250 & 120 & 250 & 380 \

Extendex & 180 & 125 & 125 & 570 \

Resistex & 375 & 180 & 320 & 125 \

& & & \

& & & \

Polymer & Monthly production & Cost of manufacture \

& $(\mathrm{kg})$ & $(£$ per $\mathrm{kg})$ \

\hline A & A & $\mathrm{k}*{1}$ & \ B & B & $\mathrm{k} 2$ & \ C & C & $\mathrm{k}*{3}$ & \

Base & D & k4 &

\end{tabular}

Production of the platforms takes place on a special fully-automated machine, that can produce platforms (of any type) at a rate of 100 platforms per day (any type), and operates for 20 days per month.

Post production requires also requires a special sonic calibration process:

Airtex $\quad 2$ minutes per platform inspected

$\begin{array}{ll}\text { Extendex } & 2 \text { minutes per platform inspected } \ \text { Resistex } & 30 \text { seconds per platform inspected }\end{array}$

Total time available in the Sonic Calibration Room (SCR) next month is 45 hours.

For the coming month, Hindle Hifi has confirmed orders to produce 500 Airtex platforms, 500 Extendex platforms and 400 Resistex platforms, a total of 1,400 platforms. The current selling prices for the products are $\mathrm{p}*{1}$ for the Airtex platform, $\mathrm{p}*{2}$ for Extendex and $\mathrm{p}_{3}$ for Resistex.

## Task

- What is the expected cost of supplying exactly the confirmed orders next month?
- What is the expected profit associated with the confirmed orders next month?
- If Hindle Hifi satisfies the confirmed orders and is free to make more platforms, then what is the maximum profit possible1, and how many of the three platforms should they make?

[For question 4 onwards, you can assume that Hindle Hifi does not have to satisfy the confirmed orders next month, and is free to make any number of the three types of platforms.] - What would the maximum profit be1, and how many of the three platforms should they make?
- If an additional 5 hours are available in the Sonic Calibration Room this month, how would this impact on the maximum profit1 and optimal plan?
- If the machine time could be extended by an additional 2 days this month, how would this impact on the maximum profit1 and optimal plan?
- If the machine time could be extended by an additional 2 days this month and an additional 5 hours are available in the Sonic Calibration Room this month, how would this impact on the maximum profit1 and optimal plan?
- Perform a sensitivity analysis on the selling price of Airtex, from £45 to £60, in £1 increments, and show graphically how it relates to the number of Airtex platforms made1.

You can assume all the other production conditions are the same as task 4.

Comment briefly on the sensitivity chart. - Assuming at least 200 platforms have to be made for each of the three products, perform a sensitivity analysis on the machine time between 10 and 20 days per month, in 1 day increments, and show graphically how it relates to both the cost of production and the optimal profit1. You can assume all the other production conditions are the same as task 4.

Comment briefly on the sensitivity chart. - In two months’ time, the production facility will be partially closed for a month for refurbishments to take place. The production of all four polymers during this month will be significantly reduced, and the estimate is that production will be 10% of their current monthly production.

The platform machine and SCR will also be impacted and will be only operate at around half of the current activity.

During this refurbishment period Hindle Hifi have decided to focus solely on making Airtex platforms.

a) How many Airtex platforms can be made under these reduced production conditions?

b) If Hindle Hifi want to produce E platforms during this period, what is the lowest percentage of polymer production that is necessary to achieve this2?

## Hindle Hifi

### Model Design

ModHigh marks will go to a model which follows the design principles of the module, as laid out in the documentation and described during the lectures. The model should be simple and elegant, with no unnecessary replication of sheets or optimisation models. The model should also be flexible, transparent and be able to reproduce the answers given to all the tasks.

### Data Collection

The data for each student is held on Moodle in a folder called ‘Exam Data’.

Each student will receive a unique dataset, based on a code number.

The code numbers will also be listed on Moodle.

You MUST use the correct dataset, as all are unique.

Failure to do so will be seen as plagiarism

### Submission

You are required to upload to Moodle a single Excel 2019 model addressing the tasks.

The model rules are:

✓ The model should open on the provided User sheet

✓ All answers/links should be presented in the provided cells on the User sheet

✓ The User sheet should include your name and ID/library number

✓ Only correct results receive marks

✓ The model should operate successfully on a University-spec. PC

✓ For tasks 7 and 8 a link should be created (macro button or hyperlink) to the location of the sensitivity analysis

Do not move or re-position any of the answer cells on the User sheet

The User sheet should not include any additional tables or charts

The model should not be password protected or contain external links

No sheets should be hidden

Failure to adopt these rules will result in a mark penalty