Upload
jovita
View
29
Download
0
Embed Size (px)
DESCRIPTION
Job selection case. eLearning resources / MCDA team Director prof. Raimo P. Hämäläinen Helsinki University of Technology Systems Analysis Laboratory http://www.eLearning.sal.hut.fi. Contents. About the case The problem Problem structuring Preference elicitation - PowerPoint PPT Presentation
Citation preview
eLearning / MCDA
Systems Analysis LaboratoryHelsinki University of Technology
Job selection case
eLearning resources / MCDA team
Director prof. Raimo P. Hämäläinen
Helsinki University of Technology
Systems Analysis Laboratory
http://www.eLearning.sal.hut.fi
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Contents
About the case
The problem
Problem structuring
Preference elicitation
Results and sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The Job selection case
In this case value tree analysis is applied to a job selection problem.
The main purpose is to illustrate the DA process and the use of different attribute weighting techniques.
The related theory is summarized before each step. More detailed discussion on the theoretical aspects
can be found in the corresponding theory part. You are encouraged to create your own model while
following the case.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The problem
Assume that you have four job offers to choose between;
1) a place as a researcher in a governmental research institute
2) a place as a consultant in a multinational consulting firm
3) a place as a decision analyst in a large domestic firm
4) a place in a small IT firm
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Governmental Research Institute
The first offer is a place as a researcher in a Governmental Research Institute close to the city-centre, 45 minutes from your home. The head of the research department has sent you an offer letter in which he promises a starting salary of 1900€ a month with standard 37.5 weekly working hours and a permanent place in their research team. In the letter he also mentioned several training programs and courses related to the different research areas which are offered to the personnel. The job would be technically challenging, focused and and gives opportunities for further studying. As there is no continuing need for domestic travelling the Research Institute does not provide their employees with company-owned cars. However, there are likely to be conferences all over Europe where you are assumed to attend every now and then (20 travelling days a year).
The problem
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Multinational consulting firm
The second offer is from a multinational consulting firm. They have offered you a place for six months trial period, after which you could act as a junior consultant. The salary from the trial period is 2700€ per month, after which it is likely to rise to 3500€ in three years. According to the senior partner of the department, there is no reason to believe that they would not continue the work agreement after the trial period, but it is merely a matter of company’s overall employment policy and your own will. The luxurious office of the company is located in the city-centre, 50 minutes from your home, but they have customers and departments all over Europe, where you are most likely to visit continuously (160 travelling days a year). All company’s employees are young and they are expected to work hard 55 hours per week. The job would be neither highly technical nor too challenging, but it would include variable tasks and a substantial amount of management training. In the interview for the job, the senior partner also mentioned about social activities, such as golf club and courses, and company wide theme programmes which are set up to contribute employees’ overall well-being. However, one of the consultants told know that only few of them were actually involved in those activities.
The problem
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
A place as a decision analyst
The third job offer is a place as a decision analyst in a large domestic firm. The office is located in an industrial area, less than one-hour travel from your home. The salary is 2200€ per month and the working time 8 hours a day. Also, a possibility to have a company-owned car is offered. The firm has a large number of active clubs and possibilities to do sports, and even a sports centre, which offers free services for all employees. Except the familiarisation period at the beginning, the job would not require or include further training or studying. However it would be challenging and include some variability and two to three day trips to the other domestic departments (100 travelling days a year). As opposed to the other job offers you would also have an own room with a view to the sea.
The problem
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Small IT firm
The fourth offer is from a small, promising, and fast growing IT firm established two years ago. The atmosphere is relaxed and employees are young, all under 35. The job description includes various activities from several areas of the business, some training, but only a limited amount of travelling (30 travelling days a year). The activities do not offer a great challenge, but most of them seem to be interesting. The salary is 2300€ per month and they expect you to work 42,5 hours per week and overtime if needed. The office is in the city centre, close to the bus station, which is about 40 minutes travel from your home. In the interview for the job they promised you a company-owned car and a possibility to use company’s cottage close to a popular downhill skiing centre in the Alps.
