1. Assignment of Weights
Other methods, besides arbitrary, for weight assignment exist
There are both direct and indirect weight elicitation techniques
Source: The Engineering Design of Systems
Models and Methods
By Dennis M. Buede
(Chapter 13)

2. Alternative Weighting Methods
Direct Weight Elicitation Techniques
Rank-Order Centroid Technique
List Objectives in order from most important to least important
Use one of the following formulas for assigning weights

3. Alternative Weighting Methods
Rank Sum:
Rank Exponent :
ri is the rank of the ith objective
K is the total number of objectives
ri is the rank of the ith objective
K is the total number of objectives
z is an undefined measure of the dispersion in the weights

4. Alternative Weighting Methods
3. Rank Reciprocal:
Rank Order Centroid:
ri is the rank of the ith objective
K is the total number of objectives

5. Alternative Weighting Methods
Indirect Weight Elicitation Techniques
Trade Offs:
Objectives ranked in order of their overall swing in value
Stakeholders asked if overall swing weight of the second objective is as great as the swing from the lowest to some intermediate point of the value scale of the first objective.
The third objective is can now be compared to intermediate points on either the first or second ranked objective and so on…
Method works well when the value curves are firmly established and when the value curves are continuous

6. Alternative Weighting Methods
Analytical Hierarchy Process:
Stakeholders asked to compare objectives two at a time
Comparisons made using a numerical scale that ranges from 9 times more valuable to one ninth as valuable (an equivalent verbal scale can also be used)
If there are K objectives then K(K-1)/2 comparison questions would be asked
The responses are input into a matrix upon which an eigenvector calculation is performed
The eigenvector is normalized thus returning the determined weights

7. Alternative Weighting Methods
Balance Beam Approach (This method was used to determine the weights)
Stakeholders establish a rank order of the overall swing weights of the objectives.
A series of questions is posed beginning with “Is the overall swing in the value of the first objective (a) greater, (b) less than, or (c) equal to the overall swing in values of the second and third objectives
If answer is “less than” then the third objective is dropped and replaced by the fourth objective. (If “greater than” then the fourth objective is added to the second and third )
The goal is to establish a series of equations that define the swing weights for all of the objectives
The least valued objective is given a weight of 1 and then the stake holders are asked to assign a swing weight to the second least weighted objected then this information is used to solve the system of equations
The results are then normalized into weights with values between 0 and 1

8. Example: Bicycle Wheel
The company 322 Bikes decides to design a new rear wheel due to high failure rates with the current design.
Three representatives set out to interview potential customers and returned with that following results…

9. Example: Bicycle Wheel
Marketing Representative A:
“The most important feature that customers require is that the product must sustain wear and tear for a long period of time.”
Marketing Representative B:
“Also, our customers want a strong and affordable item.”
Marketing Representative C:
“They want a strong wheel but they also don’t want it to weight a lot.”

10. Example: Bicycle Wheel
From the customer needs, the design department of 322 Bikes reduced the customer needs into three key concepts:
Long Product Lifetime
Low Weight
Low Cost
This example will be carried out through the rest of the semester. It will be used to illustrate the use of Decision Making under Uncertainty.

11. Example: Bicycle Wheel
A good design will be judged on the performance criteria (Evaluation Measures) which are:
Product life time
Weight
Cost
First, we arrange these evaluation measures in order of importance:
Cost: Consumer are initially concerned with price.
Weight: More discerning consumer are also concerned with the weight.
Lifetime: Lifetime is important but consumers assume that the wheel will last a reasonable amount of time.

12. Example: Bicycle WheelEM
Rank Sum
Rank Exponent (dispersion=0.2)
Rank Reciprocal
Rank Order Centroid
Cost
0.50
0.37
0.55
0.61
Weight
0.33
0.34
0.27
0.28
Lifetime
0.17
0.29
0.18
0.11
The above are the relative weights calculated using the different direct weighing techniques.
Note that, in each column, the total weights add up to 1. The relative importance of each Evaluation Measure is denoted by what percentage of the whole each EM occupies. The higher the value, the more important the EM.

13. Example: Bicycle Wheel
Balance Beam Approach (Indirect Method)
System of equation are as follows:
The smallest EM, Lifetime’s weight, is set to 1.
From the equations, the other weights are chosen as follows:
Weight = 1.2
Cost = 1.5 (this means that Cost is 1.5 times as important as Lifetime.)

14. Example: Bicycle Wheel
The normalized weights are then:
Please note: All of the above methods are implemented in an Excel macro. If you are unsure of which method to use, it is easy to perform a few different weight calculations and then choose the results that best match your preferences.