Reference no: EM132699941
The file named "StatAssignmentData.xlsx" includes the delivery data captured by a major online grocery retailer through their loyalty programme as well as the results of a home delivery satisfaction survey using a sample of 6,491 orders of the online grocery retailer in the first five days of January 2019. In particular, the dataset contains information about the following variables:
• Customer satisfaction score (A value between 1 and 6 with 1 being not at all satisfied and 6 being fully satisfied. The score is calculated based the average rating of multiple satisfaction questions.)
• Delivery tracking (A variable consisting of "available" where the delivery can be tracked and "Not available" where the delivery cannot be tracked)
• Number of Items in the basket (Number of items that were included in the order)
• % of perishable items in the basket ((Total value of perishable items that were included in the order/Total value of the order) x 100)
• Customer's sensitivity to delivery cost (A value between 0 and 5 with 0 being not at all sensitive and 5 being highly sensitive)
• Customer engagement score (The sum of the number of clicks on different delivery service functions between the order and the delivery time)
• Number of previous online orders (Over the last year)
• The time between order and delivery of the last order (in hours)
• The delivery delay of more than 24 hours (A variable consisting of "no" and "yes")
The director of supply chain is preparing a report for the board and has asked you to analyse the data and derive insights and conclusions.
Probability Distributions and Confidence Interval Building
1. What is the probability that for at least 50 out of 100 randomly selected orders tracking was available? Use the sample data of 6,491 orders to calculate the probability of success.
2. Construct a 99% confidence interval for the true average of customer satisfaction score. How the confidence interval would change if you reduce the confidence level?
Hypothesis Testing
3. Can the director conclude that the satisfaction score of those customers whose delivery was trackable is greater than the satisfaction scores of those whose delivery was not?
a. Conduct the appropriate test at alpha = 0.01 significance level and interpret the results
b. How confident are you with your decision?
Regression
4. The supply chain director would like to analyse the relationship of the variables in the dataset with customer delivery satisfaction score and derive a regression model.
a. Develop an appropriate multiple regression model to explain the variability in customer satisfaction scores. Assume alpha = 0.01
b. Interpret the regression results.
c. Discuss the outliers and normality assumptions and comment on the suitability of a multiple linear regression model
d. How can you potentially improve the model?
Application of Inferential Statistics
5. We frequently rely on inferential statistics to inform operational, tactical, and strategic decisions in many areas of supply chain management. Choose two examples of the application of inferential statistics in procurement, logistics and supply chain management. Briefly discuss the context, relevant managerial problem and elaborate how the knowledge of inferential statistics may aid the decision making in each example. Please make your response in no more than 150 words per example [8 marks; 4 marks per example]
Linear Programming
6. Cranfield Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times in minutes required on each machine for each component are as follows:
|
Component
|
Shaper
|
Grinder
|
|
1
|
3
|
4
|
|
2
|
2
|
5
|
|
3
|
2
|
2
|
The shaper is available for 120 hours and the grinder is available for 110 hours. No more than 200 units of Component 3 can be sold, but up to 1,000 units of each of the other components can be sold. The company already has orders for 600 units of Component 1 that must be satisfied. The profit contributions of Components 1-3 are
£16, £12, and £18 respectively.
a. Formulate and solve for the recommended production quantities.
b. What are the objective function coefficient ranges for the three components? Interpret these ranges for the company management.
c. What are the right-hand-side ranges? Interpret these ranges for company management.
d. If more time could be made available on the grinder, how much would it be worth?
e. If 500 more units of Component 3 could be sold by reducing the sales price by £4, should the company reduce the price? Explain.
f. In a typical product mix model where a company must decide how much of each product to produce, discuss possible situations where there may not be any feasible solution. Could this be realistic? If you had such a situation in your company, how might you proceed?
Decision Models
7. Cranfield Manufacturing Ltd must decide to manufacture a component part at its Milton Keynes plant or purchase the component part from a supplier based in Northampton. The resulting profit is dependent upon the demand for the product. The following payoff table with three states of nature for the demand (low, medium, high) shows the projected profit in thousands of pounds:
|
Decision Alternative
|
Low Demand (s1)
|
Medium Demand (s2)
|
High Demand (s3)
|
|
Manufacture (d1)
|
-20
|
40
|
100
|
|
Purchase (d2)
|
10
|
45
|
70
|
The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30.
a. Use a decision tree to recommend Cranfield Manufacturing a decision.
b. Use EVPI to determine whether Cranfield Manufacturing should attempt to obtain a better estimate of demand.
c. A test market study of the potential demand for the product is expected to report either favourable (F) or unfavourable (U) result. The relevant conditional probabilities are as follows:
P(F | s1) = 0.10; P(F | s2) = 0.40; P(F | s3) = 0.60;
P(U | s1) = 0.90; P(U | s2) = 0.60; P(U | s3) = 0.40.
What is the probability that the market research report will be favourable?
d. What is Cranfield Manufacturing's optimal decision strategy assuming conducting market research is a possible course of action?
e. How much would Cranfield Manufacturing be willing to pay for market research?
f. What are some limitations of the analysis approach you have taken to address Cranfield Manufacturing's decision problem?
Style and Presentation
You will receive marks for the style and presentation of your assignment. Please pay attention to
1. Writing grammatically correctly and concisely.
2. Providing captions for your tables and figures and citing them in the text.
3. Using appropriate level of accuracy (no need for 5 figures after the decimal point. We recommend 3).
4. Presenting your assignment in a report structure so we can map your answers to the questions we have asked.
5. Citing the references you used in preparing your answers.
Attachment:- ATS Assignment.rar