# Optimisation and Decision Modelling

## COURSEWORK BRIEF:

• 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 of your report. Make sure not to exceed 2000 words (this is a MAXIMUM and not a target), excluding appendixes which should display excel models and corresponding outputs (only include the most relevant parts), etc.
• 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.
• Any . Excel Solver is the software you need to use in this coursework.

Farm Management

The Smith family has owned a 640-acre farm for several generations. However, ownership has recently passed to the next generation of Dave and his wife Ruth, who feel there is a need for a more scientific approach to manage their farm. They have called you in as a business analyst to advise them on the best way of running the farm.

The Smith family can produce a total of 4,000 person-hours’ worth of labour during the winter and spring months and 4,500 person-hours during the summer and autumn months. If they do not need all this time they can work on neighbouring farms for £5 per hour during the winter and spring months and £5.50 during the summer and autumn months.

The farm supports two types of livestock, dairy cows and hens and three types of cash crops – rape, corn and wheat. All three are cash crops, but the corn also is a feed crop for the cows and the wheat also is used for chicken feed. The crops are harvested during the late summer and autumn. During the winter months, they need to decide what mix of livestock and crops they should aim for in the coming year. Their last harvest, which was very successful, has provided them with a sum of

£21,000 which they feel they can use to buy more livestock. The cost of seed is sufficiently small to

be considered part of the routine expenses. The farm at present has 30 cows valued at £35,000 and 2,000 hens valued at £5,000. They wish to keep all this livestock and perhaps purchase more. Each cow bought would cost £2,000 and each hen would cost £3. Over a year the value of a herd of cows decreases by about 10% and the value of a flock of hens will decrease by about 25% due to aging.

Each cow requires 2 acres of land for grazing and 8 person-hours of work per month while producing an annual net cash income of £700 for the family. Hens do not require any acreage but need 0.05 person-hours a month and produce an annual net cash income of £4.50. The chicken house can accommodate a maximum of 5,000 hens and the milking parlour puts a limit of 42 on the number of cows.

For each acre of crops planted, the following table gives the number of person hours of work required in the first and second halves of the year as well as an estimate of the crops net value in either income or savings in livestock feed.

To provide feed, there should be at least 1 acre of corn for each cow and at least 0.05 acres of wheat for each hen in the next year’s flock. The Smith family estimates that they need £40,000 each year for their living expenses and the basic running of the farm. You have been hired as a business analyst to prepare a report on several issues they are seeking advice on:

1. Advise the Smith family on how many livestock they should buy and what acreage of the different crops they should plant to maximise their net wealth at the end of the next year.
2. They are interested in how much they should be willing to pay for any farmland that may become available to rent over the coming winter.
3. They are concerned that the price of cows may not stay at £2,000, but may vary between

£1,000 and £3,000. What are the strategies they need to adopt if the prices change in this range and what affect will it have on the net wealth?

• It is felt that Phil Bowman, the patriarch of the family cannot go on working much longer. This would cut their available labour to 3,000 and 3,500 hours in the winter/spring and

summer/autumn, respectively. What effect will this have on their plans, and should they seek to employ someone in his place? If so, what sort of hours and wage levels should they offer?

• A bank is offering to lend them money at a special rate of 10% to purchase more livestock beyond the £21,000 they had set aside. Should they take advantage of this?
• They could build an extension to the milking parlour at a cost of £3,000 for each extra pair of cows it can take. How large an extension, if any extension at all should be built?
• The details on the above table for crops grown reflect the situation if there are no large-scale frosts that delay the spring sowing. If there are late frosts, the resultant data would be:

The Smith family are concerned about this alternative scenario. They want to know what they should be doing if this is the situation that will arise in order to maximise their net wealth. They also want to know what their net wealth would be if they continued using the policy suggested in a) in this scenario.

• The Smith family are arguing how to deal with these two possible scenarios (a and g), which they consider to be equally likely. Dave suggests that they take the average of the statistics in the two tables and solve the model using these statistics. Ruth pointed out that though they have to decide now how many livestock to buy, they will know which scenario is occurring before they have to plant the crops and so can plant different amounts depending on the scenarios that occur. They want you to advise what they should do under these two scenarios and whether they lead to the same expected net wealth.

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 ability to select and use proper methodologies to analyse and interpret difference scenarios with evidence (75 marks).
• (12 marks for Question a, and 9 marks each for the rest of questions).

Nature of Assessment: This is a SUMMATIVE ASSESSMENT. See ‘Weighting’ section above for the percentage that 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 coursework submission.

You should always include the word count (from Microsoft Word, not Turnitin), at the end of your coursework submission, 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 appear on any part of your assignment.

References: You should use the Harvard style to reference your assignment. The library provide guidance on how to reference in the Harvard style and this is available

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 is processed 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.

You are allowed to submit your work multiple times up to the assignment deadline (for example, if you decide to make any amendments after your original submission).

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.

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 academic performance, information regarding the regulations governing Special Considerations can be accessed via the Calendar

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 Calendar

Academic Integrity Policy: Please note that you can access Academic Integrity Guidance for Students via the Quality Handbook Please note any suspected cases of Academic Integrity will be notified to the Academic Integrity Officer for investigation.

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. Please note that all marks are provisional until approved by the board of examiners.

Student Support: Study skills and language support for Southampton Business School students is available

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