MANG6046 Optimisation and Decision Modelling

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COURSEWORK BRIEF:

Module Code: MANG6046

Assessment: Individual coursework

Weighting: 80%

Module Title: Optimisation and Decision Modelling
Module Leader: Dr Yue Wu
Submission Due Date: @ 16:00 10th January 2025
Word Count: 2000
Method of Submission: Electronic via Blackboard Turnitin ONLY (Please ensure that your name does not appear on any part of your work)
Any submitted after 16:00 on the deadline date will be subject to the standard University late penalties (see below), unless an extension has been granted, in writing by the Senior Tutor, in advance of the deadline.

Days Late:
 Mark:
1
 (final agreed mark) * 0.9
2
 (final agreed mark) * 0.8
3
 (final agreed mark) * 0.7
4
 (final agreed mark) * 0.6
5
 (final agreed mark) * 0.5
More than 5
 0

This assessment relates to the following module learning outcomes:

A. Knowledge and Understanding
 A1~A5
B. Subject Specific Intellectual and Research Skills
 B1~B2
C. Transferable and Generic Skills
 C1~C4

Coursework Brief:

This piece of work will count for 80% of the overall mark for MANG6046. You need to submit a report of your comment on a project and an Excel file (not multiple Excel files) in two separate folders (one is called Individual Coursework_Reports Only; the other is called Individual Coursework_Excel Files Only) electronically via Blackboard by the due date shown above. Please make sure that the report and the Excel file have the same filename, starting with your student ID.

It is important to be reminded that we do not tolerate plagiarism. Please check the corresponding university regulation. Ensure that you take frequent and multiple backups of your work, since excuses concerning lost or corrupted files will not be treated sympathetically.

General guidelines
  • Include a front page as a separate sheet, indicating the module title, word count, student ID, etc.
  • Your report should be able to stand alone and be sufficiently detailed to not require looking at your Excel file to fully understand your approach—the Excel file is for the purpose of checking plagiarism, etc.
  • Structure your report. Make sure not to exceed 2000 words (this is a maximum and not a target), excluding appendixes.
  • Include all formulations of mathematical models (not only Excel spreadsheet models) with a statement of any assumptions that are made. Clearly defining and explaining decision variables, constraints, and objective functions for each scenario that is discussed.
  • A brief description of how you solve the models.
  • A presentation of the results, analysis, and recommendations based on the techniques that you learn from this module or other resources.
  • Other parts you may want to present.
  • Excel spreadsheets and corresponding output should be in appendices (only including the most relevant parts).
  • Excel Solver is the software you need to use in this coursework.

School Allocation

The Highland city council has decided to close one of its secondary schools (sixth, seventh and eighth grade) at the end of this year and reassign all of next year’s secondary school students to three remaining secondary schools. The council provides busing for all secondary school students who must travel more than approximately a mile so the council wants to have a plan for reassigning the students that will minimize the total busing cost. The annual cost per student for busing from each of the six residential areas of Highland to each of the schools is given below along with other data for next year, where 0 indicates that busing is not needed, and a dash indicates an infeasible assignment.

Area

No. of
students

Percentage in
6th grade

Percentage in
7th grade

Percentage in
8th grade

Bussing cost per student
School 1
 School 2
 School 3
1
 450
 32
 38
 30
 300
 0
 700
2
 600
 37
 28
 35
 -
 400
 500
3
 550
 30
 32
 38
 600
 300
 200
4
 350
 28
 40
 32
 200
 500
 -
5
 500
 39
 34
 27
 0
 -
 400
6
 450
 34
 28
 38
 500
 300
 0
School Capacity:
 900
 1100
 1000

The council also has imposed the restriction that each grade must constitute between 30 and 36 percent of each school’s population. The above table shows the percentage of each area’s secondary school population for next year that falls into each of the three grades. The school attendance zone boundaries can be drawn so as to split any given area among more than one school, but assume that the percentage shown in the table will continue to hold for any partial assignment of an area to a school.

