**This section will cover learning outcomes 1, 2 & 3.**

- Evaluate the necessity for quantitative analysis in Supply Chain and Logistics operations
- Apply appropriate theory and methods to a Supply chain scenario to aid decision making improvements.
- Critically evaluate the results of such an analysis and new knowledge learnt in the business context.

**Coursework scenario**

Random Computers is a wholesale firm that distributes computers to customers. The arrival of Sam Snear the new Managing Director has brought a new business strategy based on efficiency and reduction of costs.

**Task 1: (20 marks)**

Previously Random Computers had maintained ample inventories of computers in the warehouse to fulfil orders immediately. So rough forecasts of demand was adequate to make decisions about stock replenishment. Scientific management is to be used to reduce inventory levels and minimise total inventory costs.

The logistics Manager Jo Branding has developed a system of forecasting based on statistical forecasting that considers seasonal effects. The system is to generate three sets of forecasts:

- Moving average method
- Exponential smoothing
- Exponential smoothing with trend.

Jo will base her monthly inventory levels on the monthly sales of laptops over the past 3 years see fig1.

Past Sales | ||||

Month | Year 1 | Year 2 | Year3 | Forecast |

January | 372 | 337 | 358 | |

February | 359 | 361 | 376 | |

March | 385 | 364 | 403 | |

April | 388 | 416 | 434 | |

May | 432 | 443 | 451 | |

June | 476 | 502 | 489 | |

July | 440 | 435 | 453 | |

August | 491 | 512 | 538 | |

September | 385 | 370 | 339 | |

October | 332 | 321 | 355 | |

November | 587 | 649 | 614 | |

December | 363 | 535 | 557 |

Figure 1: The monthly sales of laptops over the past 3 years

- You will need determine the seasonal factors for each of the 12 months based on past sales. Use these seasonal factors to apply a moving average based method to forecast monthly sales for each month. You will need to choose and justify how many months of previous data for your monthly moving average.

**(4 marks)**

- Apply the exponential smoothing method to forecast the monthly sales for each month. You must decide and justify the initial estimate and the value of the smoothing constant (a).

**(4 marks)**

- Using the seasonal effect apply exponential smoothing with trend to forecast monthly sales. Use the initial estimates and (a) value that you chose for section (b). Also use zero for the trend and suggest a value for (b).

**(4 marks)**

- Compare and comment on your MAD and MSE values for sections (a), (b) and (c).

**(2 marks)**

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- Based on these results how should Jo determine her inventory levels (i.e. estimate the reorder level and reorder quantity) if the maximum lead time-time is 2 weeks and the minimum lead time is 1 week. The capacity of the warehouse is 800 items

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**(6 marks)**

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** Total (20 Marks)**

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**Task 2: (20 marks) **

Random Computers used to order laptops from the manufacturer in bulk and store them at the distribution centre until orders arrived from customers. Sam Sneer wants to reduce the storage costs and make the operation more efficient by reducing the order size down from the current policy of placing a monthly order of approximately 400 laptops. Random computers has notified Jo that the warehouse rent is £30 000, the annual delivery charges are £96 000, the wages for the purchase staff are £192 000 and the warehouse stores are £144 000. Purchase department overheads are £48 000 and the cost of warehouse insurance is currently £10 000.

- Calculate the cost of placing an order.
**(2 marks)** - Calculate the cost of holding a laptop.
**(2 marks)** - Calculate the total annual ordering cost when ordering in quantities of 100 laptops
**(2 marks)** - Calculate the total annual holding cost when ordering in quantities of 100 laptops
**(2 marks)** - Calculate the current total annual inventory cost
**(2 marks)** - Calculate the Economic Order Quantity EOQ
**(2 marks)** - Critically discuss how much saving can be made using EOQ and advise what organisational changes you would advise when implementing the change to ordering EOQ amount.

