Chapter 2, Problem 12P

Summary Introduction

To determine: The range of values for ‘w’ such that Company C is a recommended outsourcing provider using factor rating method.

Introduction:

Factor-rating method:

The factor-rating method is a quantitative approach to make a decision from various alternatives such that the decision is beneficial to the firm involved. This method is utilized to decide on new layout, new locations, best supplier, outsourcing providers etc.

Answer to Problem 12P

Company C is recommended for all values of w such that 1 ≤ w ≤ 25.

Explanation of Solution

Given information:

		Ratings of Outsource providers
Factor	Weight	A	B	C	D
Labor	W	5	4	3	5
Quality Procedures	30	2	3	5	1
Logistics System	5	3	4	3	5
Price	25	5	3	4	4
Trustworthiness	5	3	2	3	5
Technology in place	15	2	5	4	4
Management team	15	5	4	2	1

Weights or an scale = 1 - 30

Formula to calculate weighted rating:

$\text{Weighted Rating = Importance Weight × rating}$

Formula to calculate Total weighted rating:

$\text{Total weighted rating = }{\displaystyle \sum \text{Individual}\text{weighted rating}}$

Calculation for A:

Calculation of weighted rating:

The weighted rating is calculated by multiplying the importance weighted with individual rating.

Labor:

$\begin{array}{c}\text{Labor = w }\times \text{ 5}\\ \text{= 5w}\end{array}$

The weighted rating for Labor is 5w.

Quality procedures:

$\begin{array}{c}\text{Quality procedures = 30 }\times \text{ 2}\\ \text{= 60}\end{array}$

The weighted rating for Quality procedures is 60.

Logistics System:

$\begin{array}{c}\text{Logistiscs System = 5 }\times \text{ 3}\\ \text{= 15}\end{array}$

The weighted rating for Logistics System is 15.

Price:

$\begin{array}{c}\text{Price = 25 }\times \text{ 5}\\ \text{= 125}\end{array}$

The weighted rating for Price is 125.

Trustworthiness:

$\begin{array}{c}\text{Trustworthiness = 5 }\times \text{ 3}\\ \text{= 15}\end{array}$

The weighted rating for Trustworthiness is 15.

Technology in place:

$\begin{array}{c}\text{Technology in place = 15 }\times \text{ 2}\\ \text{= 30}\end{array}$

The weighted rating for Technology in place is 30.

Management Team:

$\begin{array}{c}\text{Management team = 15 }\times \text{ 5}\\ \text{= 75}\end{array}$

The weighted rating for Management Team is 75.

Calculation of total weighted rating:

The total weighted rating is calculated by the summation of the individual weighted ratings.

$\begin{array}{c}\text{Total weighted rating = 5w + 60 + 15 + 125 + 15 + 30 + 75}\\ \text{= 5w + 320}\end{array}$

The total weighted rating for A is 5w + 320.

Calculation for B:

Calculation of weighted rating:

The weighted rating is calculated by multiplying the importance weighted with individual rating.

Labor:

$\begin{array}{c}\text{Labor = w }\times \text{ 4}\\ \text{= 4w}\end{array}$

The weighted rating for Labor is 4w.

Quality procedures:

$\begin{array}{c}\text{Quality procedures = 30 }\times \text{ 3}\\ \text{= 90}\end{array}$

The weighted rating for Quality procedures is 90.

Logistics System:

$\begin{array}{c}\text{Logistiscs System = 5 }\times \text{ 4}\\ \text{= 20}\end{array}$

The weighted rating for Logistics System is 20.

Price:

$\begin{array}{c}\text{Price = 25 }\times \text{ 3}\\ \text{= 75}\end{array}$

The weighted rating for Price is 75.

Trustworthiness:

$\begin{array}{c}\text{Trustworthiness = 5 }\times \text{ 2}\\ \text{= 10}\end{array}$

The weighted rating for Trustworthiness is 10.

Technology in place:

$\begin{array}{c}\text{Technology in place = 15 }\times \text{ 5}\\ \text{= 75}\end{array}$

The weighted rating for Technology in place is 75.

Management Team:

$\begin{array}{c}\text{Management team = 15 }\times \text{ 4}\\ \text{= 60}\end{array}$

The weighted rating for Management Team is 60.

Calculation of total weighted rating:

The total weighted rating is calculated by the summation of the individual weighted ratings.

$\begin{array}{c}\text{Total weighted rating = 4w + 90 + 20 + 75 + 10 + 75 + 60}\\ \text{= 4w + 330}\end{array}$

The total weighted rating for B is 4w + 330.

Calculation for C:

Calculation of weighted rating:

The weighted rating is calculated by multiplying the importance weighted with individual rating.