The problem
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Atmosphere
As the firms differ considerably in their culture and atmosphere you decided to interview a couple of arbitrarily chosen employees from each firm. To ease the comparison of the opinions you asked the subjects to rate the atmosphere and corporate culture from 0 (poor) to 5 (very good). The results are shown in Table 1.
Table 1. Average ratings of corporate cultures and atmospheres.
The problem
Company Average ratingResearch Institute 3.2Consulting Firm 2.5Large Corporation 3.7Small IT Firm 4.5
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Salary
Table 2. Expected salaries in three years.
You have also come up with the following estimates for the expected salaryin three years time.
The problem
CompanyExpected salary in
three years / €
Research Institute 2500Consulting Firm 3500Large Corporation 2800Small IT Firm 3000
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Thinking task
How would you approach the problem? Are there ways to model the problem? What would be the factors affecting your
decision?
The problem
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Decision analytic problem structuring
Define the decision context
Generate the objectives
Identify the decision alternatives
Hierarchical organisation of the objectives
Specify the attributes
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Decision context is the setting in which the decision occurs
Use the figure to define the decision context for the Job selection problem.
· Start with the easiest.
· Proceed to more complicated areas.
· At the end, select and highlight the most important ones.
How does the nature of possible job opportunities affect the decision context?
See the “Problem structuring / Defining the decision context” section in the theory part.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example of a decision context
•DM: I am. I’m also the only person responsible for the consequences.
•Decision problem: To choose a job among the places offered.
•Decision alternatives: Large Corporation, Small IT Firm, Consulting Firm, Research Institute.
•Values: Leisure time appreciated high, career opportunities fairly important, also continuing education considered as important
•Stakeholders: Family, friends, employer, tax authorities, …
•Information sources: Offer letters, interviews for the job, friends, …
•Social context: Spouse places pressures to do shorter working days.
•Consequences of each alternative: What if alternative X were selected...
•...
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Generating objectives
List all the objectives that you find relevant Specify their meaning carefully
object direction
You may use Wish list Alternatives:
What makes the difference between the alternatives? Consequences Different perspectives
See the “Problem structuring / Identifying and generating objectives” section in the theory part.
Problem structuring
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Possible objectiveswith their descriptions
What other objectives might there be?
objective description
networkingMaximise new contacts with persons and bodies who can potentially influence your personal career opportunitites.
continuing education Maximise possibilities for continuing education.
fit with interests Maximise the match between tasks and personal interests.
tasks diversity Maximise possibilities for carrying out different tasks.
challengeMaximise the correspondence between task requirements and professional skills and opportunities for further professional growth.
working environment Maximise the positive effect of working environment.atmosphere Maximise the positive effect of corporate culture and atmosphere.
facilitiesMaximise the positive effect of facilities and physical working environment.
starting salary Maximise the starting salary.expected salary in 3
yearsMaximise the expected salary in three years.
fringe benefits Maximise fringe benefits.
effects on leisure time Mimimise the extent to which the work constrains the leisure time.
working hours Minimise working hours.
daily commuting Minimise daily commuting.
business travel Minimise the amount of extended trips.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Identifying decision alternatives
Identify possible decision alternatives To stimulate the process
a) use fundamental objectives If there were only one objective, two objectives...
b) use means objectives
c) remove constraints If time were no concern...
c) use different perspectives How would you see the situation after ten years?
See the “Problem structuring / Generating and identifying decision alternatives” section in the theory part.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The feasible decision alternatives
1) Research Institute
2) Consulting Firm
3) Large Corporation
4) Small IT Firm
As you are only interested in these job offers, there is no need to generate additional decision alternatives.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Problem structuring
Hierarchical organisation of objectives
1) Identify the overall fundamental objective.
2) Clarify its meaning by developing more specific objectives.
3) Continue until an attribute can be associated with each lowest
level objective.
4) Add alternatives to the hierarchy and link them to the attributes.
5) Validate the structure. See the “Hierarchical modelling of objectives - Checking the structure” section.
6) Iterate steps 1- 5, if necessary.
