Task 1. Susan’s Suggestion   After careful examination of the company’s financial records, Susan suggests that the company requires extra capacity to increase the volume of production. In order to increase the capacity, she has investigated two potential options. The first option is to build an extension to its current production plant in Wales, and the second option is to build an extra production plant in Hungary. She has evaluated the options and calculated that the profitability will improve by £650,000 if its current production plant in Wales is extended, and if they build a new factory in Hungary, the profitability will improve by £750,000. However, if the company does not get planning permission before 2018, and therefore, if extension/construction is delayed, the company will face a financial loss due to contractual production commitments. A net loss of £350,000 is estimated if the construction in Hungary gets delayed, and the company will lose some £250,000 if the extension in Wales is delayed.   Historical data shows that with 85% chance the Welsh Government will issue planning permission before 2018. In terms of the situation in Hungary, the oversea research teams told Susan that the local government in Hungary is getting concerned about the impact of foreign manufacturing firms on its local community, and as a result, only 10% of foreign companies have received their planning permission within a year. However, the research team have found that if the company promises to contribute to the development of the local community, the process can be sped up and, with 80% chance, planning permission will be issued within a year. So far the financial value of the contribution is estimated around £20,000.  

  • Construct a decision tree for this problem. Be sure to clearly mark the decisions, events, probabilities, and payoffs on the tree
  • What recommendations should you give to the CEO if the company’s objective is to maximise expected monetary value (EMV)?
  • If the financial value of the contribution to the Hungarian local community is estimated around £10,000 instead, how would this affect the optimal strategy? What is the most money the company should be willing to promise to the local government in Hungary?
    Task 2. Jane’s Suggestion   The marketing team of Dragon Wool Ltd conducted a customer survey last year in order to find new business opportunities. The marketing team asked their customers if there were other product ranges which customers would like to see developed, and how much they were willing to pay for those products. According to the survey, two potential items were suggested – a shawl and a jumper. The survey also revealed that customers care more about the design when they purchase a shawl, whilst quality is the key decision point when choosing a jumper. The estimated selling price for a shawl and a jumper is around £35 and £30 respectively.   With this result, Jane had a meeting with the design and production team and investigated the manufacturing options for both items. Detailed information is listed below.   Raw materials Dragon Wool uses both natural fibres, such as wool and silk, and synthetic fibres, such as polyacrylic and polyester, to make their woollen products. In order to produce a single shawl, 2000 meters of yarn is required, mixing 800 meters of natural fibres and 1200 meters of synthetic fibres. Production of a single jumper requires 1600 meters of yarn, combining 980 meters of natural fibres and 620 meters of synthetic fibres. The company can order maximum 52,000 meters of natural fibre yarn and 62,000 meters of synthetic fibre yarn from their suppliers per week when production for both items starts. Natural fibre yarn costs £0.02 per meter, and synthetic fibre yarn costs £0.01 per meter.   Production process Technically the manufacture of shawls and jumpers shares the same production process and machines. However, due to the design-focused approach, a shawl requires longer time in the knitting section, which takes around 4 hours, compared to a jumper, which takes around 1 hour. On the other hand, a jumper takes longer time to wash and dry due to the high portion of nature fibres. In the washing and drying section, a jumper takes 3 hours and a shawl takes 1.2 hours. Using the capacity of the company, 5 people can be employed on the knitting section, and 3 on the washing and drying section. All employees work 40 hours each week.  
  • List all the constraints
  • Write down the equations for Profit, Cost, and Net Profit on a weekly basis
  • Draw a linear programming graph to represent this problem
  • Assume that Dragon Wool wants to maximise its net profit. Build a linear programming model in Excel spreadsheet that is self-explanatory to the CEO and the managers of Dragon Wool. Solve the problem using ‘Solver’ in the Data section. Provide copies of the Answer Report and Sensitivity Report (tables only)
  • How many shawls and jumpers should Dragon Wool produce per week? What are the total net profit, profit and costs in this case?
  • If the company builds a new factory in Hungary, the company can have extra yarn supply from local producers. Assuming that the supply increases to 60,000 meters (natural fibres) and 70,000 meters (synthetic fibres), how does it affect the final combination of the two products? What is the new net profit per week?
  • Compare your original answer to the question 6 answer, explain the concept of binding and not binding constraints
    Task 3. Mark’s suggestion   The manufacture of the company’s woollen products consists of the following production process.  
Activity Section Description
A Yarn Inventory Check Checking the inventory level of yarn in the warehouse
B Design Producing design charts for products
C Winding Winding and coning the yarns by using the winding machine
D Knitting Knitting the panel according to design charts
E Linking Linking the different knitted panels to produce a complete product
F Inspection Light check inspection of the final products. Defects are marked and sent to the Mending section. Otherwise, are passed to the Washing/ Drying section
G Mending Mending or repairing defects
H Washing/Drying Washing and drying the finished woollen products. Natural fibre types take longer time to dry than synthetic fibre types
I Packaging Labelling, attaching price tag, folding, packaging, ready to sell
  After inspecting the production process for 3 months, Mark evaluated the average normal time and cost to produce woollen products and the crash time and cost to improve the efficiency of the process. Results are listed below.  
Activity Immediate predecessors Normal Time (hours) Normal Cost (£) Crash Time (hours) Crash Cost (£)
A None 2 10 1.5 14
B None 2.5 30 2 36
C A 2 15 1.8 18
D B, C 4 36 2 52
E D 2 22 1.5 28
F E 3 25 3 25
G F 1.5 18 1.5 18
H F, G 3.5 40 2.5 49
I H 2 28 2 28
  • Using this information, draw a network diagram of this process
  • Identify the critical path, and calculate the normal completion hours
  • There are indirect costs of £10 per hour. Calculate the total costs to complete the process
  • Mark believes that if the process can be completed within 18 hours, the total production costs would decrease. By successively crashing activities, find the activity (or activities) that can crash and calculate the total minimum cost
  • Susan, the Head of Finance, told Mark that unless there is more than 10% cost reduction, it is not worth crashing the activities. Based on your answer in question 4, is it worth crashing activities?
  • There exists the possibility of upgrading the washing and drying machine, which would reduce the normal cost and time to £25 and 0.5 hours respectively. Following the same advice from Susan above, is it worth getting it upgraded?
    Task 4. Summary   Finally, summarise the case, discussing the potential risks of each suggestion, and conclude your report with suitable advice to the CEO of Dragon Wool Ltd.]]>

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