Labor:

$\begin{array}{c}\text{Labor = w }\times \text{ 3}\\ \text{= 3w}\end{array}$

The weighted rating for Labor is 3w.

Quality procedures:

$\begin{array}{c}\text{Quality procedures = 30 }\times \text{ 5}\\ \text{= 150}\end{array}$

The weighted rating for Quality procedures is 150.

Logistics System:

$\begin{array}{c}\text{Logistiscs System = 5 }\times \text{ 3}\\ \text{= 15}\end{array}$

The weighted rating for Logistics System is 15.

Price:

$\begin{array}{c}\text{Price = 25 }\times \text{ 4}\\ \text{= 100}\end{array}$

The weighted rating for Price is 100.

Trustworthiness:

$\begin{array}{c}\text{Trustworthiness = 5 }\times \text{ 3}\\ \text{= 15}\end{array}$

The weighted rating for Trustworthiness is 15.

Technology in place:

$\begin{array}{c}\text{Technology in place = 15 }\times \text{ 4}\\ \text{= 60}\end{array}$

The weighted rating for Technology in place is 60.

Management Team:

$\begin{array}{c}\text{Management team = 15 }\times \text{ 2}\\ \text{= 30}\end{array}$

The weighted rating for Management Team is 30.

Calculation of total weighted rating:

The total weighted rating is calculated by the summation of the individual weighted ratings.

$\begin{array}{c}\text{Total weighted rating = 3w + 150 + 15 + 100 + 15 + 60 + 30}\\ \text{= 3w + 370}\end{array}$

The total weighted rating for C is 3w + 370.

Calculation for D:

Calculation of weighted rating:

The weighted rating is calculated by multiplying the importance weighted with individual rating.

Labor:

$\begin{array}{c}\text{Labor = w }\times \text{ 5}\\ \text{= 5w}\end{array}$

The weighted rating for Labor is 5w.

Quality procedures:

$\begin{array}{c}\text{Quality procedures = 30 }\times \text{ 1}\\ \text{= 30}\end{array}$

The weighted rating for Quality procedures is 30.

Logistics System:

$\begin{array}{c}\text{Logistiscs System = 5 }\times \text{ 5}\\ \text{= 25}\end{array}$

The weighted rating for Logistics System is 25.

Price:

$\begin{array}{c}\text{Price = 25 }\times \text{ 4}\\ \text{= 100}\end{array}$

The weighted rating for Price is 100.

Trustworthiness:

$\begin{array}{c}\text{Trustworthiness = 5 }\times \text{ 5}\\ \text{= 25}\end{array}$

The weighted rating for Trustworthiness is 25.

Technology in place:

$\begin{array}{c}\text{Technology in place = 15 }\times \text{ 4}\\ \text{= 60}\end{array}$

The weighted rating for Technology in place is 60.

Management Team:

$\begin{array}{c}\text{Management team = 15 }\times \text{ 1}\\ \text{= 15}\end{array}$

The weighted rating for Management Team is 15.

Calculation of total weighted rating:

The total weighted rating is calculated by the summation of the individual weighted ratings.

$\begin{array}{c}\text{Total weighted rating = 5w + 30 + 25 + 100 + 25 + 60 + 15}\\ \text{= 5w + 255}\end{array}$

The total weighted rating for D is 5w + 255.

Calculation of range of values for w:

The range of values is calculated by equating the total weighted rating of C with all the other outsourcing providers.

Equating C with A:

$\begin{array}{c}\text{3w + 370 }\ge \text{ 5w + 320}\\ \text{370 - 320 }\ge \text{ 5w - 3w}\\ \text{50 }\ge \text{ 2w}\\ \text{25 }\ge \text{ w}\end{array}$ (1)

Equating C with B:

$\begin{array}{c}\text{3w + 370 }\ge \text{ 4w + 330}\\ \text{370 - 330 }\ge \text{ 4w - 3w}\\ \text{40 }\ge \text{ w}\end{array}$ (2)

Equating C with D:

$\begin{array}{c}\text{3w + 370 }\ge \text{ 5w + 255}\\ \text{370 - 255 }\ge \text{ 5w - 3w}\\ \text{115 }\ge \text{ 2w}\\ \text{57}\text{.5 }\ge \text{ w}\end{array}$ (3)

The weights are scaled from 1 – 30 as given in the question. The value of w can only be in the range of 1 to 30. From (1), (2), and (3) the range of ‘w’ so that C is the best outsourcing provider is w ≤ 25. It means that ‘w’ can be assigned a value starting from 1 to 25.

Company C is recommended for all values of ‘w’ such that 1 ≤ w ≤ 25.