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09-13-2024

Next year, our MNE plans to distribute markets to appropriate distribution hubs, such as Magna. The main goal is to minimize the total cost
Read the questions very carefully

Question 1 you need to enter tables 1 and 2 into Excel

For questions 2-3-4- 5, the data is already entered into the attached Excel file

Question 1 (4 marks):

Next year, our MNE plans to distribute markets to appropriate distribution hubs, such as Magna. The main goal is to minimize the total cost.

The company will evaluate whether seeing a basket of markets as one or two clusters is better (K- mean clustering).

This company has some constraints and will know what would change in total cost value when it runs the model based on the following assumptions:

1- Maximization of the cost

2- Minimization of the cost

3- Final cost lower than 25000

4- final cost bigger than 26000

5- We can open two distribution hubs simultaneously (Low and High capacity) but cannot increase their capacity size.

After finding the total cost, you must borrow money, say 5% interest, to cover the final cost, and this cost must be amortized over 5 years, and the inflation rate over the five years is stable (say near to 0%)

Index:

n : Number of distribution hubs

m : Number of markets

D j : Annual demand from market j

K i : Potential capacity of distribution hub I

f i : Annualized fixed cost of keeping distribution hub i open.

c ij: Cost of shipping one unit from distribution hub i to market j

Constraints

1: The demand at each market be satisfied

2: No distribution hub can supply more than its capacity 3: Each distribution hub is either open or closed

Solve the model based on simplex LP.

Please don’t forget to write the details of the model

Ci: Market characteristic

E to F: Market name

Table 1:

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

C1

40

40

40

40

40

40

40

40

40

40

40

40

40

40

40

C2

1

5

8

9

5

5

5

9

9

9

9

9

55

36

9

C3

1

5

8

7

5

5

5

7

7

7

7

7

5

9

9

C4

1

5

8

7

12

15

19

22

22

26

29

5

33

36

9

C5

1

5

8

5

5

5

5

5

5

5

5

5

5

5

9

C6

1

5

8

3

3

3

5

3

5

5

5

3

5

5

9

C7

1

5

8

3

12

15

19

3

22

26

29

5

36

36

9

C8

1

1

1

1

1

1

5

1

5

5

1

1

36

36

9

C9

-1

-1

-1

1

-1

-1

5

-1

5

5

-1

-1

36

36

9

C10

1

5

8

-1

12

15

19

-3

22

26

29

-1

33

36

9

Table 2:

A to D: Distribution hub location

Inputs -cost, capacities, demands

Market location- cost of shipping per1000000units

Fixed

Low

Fixed

High

Distribution Hub location

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

Cost($)

Capacity

Cost($)

Capacity

A

81

20

117

117

20

117

20

117

117

20

117

117

20

117

117

500

5

8900

30

B

117

20

102

102

20

102

20

102

1019

20

102

102

20

102

102

400

10

566200

30

C

102

20

20

115

115

115

115

20

115

115

20

115

115

20

115

300

6

56620

30

D

115

20

20

12

12

12

12

20

12

12

20

12

12

20

8500

200

10

12589

30

Demand

12

2

3

5

6

7

10

11

5

9

8

8

1

0

0

Question 2 (4 marks):

K-means

You are an analyst at a market research company. Your task is to help a retail company analyze customer data for better market segmentation and targeted marketing. You have received a dataset containing customer information, with each row representing a customer. Please use the K-means clustering algorithm to classify the customers in Excel. You need to complete the following steps and answer the related questions.

Steps:

Standardize the Data
K-means Clustering Analysis:
Set K=2 and perform K-means clustering on the customers.
Assign each customer to the corresponding cluster and mark the clustering results in Excel. You can use either Euclidean distance or Manhattan distance.
Result Analysis: Based on the clustering results, briefly describe the characteristics of each cluster (2-3 sentences).
Please select customers 1 and 4 as Center 1 and Center 2.
Question 3 (4 marks):

KNN

You have received a dataset containing customer information, with each row representing a customer. The best approach is to use the K-Nearest Neighbors (KNN) algorithm to predict customers` loyalty in the test set (high or low) based on their purchasing behavior. Compare the predicted "loyalty" with the actual "loyalty" in the test set and calculate the classification accuracy. Finally, please explain how we can improve the accuracy.

Requirements:

Customers with the most recent purchase time less than 30 days are classified as "high loyalty," while other customers are classified as "low loyalty."
The data needs to be standardized.
K=3
Distance: You can use Manhattan distance or Euclidean distance
Question 4 (4 marks):

Naive Bayes

Please use the naive Bayes algorithm in Excel to predict whether customers in the test set will buy the product and calculate the accuracy. Finally, please explain how we can improve the accuracy.

Please be informed:

When you Calculate Posterior Probability, the calculation of denominator P(features) can be skipped because, in the same customer, the denominator will be the same; we only need to compare the numerator and choose the higher probability.
Question 5 (4 marks):

Logistic Regression

Please Use logistic regression models to predict whether users in the test set will buy the product and calculate the accuracy.

Requirements:

Job

Job Code

Student, retired

0

Engineer, Teacher

1

Manager

2

Submission Requirements:

Each model should have one Excel file containing the formula, data preprocessing, model algorithm process, and results. Ensure the data processing and analysis steps are well-documented in the Excel file for review and grading. The report should be concise and logically clear and include necessary charts and explanations.

Question 6 (4 marks):

Please criticize and try to develop the following model:

Question 7 (3 marks):

Show mathematically that a monopolist always sets its price above marginal cost and bring one example from Canada.

Question 8 (3 marks):

Delta Company, a U.S. MNC, is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR10,000. The annual cash flows over the five-year economic life of the project in ZAR are estimated to be 3,000, 4,000, 5,000, 6,000, and 7,000. The parent firm’s capital cost in dollars is 9.5 percent. Long-run inflation is forecasted to be 3 percent annually in the United States and 7 percent in South Africa. The current spot foreign exchange rate is ZAR/USD = 3.75. Determine the NPV for the project in USD by:

Calculate the NPV in ZAR using the ZAR equivalent cost of capital according to the Fisher effect and then convert it to USD at the current spot rate.
Convert all cash flows from ZAR to USD at purchasing power parity forecasted exchange rates and then calculate the NPV at the dollar cost of capital.
Are the two-dollar NPVs different or the same? Explain.
What is the NPV in dollars if the actual pattern of ZAR/USD exchange rates is: S (0) = 3.75, S (1) = 5.7, S (2) = 6.7, S (3) = 7.2, S (4) = 7.7 and S (5) = 8.2?

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