See the “Problem structuring / Hierarchical modelling of objectives” section in the theory part.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
A preliminary objectives hierarchy with alternatives illustrated with Web-HIPRE
Note: • Alternatives are shown in yellow in Web-HIPRE.
• Only the fundamental objectives are included.
• All objectives are assumed to be preferentially independent.
Is there anything you would like to change?
Does the value tree satisfy the conditions listed in the “Checking the structure” section?
Problem structuring - Hierarchical organisation of objectives
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Checking the structure
The hierarchy requires further modification; Networking may be difficult to measure and there is
no real information available on it either. According to the DM
Task diversity is not relevant; tasks are likely to change over time, and all job offers have some variability.
Facilities have only a minor importance. Daily commuting may be neglected because it is almost
the same for all jobs.
Problem structuring - Hierarchical organisation of objectives
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The final objectives hierarchy for the job selection problem
Objectives hierarchy after pruning.
Problem structuring - Hierarchical organisation of objectives
• with sound (3.26Mb)• no sound (970Kb) • animation (480Kb)
Structuring a value tree
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Specifying attributes
Attributes measure the degree to which objectives are achieved.
Attributes should be comprehensive and understandable
Attribute levels define unambiguously the extent to which an objective is achieved.
measurable It is possible to measure DM’s preferences for different attribute levels.
1) Specify attributes for each lowest level objective.
2) Assess the alternatives’ consequences with respect to those attributes.
For more see the “Specification of attributes” section in the theory part.
Problem structuring
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
- = No attribute associated with the objective. Direct rating is used when evaluating the preferences.
Problem structuring - Specifying attributes
objective description attributeprofessional growthcontinuing education Maximise possibilities for continuing
education.constructed*
fit with interests Maximise the match between tasks and personal interests.
-
challenge Maximise the correspondence between task requirements and professional skills and opportunities for further professional growth.
-
compensationstarting salary Maximise the starting salary. euros per month
expected salary in 3 years Maximise the expected salary in three years.
euros per month
fringe benefits Maximise fringe benefits. -social
working hours Minimise working hours. working hours per day
atmosphere Maximise the positive effect of corporate culture and atmosphere.
constructed*
business travel Minimise the amount of extended trips. extended travelling
days/year.
Attributes associated with the objectives
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Constructed attributes
Problem structuring - Specifying attributes
attribute level descriptioncontinuing education 1 Employees are not engouraged to further education. Except for the introductory
familiarisation, other training or cources are not provided.2 Employees are encouraged to continuing education. A limited amount of cources
are offered.3 Employees are strongly engouraged to further education. Training and special
cources are a part of the job description. A number of cources are offered.atmosphere 1-5 An index describing atmosphere and corporate culture ranging from 0 (poor) to 5
(very good).
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Consequences of the alternatives
Attribute Research Institute Consulting Firm Large Corporation Small IT Firmcontinuing education 3 3 1 2
starting salary/€ 1900 2700 2200 2300expected salary
in 3 years/€ 2500 3500 2800 3000
hours / week 37.5 55 40 42.5atmosphere 3.2 2.5 3.7 4.5
travelling days / year 20 160 100 30
Problem structuring - Specifying attributes
• with sound (1.4Mb) • no sound (200Kb)• animation (150Kb)
Entering consequences
eLearning / MCDA
Systems Analysis LaboratoryHelsinki University of Technology
Job selection case
Preference elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Preference elicitation - contents
Overview Single attribute value function elicitation Weight elicitation AHP
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
OverviewThe aim is to measure DM’s preferences on each objective.
First, single attribute value functionsvi are determined for all attributes Xi.
Value
Attribute level
Second, the relative weights of the attributes wi are determined.
1/4 1/8 3/8 1/4
n
iiiin xvwxxxV
121 )(),...,,(
Finally, the total value of an alternative a with consequences Xi(a)=xi (i=1..n)
is calculated as
Note: The equation assumes mutual preferential independence.
Value elicitation
Weight elicitation
Preference elicitation
vi(x) [0,1]1
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Single attribute value function elicitation - contents
Value function elicitation in brief Definition of attribute ranges Value measurement techniques
Assessing the form of value function Bisection Difference Standard Sequence Direct Rating Category Estimation Ratio Estimation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Single attribute value function elicitation in brief
1) Set attribute ranges All alternatives should be within
the range. Large range makes it difficult to
discriminate between alternatives. New alternatives may lay
outside the range if it is too small.
