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### Job selection case

### Job selection case objectives

### Job Selection Case value function

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
- 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).

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.

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.

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.

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.

Salary

You have also come up with the following estimates for the expected salaryin three years time.

Table 2. Expected salaries in three years.

Thinking task

- How would you approach the problem?
- Are there ways to model the problem?
- What would be the factors affecting your decision?

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.

- 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...
- ...

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.

Possible objectiveswith their descriptions

What other objectives might there be?

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?

- If there were only one objective, two objectives...

See the “Problem structuring / Generating and identifying decision alternatives” section in the theory part.

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.

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.

Problem structuring - Hierarchical organisation of objectives

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 structureThe 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

The final objectives hierarchy for the job selection problemStructuring a value tree

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Objectives hierarchy after pruning.

Problem structuring objectives

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.

- It is possible to measure DM’s preferences for different attribute levels.

- comprehensive and understandable

Problem structuring - Specifying attributes objectives

Attributes associated with the objectives- = No attribute associated with the objective. Direct rating is used when evaluating the preferences.

Problem structuring - Specifying attributes objectives

Constructed attributesProblem structuring - Specifying attributes objectives

Consequences of the alternativesEntering consequences

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Preference elicitation

Preference elicitation - contents objectives

- Overview
- Single attribute value function elicitation
- Weight elicitation
- AHP

Preference elicitation objectives

Value

Attribute level

1/4

1/8

3/8

1/4

OverviewThe aim is to measure DM’s preferences on each objective.

Value elicitation

vi(x) [0,1]

1

First, single attribute value functionsvi are determined for all attributes Xi.

Weight elicitation

Second, the relative weights of the attributes wi are determined.

Finally, the total value of an alternative awith consequences Xi(a)=xi (i=1..n)

is calculated as

Note: The equation assumes mutual preferential independence.

Single attribute value objectivesfunction 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 objectivesfunction elicitation in brief

1) Set attribute ranges

- All alternatives should be withinthe 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.

Single attribute value function elicitation objectives

Setting attributes’ ranges- No new job offers expected
- Analysis is used to compare only the existing alternatives
small ranges are most appropriate

Single attribute value function elicitation objectives

Estimating value functions for the attributesTo improve the quality of the preference estimates

- if possible, use several value measurement techniques
- iterate until satisfactory values are reached

Possible value measurement techniques

In the following, examples of the useof the value measurement techniques are shown.

- Several*
- Difference standard sequence
- Selection of functional form
- Direct rating
- Bisection
- Ratio estimation
- Category estimation
- AHP

DR = Direct rating

Value measurement techniques objectives

Value

Level of an attribute

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

Note: In Web-HIPRE ratings refers to attribute levels.

Value measurement techniques: Assessing the form of the value function

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” attributeThe smaller the number of weekly working hours...

… the larger decrease is required to produce the same increase in value.

Assessing the form of value function

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Value measurement techniques value function

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)

Value measurement techniques value function

Bisection method- The value at m1 is:
- Define the midpoint m2 between xminand 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

Value measurement techniques: Bisection method value function

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, setv(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 value function

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 value function

Value function for the “Expected salary in 3 years” attributeAssessing the form of value function

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Value measurement techniques value function

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

Value measurement techniques value function

Difference standard sequence- Normalise the values:where n is the number of attribute levels

Value measurement techniques: Difference standard sequence value function

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 value function

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 value function

A linear approximation of the value function for the “weekly working hours” attributeValue measurement techniques: Difference standard sequence value function

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.

Value measurement techniques: Difference standard sequence value function

Value function for the “weekly working hours” attributeValue measurement techniques value function

Direct rating1) 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 value function

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 value function

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

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Value measurement techniques value function

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: Category estimation value function

Category

Poor

Satisfactory

Good

Salary range

Less than 2100€

2100-2500€

More than 2500€

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 value function

Values for the salary categoriesValue measurement techniques value function

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 value function

Alternative

Business Travel

(days a year)

Research Institute

20

Consulting Firm

160

100

Large Corporation

Small IT Firm

30

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

Value measurement techniques: Ratio estimation value function

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

Value measurement techniques: Ratio estimation value function

Values for different levels of “business travel” attributeWeight elicitation - contents value function

- 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 value function

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

0.6

0.4

Multiply

0.7

0.3

0.2

0.6

0.2

0.7

0.3

0.2

0.6

0.2

0.42

0.18

0.08

0.24

0.08

- To improve the quality of weight estimates
- use several weight elicitation methods
- iterate until satisfactory weights are reached

In the following the use of different weight elicitation methods is presented...

Weight Elicitation Methods value function

SMART1) 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: SMART value function

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 value function

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

SMART

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Weight Elicitation Methods value function

SWING1) 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: SWING value function

Web-HIPRE exampleThe weights for the attributes in the “Social” category in the job selection problem are assessed with the SWING method.

Weight Elicitation Methods: SWING value function

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

SWING

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Weight Elicitation Methods value function

SMARTER1) 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 Rj rank of the attribute j

3) Normalise the weights

Weight Elicitation Methods: SMARTER value function

Web-HIPRE exampleWeights for the attributes in the “Professional” category in the job selection problem are assessed with the SMARTER method.

Weight Elicitation Methods: SMARTER value function

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.

SMARTER

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Preference elicitation value function

A=

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 ofimportance between the ith and jthobjective (or attribute, or alternative)
- Assign A(i,j) = rij

Weight Elicitation Methods value function

AHP- Check the consistency measure (CM)
- If CM > 0.20 identify and eliminate inconsistenciesin 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.

Weight Elicitation Methods: AHP value function

Web-HIPRE exampleWeights of the attributes under the “Compensation” objective in the job selection case are determined with the AHP method.

Weight Elicitation Methods: AHP value function

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

AHP

The consistency index is 0.145 the comparisons are consistent enough

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Results & Sensitivity Analysis

Results & Sensitivity Analysis - Contents value function

- 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

Results & Sensitivity Analysis value function

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

SMARTER

Direct rating

SMART

AHP

Swing

Assessing the form of the value function

Results & Sensitivity Analysis - Preference Elicitation Choices

Attributes, alternatives andcorresponding value scoresResults & Sensitivity Analysis - Preference Elicitation Choices

Attributes‘ and objectives‘ weightsResults & Sensitivity Analysis Choices

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.

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

Scores of the alternatives by the first level objectivesViewing the results

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Results & Sensitivity Analysis Professional and the Social categories, but gets zero points in the Compensation category

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

One-way sensitivity analysis Professional and the Social categories, but gets zero points in the Compensation category

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 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

Changes in “working hours” attributeThe 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

One-way sensitivity analysis

Changes in the weight of the “Compensation” objectiveVarying the weight of the “Compensation” objective in Web-HIPRE

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

One-way sensitivity analysis

Changes in the weight of“Professional” objectiveVarying the weight of the “Professional” objective in Web-HIPRE

The weight of the currently 0.48.“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

One-way sensitivity analysis

Changes in the weight of “Social” objectiveVarying the weight of the “Social” objective in Web-HIPRE

Sensitivity analysis

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Results & Sensitivity Analysis currently 0.48.

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

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