   # A common approach to clustering is called multidimensional scaling (MDS). To apply MDS, we rank each pair of objects we want to cluster from least similar (higher number) to most similar (lower number). For example, in the file P08_37.xlsx, we compared the similarity of 10 banks and found banks 5 and 10 to be most similar and banks 9 and 10 to be least similar. We now assign a location in the x - y plane to each bank. The goal is to ensure that when we rank the distances between pair of banks, the ordering of these distances matches (as closely as possible) the similarity rankings of the banks. a. Constrain each bank to have an x and y coordinate between −1 and +1 and determine the “location” of each bank. ( Hint : Use Excel’s RANK function to rank the distances from smallest to largest.) b. How does this method lead to a natural clustering of banks? c. How could you determine whether you need more than two dimensions to adequately locate the banks? ### Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

#### Solutions

Chapter
Section ### Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 8, Problem 37P
Textbook Problem
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## A common approach to clustering is called multidimensional scaling (MDS). To apply MDS, we rank each pair of objects we want to cluster from least similar (higher number) to most similar (lower number). For example, in the file P08_37.xlsx, we compared the similarity of 10 banks and found banks 5 and 10 to be most similar and banks 9 and 10 to be least similar. We now assign a location in the x-y plane to each bank. The goal is to ensure that when we rank the distances between pair of banks, the ordering of these distances matches (as closely as possible) the similarity rankings of the banks.a. Constrain each bank to have an x and y coordinate between −1 and +1 and determine the “location” of each bank. (Hint: Use Excel’s RANK function to rank the distances from smallest to largest.)b. How does this method lead to a natural clustering of banks?c. How could you determine whether you need more than two dimensions to adequately locate the banks?

a)

Summary Introduction

To determine: The location of each bank.

Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).

### Explanation of Solution

Model:

Formulae to determine the model:

b)

Summary Introduction

To determine: How the method would result in natural clustering.

Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).

c)

Summary Introduction

To determine: The way to determine whether Person X need more than two dimensions while locating a bank.

Introduction: The variation between the present value of the cash outflows and the present value of the cash inflows are known as the Net Present Value (NPV).

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