2) Estimate value functions for attributes Assessing the form of value function Bisection Difference standard sequence Direct rating* Category estimation Ratio estimation AHP*
Possible ranges for “working hours/d“ attribute
*May be used for weight elicitation also.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Setting attributes’ ranges
No new job offers expected Analysis is used to compare only the existing
alternatives
small ranges are most appropriateAttribute Research Institute Consulting Firm Large Corporation Small IT Firm Rangecontinuing education 3 3 1 2 1 - 3
starting salary/€ 1900 2700 2200 2300 1900 - 2300
expected salary in 3
years/€2500 3500 2800 3000 2500 - 3500
hours / week 37.5 55 40 42.5 37.5 - 55atmosphere 3.2 2.5 3.7 4.5 2.5 - 4.5
travelling days / year 20 160 100 30 20 - 160
Single attribute value function elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Estimating value functions for the attributes
To improve the quality of the preference estimates if possible, use several value measurement techniques iterate until satisfactory values are reached
Possible value measurement techniques
Several* • Difference standard sequence • Selection of functional form• Direct rating• Bisection • Ratio estimation • Category estimation• AHP
In the following, examples of the useof the value measurement techniques are shown.
Single attribute value function elicitation
objective attribute techniqueprofessional growthcontinuing education constructed DR, AHPfit with interests - DR, AHPchallenge - DR, AHPcompensationstarting salary euros per month several*expected salary in 3 years euros per month several*fringe benefits - DR, AHPsocialworking hours working hours
per dayseveral*
atmosphere constructed DR, AHPbusiness travel extended
travelling days/year.
several*
DR = Direct rating
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Assessing the form of value function
Define the value function by assessing the form of the
function or by curve drawing
Values for different alternatives can be read from the
value curve
Value measurement techniques
Value
Level of an attribute
Note: In Web-HIPRE ratings refers to attribute levels.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Web-HIPRE example
The value function of the “Working hours” attribute is determined with Web-HIPRE´s value function method
The results are presented on the next slide
Value measurement techniques: Assessing the form of the value function
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value function for the“working hours” attribute
Value measurement techniques: Assessing the form of the value function
The smaller the number of weekly working hours...
… the larger decrease is required to produce the same increase in value.
• with sound (1.7Mb) • no sound (300Kb)• animation (180Kb)
Assessing the form of value function
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Bisection method
Value function is constructed by comparing attribute levels pairwise and defining the attribute level that is halfway between them
Identify the least and the most preferred attribute levels xmin, xmax and set:
Define midpoint m1, for which
Value measurement techniques
v(xmin) = 0v(xmax) = 1
v(m1) - v(xmin) = v(xmax) - v(m1)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Bisection method
The value at m1 is:
Define the midpoint m2 between xmin and m1 and the midpoint
m3 between m1 and xmax, such that
Repeat until the value scale is defined with sufficient accuracy
Value measurement techniques
v(m1) = 0.5·v(xmin) + 0.5 · v(xmax) = 0.5
v(m2) = 0.5·v(xmin) + 0.5·v(m1) = 0.25v(m3) = 0.5·v(m1) + 0.5·v(xmax) = 0.75
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example
The value function for “Expected salary in 3 years” is determined with the bisection method.
Salary range is from 2500 to 3500 euros. As higher salary is preferred, set
v(xmin) = v(2500) = 0v(xmax) = v(3500) = 1
Define the midpoint m1 such that the change in value when salary changes from m1 to 2500 is equal to the change in value when salary changes from 3500 to m1. Let’s choose m1 = 2900.
