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 Thursday, 11 January 2024 Word Count/Duration: 2000 Method of Submission: Electronic via Blackboard Turnitin ONLY (You are not required to submit a hard copy) (Please ensure that your name does not appear on any part of your work) Any work 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. University Working 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: Knowledge and Understanding A1~A5Subject Specific Intellectual and Research Skills B1~B2Transferable 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 with your comments on a project (Farm Management – See below) 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 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.
| Rape | Corn | Wheat | |
| Winter/spring person hours | 1.0 | 0.9 | 0.6 |
| Summer/autumn person hours | 1.4 | 1.2 | 0.7 |
| Net value | £70 | £60 | £40 |
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:
- 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.
- 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.
- 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:
| Rape | Corn | Wheat | |
| Winter/spring person hours | 1.2 | 1.1 | 0.8 |
| Summer/autumn person hours | 1.3 | 1.1 | 0.7 |
| Net value | £50 | £50 | £30 |
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.
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