You have been hired as a business analyst to prepare a report on how to determine the catchment areas (i.e., geographical areas around a school) for the Highland Council. Formulate a mathematical model and use adequate mathematical programming techniques to write a report to address the following issues:

a) What should the Highland Council do to minimise the total busing costs?
b) The council is considering eliminating some busing for students to reduce costs. Option 1 is to eliminate busing for students travelling below 1.5 miles, where the cost per student in the table is £200. Option 2 is to eliminate busing for students travelling below 2 miles, where the cost per student in the table is £300 or less. What effects do these changes have on the catchment areas and the total busing costs?
c) The council now wants to evaluate three busing plans (the current one, Option 1, and Option 2). Busingcosts are important, but so is the inconvenience caused by forcing students to travel by foot or bicycle (more than a mile and especially more than 1.5 miles). The council wants to choose a plan that provides the best trade-off between these factors. Summarise the key information relating to this decision and advise on which option you feel the council should choose?
d) The costs of busing students from Area 6 to the secondary schools are only estimates, and it is possible there may be significant rises in them. How much the costs on the route from Area 6 to Secondary School 1 can increase without affecting your suggested plan in a). What would you suggest if the busing cost had become £550 per student? What happens if all the busing costs on all the routes in Area 6 go up? How much can they go up, and the solution in a) still remains optimal? What is the busing plan if they all go up by 10%?
e) Another possibility is to add portable classrooms to some of the secondary schools to increase theircapacity. This would only be undertaken if there were savings in busing costs, as leasing a classroom that takes 20 students will cost £2,500 each year. To analyse this option, the council decides that the busing costs from Area 6 will eventually return to the initial estimate in the table. Please advise the school whether it is worth adding any classrooms, and if so, where.
f) The council is concerned about the splitting of residential areas among multiple schools and wants to know what the catchment areas and the total busing costs would be if this is not allowed. Advice the council on how much this would increase the busing costs.
g) The council is also concerned that they may have to close one of the middle schools. If one of the schools is closed, the capacity of each of the remaining two schools increases by 500. The cost of increasing the capacity is not considered. If that were the case, which school would you recommend for closure in terms of busing costs, and how much cheaper is this option than closing other schools.
Marking criteria (the total marks are 100):
  • Criteria 1: Demonstrating knowledge and understanding of key steps of modelling and problem-solving techniques overall (15 marks).
  • Criteria 2: Demonstrating the ability to select and use proper methodologies to analyse and interpret different scenarios with evidence (75 marks).
  • (15 marks for Question a, and 10 marks each for other questions).
  • Criteria 3: Well-structured and logical discussion. Overall clarity and presentation of the report (10marks).

(Please refer to the grade descriptor on Blackboard for details.)

Nature of Assessment: This is a SUMMATIVE ASSESSMENT. See ‘Weighting’ section above for the percentagethat this assignment counts towards your final module mark.

Word Limit: +/-10% either side of the word count (see above) is deemed to be acceptable. Any text that exceeds an additional 10% will not attract any marks. The relevant word count includes items such as cover page, executive summary, title page, table of contents, tables, figures, in-text citations and section headings, if used.The relevant word count excludes your list of references and any appendices at the end of your courseworksubmission.

You should always include the word count (from Microsoft Word, not Turnitin), at the end of your courseworksubmission, before your list of references.

Title/Cover Page: You must include a title/ cover page that includes: your Student ID, Module Code, Assignment Title, Word Count. This assignment will be marked anonymously, please ensure that your name does not appearon any part of your assignment.

References: You should use the Harvard style to reference your assignment. The library provide guidance onhow to reference in the Harvard style and this is available from: http://library.soton.ac.uk/sash/referencing

Submission Deadline: Please note that the submission deadline for Southampton Business School is 16.00 for ALL assessments.

Turnitin Submission: The assignment MUST be submitted electronically via Turnitin, which is accessed via the individual module on Blackboard. Further guidance on submitting assignments is available on the Blackboard support pages.