Now v(2900) = 0.5·v(2500) + 0.5·v(3500) = 0.5
Value measurement techniques: Bisection method
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example (continued)
Define the midpoint m2 between 2500 and m1 in similar manner. Let’s state m2 = 2620.
v(2620) = 0.5·v(2500) + 0.5·v(2900) = 0.25
The midpoint m3 between m1 and 3500 is defined to be m3 = 3150. v(3150) = 0.5·v(2900) + 0.5·v(3500) = 0.75
The value function for ”Expected salary in 3 years” can be approximated using the calculated points (see the next slide)
Higher accuracy can be acquired by splitting the intervals further
The higher the salary the larger an increase is required to produce the same increase in value for the DM.
Value measurement techniques: Bisection method
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value function for the “Expected salary in 3 years” attribute
Bisection method
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
2500 2700 2900 3100 3300 3500Salary / euros
Va
lue
Value measurement techniques: Bisection method
• with sound (1.7Mb) • no sound (300Kb)• animation (180Kb)
Assessing the form of value function
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Difference standard sequence
Define attribute levels x0, x1, …, xn such that the increase in the strength of preference is equal for all steps xi to xi+1, i = 1,..,n
As the attribute levels are equally spaced in value
Let k = 1 and v(x0) = 0
Value measurement techniques
v(xi+1) - v(xi) = k for all i
v(xi) = i for all i
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Difference standard sequence
Normalise the values:
where n is the number of attribute levels
2( )
( 1)i
iv x
n n
Value measurement techniques
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example
The value function for “working hours” is determined using difference standard sequence in the job selection problem.
Find a sequence of working hours xi i = 1, 2,…, such that the increments in strength of preference from xi to xi+1 are equal for all i.
The zero level of value function and unit stimulus are first determined. As ”weekly working hours” ranges from 37.5h to 55h and less working time is
preferred to more, set v(55)=0. Let the unit step be defined by, v(50)=1. Let x1 = 55 and x2 = 50.
Value measurement techniques: Difference standard sequence
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example (continued)
Next find x3 such that the change in the strength of your preference when the
“working hours” attribute decrease from 55 to 50 hours and
from 50 to x3 hours
are equal. Let‘s select x3 = 43.
Find x4 such that decreases from 55 to 50 hours and
from 43 to x4 hours
are equal. Let‘s select x4 = 35.
The whole range of the ”weekly working hours” measure scale is covered and a linear approximation of the value function can be drawn. On the next slide, the corresponding value function is shown.
Value measurement techniques: Difference standard sequence
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
A linear approximation of the value function for the “weekly working hours” attribute
Difference standard sequence
0
0.5
1
1.5
2
2.5
3
3.5
3540455055
Weekly working hours
Val
ue
Value measurement techniques: Difference standard sequence
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example (continued)
Values are normalised by setting
where n = 4 is the number of points in the sequence
The resulting value function is illustrated on the next slide The slide shows that the smaller the number of weekly working hours the
larger decrease is required to produce the same increase in value for the DM.
The linear approximation of the value function is rather crude, because only four points were used. To get a better approximation, more points would be needed.
2 2( )
( 1) 4(4 1)i
iv x
n n
Value measurement techniques: Difference standard sequence
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value function for the “weekly working hours” attribute
Difference standard sequence
0
0.1
0.2
0.3
0.4
0.5
0.6
3540455055
Weekly working hours
Val
ue
Value measurement techniques: Difference standard sequence
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Direct rating
1) Rank the alternatives
2) Give 100 points to the best alternative
3) Give 0 points to the worst alternative
4) Rate the remaining alternatives between 0 and 100
Value measurement techniques
Note that direct rating:
• is most appropriate when the performance levels of an attribute can be judged only with subjective measures
• can be used also for weight elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value measurement techniques: Direct rating
Web-HIPRE example
The use of the direct rating method is demonstrated in the case of the job selection problem.
The value of different education possibilities is assessed using Web-HIPRE.
The results are illustrated on the next slide.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value measurement techniques: Direct rating
Direct rating with Web-HIPRE
With regard to the continuing education attribute
• Research Institute is the best alternative
• Large corporation is the worst alternative
• Others are rated in between
• with sound (1.2Mb) • no sound (220Kb)• animation (140Kb)
Direct rating
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
The category estimation method
The DM’s responses are reduced to a small number of categories
Assign values to the categories in a similar manner as in the direct rating method: Give 100 points to the best category Give 0 points to the worst category Rate the remaining categories between 0 and 100
Value measurement techniques
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Example
Assume that the following category scale is used to judge the preferences
for the starting salary attribute.