**(8 marks)**

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**Task 3: (20 marks)**

Random computers operate three warehouses (WH1, WH2 and WH3) which supply to five wholesalers (WS1,WS2,WS3,WS4 and WS5) which in turn supply ten customers (C1-C10).

The cost of distribution from warehouses to wholesalers is given in figure 2 and the cost of distribution from wholesalers to customers is given figure 3.

WS1 | WS2 | WS3 | WS4 | WS5 | |

WH1 | 10 | 9 | 13 | – | – |

WH2 | 11 | 12 | 12 | 12 | 14 |

WH3 | – | – | 11 | 12 | 13 |

Figure 2: The cost of distribution from warehouses to wholesalers

C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 | |

WS1 | 7 | 9 | 10 | 8 | 10 | |||||

WS2 | 8 | 8 | 10 | 8 | 9 | 7 | ||||

WS3 | 9 | 9 | 8 | 8 | 9 | 11 | ||||

WS4 | 9 | 9 | 9 | 9 | 12 | 11 | ||||

WS5 | 8 | 8 | 9 | 10 | 9 |

Figure 3. The cost of distribution from wholesalers to customers

- What is the minimum cost of distribution for the whole supply chain for the month of March 2020 if the stock level in WH1 is 150, WH2 is 150 and WH3 is 100 and the customer orders are given in Figure 4.

Order | C1 | C2 | C3 | C4 | C5 | C6 | C7 | C8 | C9 | C10 |

35 | 45 | 38 | 40 | 42 | 58 | 41 | 40 | 39 | 22 |

Figure 4. Number of customer orders.

**(6 marks)**

- Analysis the minimum cost for March 2020 and recommend to Sam Sneer which wholesaler should be dropped to minimise the cost of the whole supply chain. What increase in cost would be incurred? Screenshot your Excel spreadsheet and annotate to justify your solution.

**(6 marks)**

- Sam criticises Jo because there is capacity of 50 units on all routes due to haulage limitations. Jo now alters her solution in Q3(a) by making the maximum amount to be shipped down each route a maximum of 50 units. What is the minimum total supply chain cost now? Does this affect your discussion to drop one of the wholesalers, discuss.

**(8 marks)**

**Task 4: (20 marks) **

Sam Sneer has analysed customer trends and thinks there is a gap in the market for a light weight slim laptop. There are two options for production. One is to outsource production to Acorn computers sharing the production facilities they have. If sales are moderate this will work out well for Acorn as it will utilise spare capacity at the plant. However if sales are strong Random Computers are considering opening their own production facility which would satisfy the largest sales projection. If sales were only moderate the new plant would be under-utilised and therefore less efficient.

The new design is unproven and sales are therefore hard to predict. Random computers predicts there is a 70% chance of strong sales giving annual sales of 9 000 and 30% chance of moderate sales giving annual sales 4 500. The revenue for a slim laptop would be £200 per laptop sold. Production costs for the laptop are given in figure 5.

Moderate Sales | Strong Sales | |

Sharing acorn facilities | 100 | 150 |

Randon’s own factory | 140 | 120 |

Figure 5 Expected cost of production per laptop (£’s)

The annual cost of production at Acorns plant would be £ 100 000. The cost of running their own plant would be £ 200 000.

- Construct a decision tree to determine which production method would optimise the expected annual profit.
**(8 marks)**

The sales of the new design is very uncertain so Random computers have decided to conduct a marketing survey to predict the likelihood of strong sales. The survey will give a percentage possibility of a positive or a negative survey. Using past data laptops, Random Computers know that strong sales occurred when 75% of the customer surveys gave a positive response and 25% giving a negative response. Moderate sales occurred when 20% of customer surveys were positive and 80% for moderate sales. Use Bayes formula to calculate posterior probabilities and redraw the decision tree. What is the expected annual profit ignoring the cost of the survey? **(8 marks)**

- Is it worthwhile conducting a survey? How much would it cost to make it worthwhile?
**(4 marks)**

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**Task 5: (20 marks)**