Question 1
The following time series shows the sales of a retailer over the past 15 weeks.
Week Sales ($)
1 1,123
2 1,157
3 1,138
4 1,120
5 1,130
6 1,132
7 1,188
8 1,151
9 1,129
10 1,118
11 1,125
12 1,147
13 1,162
14 1,190
15 1,137
a) Construct a time series plot and discuss the type of pattern exists in the data.
b) Use α=0.3 to develop the exponential smoothing values for the time series and compute the forecast of demand for the week 16.
c) Use trial and error to find a value of the exponential smoothing coefficient α among possible values of 0.05, 0.1, 0.2, 0.21, 0.3, 0.4, and 0.5 that results in a relatively small mean squared error (MSE).
[3+3+3=9 marks]
Question 2
Robin Tires, Inc. makes two types of tires, one for SUVs and the other for Hatchbacks. The firm has the following limits—500 hours for production, 250 hours for packaging, and 150 hours for shipping. The times required per tire type is given in the following table.
Type Production Hours Packaging Shipping Profit/Tire
SUV Tires 2 1.5 1 $22
Hatchback tires 1.5 1 0.5 $12
Assume that the company is interested in maximizing the total profit contribution. Use Excel Solver to find the optimal solution and complete the following tasks:
a) Formulate this profit-maximization problem by describing the decision variables, constraints, and objective function.
b) Construct a spreadsheet model in Excel and find the optimal hours of production time that will be scheduled in each department.
c) What is the slack time in each department? Discuss your answers. (Word limit: 150)
d) Perform the sensitivity analysis and find the change in profit if one more hour is available for packaging. Discuss your findings. (Word limit: 150)
e) Similar to task d), what is the change in profit if one more hour is available for shipping? Discuss your findings. (Word limit: 150)
[3+4+3+3+3=16 marks]
Question 3
You are required to formulate a research problem in a field and use multiple linear regression technique to model the chosen problem. The potential fields are relevant to, but are not limited to, the following:
• Logistics management
• Supply chain management
• Warehousing management
• International trade
• Transport management
• Business policy and regulations
Analyse the chosen problem through completing the following tasks:
a) Clearly state the formulated research problem and explain its background and importance. (Word limit: 100)
b) Determine the potential dependent and independent variables (at least one categorical and one quantitative independent variables). Justify the choice of variables. (Word limit: 100)
c) Collect real data for the chosen variables with the minimum sample size of 30 and perform the multiple linear regression model in Excel.
d) Interpret the estimation result in terms of R^2, F-test, and individual t-tests.
[2+3+2+3=10 marks]
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