Values for different categories are assessed as in the direct rating method. A larger salary is preferred to a smaller one
100 points to the “Good“ category 0 points to the “Poor“ category
The “Satisfactory“ category is assigned with 62 points.
Value measurement techniques: Category estimation
Category
Salary range
Poor Satisfactory Good
More than 2500€2100-2500€Less than 2100€
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Values for the salary categories
Value measurement techniques: Category estimation
0.62
1
0
0
0.2
0.4
0.6
0.8
1
1
Categories
Value
less than2100euros
2100-2500euros
more than2500euros
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Ratio estimation
Choose one of the alternatives as a standard With respect to the selected attribute, compare the
other alternatives with the standard by using ratio statements
Give 1 point to the best alternative Use preference ratios to calculate the scores of the
other alternatives
Value measurement techniques
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value measurement techniques: Ratio estimation
Example
Ratio estimation is used to determine the scores of the different levels of the “Business travel” attribute
Business travel days are summarised in the table below:
Consulting Firm is chosen as the standard alternative
Research InstituteConsulting Firm
Large CorporationSmall IT Firm
2016010030
Alternative Business Travel(days a year)
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Value measurement techniques: Ratio estimation
Example (continued)
The other alternatives are compared with the standard: 100 days is 2.5 times better than 160 days 30 days is 4.3 times better than 160 days 20 days is 4.5 times better than 160 days
The best alternative gets 1 point. The scores of the other alternatives are obtained from the ratios: v(20) = 1 v(30) = 0.22 · 4.3 = 0.95 v(100) = 0.22 · 2.5 = 0.55 v(160) = 1/4.5 = 0.22
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Values for different levels of “business travel” attribute
Ratio Estimation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120 140 160 180
Business Travel (days/year)
Valu
e
Value measurement techniques: Ratio estimation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Weight elicitation - contents
About weight elicitation SMART SWING SMARTER AHP*
* Used also for value elicitation
Note that also Direct rating can be used for weight elicitation. For more see the corresponding part in the value elicitation section.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
About weight elicitation
In the Job selection case hierarchical weighting is used.
1) Weights are defined for each hierarchical level...
2) ...and multiplied down to get the final lower level weights.
0.6 0.4
0.7 0.3 0.2 0.6 0.2
0.6 0.4
0.7 0.3 0.2 0.6 0.2
Multiply
0.42 0.18 0.08 0.24 0.08
In the following the use of different weight elicitation methods is presented...
To improve the quality of weight estimates• use several weight elicitation methods• iterate until satisfactory weights are reached
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
SMART
1) Assign 10 points to the least important attribute (objective)
wleast = 10
2) Compare other attributes with xleast and weigh them
accordinglywi > 10, i least
3) Normalise the weights
w’k = wk/(iwi ), i =1...n, n=number of attributes (sub-objectives)
Weight Elicitation Methods
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Web-HIPRE example
The weights for the attributes under the “Compensation” objective in the job selection problem are determined with the SMART method.
Weight Elicitation Methods: SMART
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Weighting attributes under the “Compensation” objective
• ”Fringe benefits” is the least important attribute 10 points
• ”Starting salary” is the second most important with 40 points
• ”Expexted salary in 3 years” is the most important attribute with 65 points.
points
normalised weights
Weight Elicitation Methods: SMART
• with sound (1.2Mb) • no sound (200Kb)• animation (130Kb)
SMART
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
SWING
1) Rank the attributes in the order of importance.
2) Suppose that the attributes are at their worst level and that you can shift one attribute to its highest level. Assign it with 100 points.
3) Select another attribute to be shifted to the highest level and give it points relative to the first attribute.
4) Continue until all attributes have been assessed.
5) Normalise the weights.
Weight Elicitation Methods
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Web-HIPRE example
The weights for the attributes in the “Social” category in the job selection problem are assessed with the SWING method.
