job selection case

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


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.


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


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


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


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


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


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


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


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


Decision analytic problem structuring

Define the decision context

Generate the objectives

Identify the decision alternatives

Hierarchical organisation of the objectives

Specify the attributes


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


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


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


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.


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


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


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.


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


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.



The final objectives hierarchy for the job selection problem

Objectives hierarchy after pruning.


• with sound (3.26Mb)• no sound (970Kb) • animation (480Kb)

Structuring a value tree


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


- = 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


Constructed 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).


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


• with sound (1.4Mb) • no sound (200Kb)• animation (150Kb)

Entering consequences

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Job selection case



Preference elicitation - contents

Overview Single attribute value function elicitation Weight elicitation AHP


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


vi(x) [0,1]1


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


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.


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


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


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.


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


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.




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


v(xmin) = 0v(xmax) = 1

v(m1) - v(xmin) = v(xmax) - v(m1)


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


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


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


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 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





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


v(xi+1) - v(xi) = k for all i

v(xi) = i for all i



Normalise the values:

where n is the number of attribute levels

2( )

( 1)i

iv x

n n



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


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.



A linear approximation of the value function for the “weekly working hours” attribute


0

0.5

1

1.5

2

2.5

3

3.5

3540455055

Weekly working hours

Val

ue



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 function for the “weekly working hours” attribute


0

0.1

0.2

0.3

0.4

0.5

0.6

3540455055

Weekly working hours

Val

ue



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


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


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.


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


Direct rating


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



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€


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


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: 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)



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


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



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.


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


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


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


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


SMART


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.



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


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


SWING


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



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


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

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SMARTER


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=



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)


For more see the AHP section in the theory part.


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


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

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Job Selection Case

Results & Sensitivity Analysis


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


Used preference elicitation methods

The job selection value tree with used preference elicitation methods shown in Web-HIPRE:


SMART

Assessing the form of the value function

AHP

Direct ratingSMARTER

Swing


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


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


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.



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



Viewing the results


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



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



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.



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



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



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



Sensitivity analysis


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


job selection case

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