It is important that you allow enough time prior to the submission deadline to ensure your submission isprocessed on time as all late submissions are subject to a late penalty. We would recommend you allow 30 minutes to upload your work and check the submission has been processed and is correct. Please make sure you submit to the correct assignment link.

Email submission receipts are not currently supported with Turnitin Feedback Studio LTI integrations, however following a submission, students are presented with a banner within their assignment dashboard that provides a link to download a submission receipt. You can also access your assignment dashboard at any time to download a copy of the submission receipt using the receipt icon. It is vital that you make a note of your Submission ID (Digital Receipt Number). This is a unique receipt number for your submission, and is proof of successful submission. You may be required to provide this number at a later date. We recommend that you take a screenshot of this page, or note the number down on a piece of paper.

The last submission prior to the deadline will be treated as the final submission and will be the copy that is assessed by the marker.

It is your responsibility to ensure that the version received by the deadline is the final version, resubmissions after the deadline will not be accepted in any circumstances.

Important: If you have any problems during the submission process you should contact ServiceLine immediately by email at [email protected] or by phone on +44 (0)23 8059 5656.

Late Penalties: Further information on penalties for work submitted after the deadline can be found here.

Special Considerations: If you believe that illness or other circumstances have adversely affected your academicperformance, information regarding the regulations governing Special Considerations can be accessed via the Governance and Policies landing pages: Regulations Governing Special Considerations (including Deadline Extension Requests) for all Taught Programmes and Taught Assessed Components of Research Degrees 2023-24 | University of Southampton

Extension Requests: : Extension requests along with supporting evidence should be submitted to the Student Office as soon as possible before the submission date. Information regarding the regulations governing extension requests can be accessed via the Governance and Policies landing pages: Regulations Governing Special Considerations (including Deadline Extension Requests) for all Taught Programmes and Taught Assessed Components of Research Degrees 2023-24 | University of Southampton

Academic Conduct & Responsibility: Please note that you can access Academic Conduct & Responsibility Guidance for Students via the Quality Handbook: http://www.southampton.ac.uk/quality/assessment/academic_integrity.page?. Please note any suspected cases of Academic Responsibility Conduct will be notified to the Academic Conduct Officer for investigation.

In 2023/24, the most common reasons for a breach of the regulations governing Academic Responsibility Conduct on your programme were:

Breach
 How to avoid
Plagiarism – using the work, words, or ideas of another without proper acknowledgement. This includes citing work that you haven’t read.
- Always cite your sources.
- Only cite what you have read and used.
- “Direct quotes must be in quotation marks” with a page number if applicable.
- If you read about the work of another in a source, say ‘cited in’ and cite where you read it (see here for more info).
Collusion – Collaborating with others in an unauthorized way to produce academic work meant to be done independently.

- Unless permitted in a group assignment, don’t work with/alongside others.

- Don’t share your work with others.

- Ensure you are clear on where the line is. If in doubt, don’t do it.

External authorship
– Obtaining or attempting to obtain unauthorized input from another person or service for academic work, e.g GenAI

- Ensure you are clear on if you are permitted to use GenAI.

- Ensure your work is always your own.

- Never send your work to others or upload it to a website.

- Keep records of your work including notes, drafts, and reading.

Penalties for the above include mark reduction, resubmitting for a capped mark, or a ‘0’ for the
module.
If you are in any doubt, please ask.
Further learning and advice can be found in the Academic Conduct & Responsibility Toolkit, and the Library Website.

Feedback: Southampton Business School is committed to providing feedback within 4 weeks (University working days). Once the marks are released and you have received your feedback, you can meet with your Module Leader / Module Lecturer / Personal Academic Tutor to discuss the feedback within 4 weeks from the release of marks date. Any additional arrangements for feedback are listed in the Module Profile.

Student Support: Study skills and language support for Southampton Business School students is available at: http://www.sbsaob.soton.ac.uk/study-skills-and-language-support/. 

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