Weight Elicitation Methods: SWING
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Weighting attributes under the ”Social” objective
• ”Working hours” is the most important attribute 100 points.
• ”Business travel” is the second most important with 55 points.
• ”Atmosphere” is the least important attribute with 50 points.
points
normalised weights
Weight Elicitation Methods: SWING
• with sound (1.1Mb) • no sound (190Kb)• animation (150Kb)
SWING
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
SMARTER
1) Rank the attributes in order of importance
2) Calculate weights from the formula
wj = (n + 1 – Rj),
where n is the number of attributes and R j rank of the attribute j
3) Normalise the weights
Weight Elicitation Methods
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Web-HIPRE example
Weights for the attributes in the “Professional” category in the job selection problem are assessed with the SMARTER method.
Weight Elicitation Methods: SMARTER
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Weighting attributes under the ”Professional” objective
• “Fit with interests” is the most important attribute
• The second most important attribute is “Challenge”
• “Continuing Education” is the least important attribute.
Note: weights are calculated from the ranks.
Weight Elicitation Methods: SMARTER
• with sound (980Kb) • no sound (200Kb)• animation (130Kb)
SMARTER
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
AHP Compare each pair of
sub-objectives under an objective, or attributes under an objective, or alternatives with respect to a given attribute
Store preference ratios in a comparison matrix for every i and j, give rij, the ratio of
importance between the ith and jthobjective (or attribute, or alternative)
Assign A(i,j) = rij
nnn
n
rr
rr
...
.........
...
1
111
A=
Preference elicitation
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
AHP
Check the consistency measure (CM) If CM > 0.20 identify and eliminate inconsistencies
in preference statements
Compute the eigenvector which corresponds to the
largest eigenvalue of the comparison matrix Normalise the vector to obtain attributes’ weights
(or objectives’ weights, or value scores of the alternatives with respect to a given
attribute)
Weight Elicitation Methods
For more see the AHP section in the theory part.
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Web-HIPRE example
Weights of the attributes under the “Compensation” objective in the job selection case are determined with the AHP method.
Weight Elicitation Methods: AHP
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Weighting attributes under the ”Compensation” objective
• “Expected salary in 3 years” is the most important
• ”Starting salary” the second most important
• “Fringe benefits” the least important attribute.
• Expected salary is 4.9 times more important than fringe benefits• Starting salary is 3.0 times more important than fringe benefits• Expected salary is 3.7 times more important than starting salary
The consistency index is 0.145 the comparisons are consistent enough
Weight Elicitation Methods: AHP
• with sound (1.9Mb) • no sound (1.5Mb)• animation (200Kb)
AHP
eLearning / MCDA
Systems Analysis LaboratoryHelsinki University of Technology
Job Selection Case
Results & Sensitivity Analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Results & Sensitivity Analysis - Contents
Used preference elicitation methods Attibutes, alternatives and corresponding value
scores Attributes‘ and objectives‘ weights Recommended decision Scores of the alternatives by the first level
objectives One-way sensitivity analysis Conclusion
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Used preference elicitation methods
The job selection value tree with used preference elicitation methods shown in Web-HIPRE:
Results & Sensitivity Analysis
SMART
Assessing the form of the value function
AHP
Direct ratingSMARTER
Swing
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Attributes, alternatives andcorresponding value scores
Results & Sensitivity Analysis - Preference Elicitation Choices
Attribute Value elic method Res. Institute Consulting Firm Large Corp. Small IT FirmContinuing educ. Direct rating 0.499 (1.00)* 0.167 (0.335)* 0 (0)* 0.334 (0.670)*Challenge Direct rating 0.339 (0.705)* 0.481 (1)* 0 (0)* 0.180 (0.375)*Fit with interests Direct rating 0.291 (0.645)* 0 (0)* 0.450 (1)* 0.259 (0.575)*Starting salary Category estim 0 (0)* 0.446 (1.00)* 0.277 (0.620)* 0.277 (0.620)*Exp salary in 3 y Function selection 0.58 0.943 0.821 0.862Fringe benefits Direct rating 0 (0)* 0.513 (1)* 0.205 (0.400)* 0.282 (0.550)*Working hours Function selection 0.906 0.407 0.877 0.84Business travel AHP 0.46 0.075 0.129 0.337Atmosphere Direct rating 0.207 (0.445)* 0 (0)* 0.328 (0.705)* 0.465 (1)** normalised value in brackets
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Attributes‘ and objectives‘ weights
Results & Sensitivity Analysis - Preference Elicitation Choices
Objective Weighting method Attributes/Subobjectives WeightIdeal Job SMART Compensation 0.295
Professional 0.477Social 0.227
Compensation AHP Fringe benefits 0.103Expected salary in 3 years 0.662Starting salary 0.235
Social SWING Working hours 0.488Business travel 0.268Atmosphere 0.244
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Recommended decision
Small IT firm is the recommended alternative with the highest total value (0.442)
Large corporation and consulting firm options are almost equally preferred (total values 0.407 and 0.405 respectively)
Research Institute is clearly the least preferred alternative (total value of 0.290)
Solution of the job selection problem in Web-HIPRE. Only first-level objectives are shown.
Results & Sensitivity Analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Scores of the alternatives by the first level objectives
Research Institute is the best alternative regarding to the Professional and the Social categories, but gets zero points in the Compensation category
Results & Sensitivity Analysis
• with sound (1.6Mb) • no sound (290Kb)• animation (220Kb)
Viewing the results
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
One-way sensitivity analysis
What happens to the solution of the job selection problem if one of the parameters affecting the solution changes? What if for example the working hours in the IT firm option increase to 50 h/week or the salary in the Research Institute rises to 2900 euros/month?
In other words, we would like to know how sensitive our solution is to changes in the objective weights, attribute scores and attribute ratings
In one-way sensitivity analysis one parameter at time is varied Total values of decision alternatives are drawn as a function of the
variable under consideration Next, we apply one-way sensitivity analysis to the job selection case
Results & Sensitivity Analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in “working hours” attribute
If working hours in the IT firm rise to 53 h/week or over and nothing else in the model changes, Large Corporation becomes the most preferred alternative
If working hours in the Consulting firm were 47 h/week or less instead of the current 55 h/week, it would be considered the best alternative
One-way sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in “working hours” attribute
Changes in the weekly working hours in Large corporation‘s job offer would not affect the recommended solution even if they decreased to zero. The ranking order of the other alternatives would change though.
Changes in the weekly working hours in the Research Institute‘s job offer don‘t have any effect on the solution or on the preference order of rest of the alternatives.
One-way sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in the weight of the “Compensation” objective
The Research Institute becomes the most preferred alternative if the weight of Compensation objective drops to 0.08 or less (current value 0.3)
If the weight of Compensation rises to 0.46 or higher, Consulting Firm becomes the recommended alternative
Both of these scenarios are unlikely to happen unless the preferences of the DM change competely Varying the weight of the “Compensation”
objective in Web-HIPRE
One-way sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in the weight of“Professional” objective
The total weight of the “Professional” objective is currently 0.48.
If the weight were > 0.74, Consulting Firm would be the recommended alternative
If the weight were > 0.83, Research Institute would be the best option
Changes of this scale are not likely to happen
Varying the weight of the “Professional” objective in Web-HIPRE
One-way sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Changes in the weight of “Social” objective
The weight of the “Social” objective is originally 0.23
If the weight decreases to < 0.15, the IT Firm is replaced by the Consulting Firm as the recommended alternative
If the weight rises to the extremely unlikely value of 0.99, the Research Institute becomes the recommended alternative
Varying the weight of the “Social” objective in Web-HIPRE
One-way sensitivity analysis
• with sound (1.6Mb) • no sound (330Kb)• animation (240Kb)
Sensitivity analysis
eLearning / MCDASystems Analysis LaboratoryHelsinki University of Technology
Conclusion
Small IT Firm is the recommended solution, i.e. the most preferred alternative
The solution is not sensitive to changes in the weights of the first level objectives or weekly working hours of any single alternative
Sensitivity to other aspects of the model requires further studying, however
Results & Sensitivity Analysis