1. Job selection case eLearning resources / MCDA team
Director prof. Raimo P. Hämäläinen
Helsinki University of Technology
Systems Analysis Laboratory

2. Contents About the case The problem Problem structuring
Preference elicitation
Results and sensitivity analysis

3. 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.

4. 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

5. Governmental Research Institute
The problem
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).

6. Multinational consulting firm
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.

7. A place as a decision analyst
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.

8. 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.

9. 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.

10. The problem
Salary
You have also come up with the following estimates for the expected salary in three years time.
Table 2. Expected salaries in three years.

11. Thinking task How would you approach the problem?
Are there ways to model the problem?
What would be the factors affecting your decision?

12. Decision analytic problem structuring
Define the decision context
Generate the objectives
Identify the decision alternatives
Hierarchical organisation of the objectives
Specify the attributes

13. Decision context is the setting in which the decision occurs
Problem structuring
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.

14. Example of a decision context
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...
...

15. Generating objectives
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.

16. Possible objectives with their descriptions
Problem structuring
Possible objectives with their descriptions
What other objectives might there be?

17. Identifying decision alternatives
Problem structuring
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.

18. The feasible decision alternatives
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.

19. Hierarchical organisation of objectives
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.

20. 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?

21. Checking the structure
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.

22. The final objectives hierarchy for the job selection problem
Problem structuring - Hierarchical organisation of objectives
The final objectives hierarchy for the job selection problem
Structuring a value tree
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Objectives hierarchy after pruning.

23. Specifying attributes
Problem structuring
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.

24. Attributes associated with the objectives
Problem structuring - Specifying attributes
Attributes associated with the objectives
- = No attribute associated with the objective Direct rating is used when evaluating the preferences.

25. Constructed attributes
Problem structuring - Specifying attributes
Constructed attributes

26. Consequences of the alternatives
Problem structuring - Specifying attributes
Consequences of the alternatives
Entering consequences
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27. Preference elicitation
Job selection case
Preference elicitation

28. Preference elicitation - contents
Overview
Single attribute value function elicitation
Weight elicitation
AHP

29. Overview The aim is to measure DM’s preferences on each objective.
Preference elicitation
Overview
The aim is to measure DM’s preferences on each objective.
Value elicitation
Value
Attribute level
vi(x)  [0,1] 1
First, single attribute value functions vi are determined for all attributes Xi.
Weight elicitation
1/4
1/8
3/8
Second, the relative weights of the attributes wi are determined.
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.

30. 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

31. 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.

32. Setting attributes’ ranges
Single attribute value function elicitation
Setting attributes’ ranges
No new job offers expected
Analysis is used to compare only the existing alternatives
small ranges are most appropriate

33. Estimating value functions for the attributes
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
In the following, examples of the use of 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

34. Assessing the form of value function
Value measurement techniques
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
Level of an attribute
Note: In Web-HIPRE ratings refers to attribute levels.

35. 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

36. Value function for the “working hours” attribute
Value measurement techniques: Assessing the form of the value function
Value function for the “working hours” attribute
The 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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37. Value measurement techniques
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) = 0 v(xmax) = 1
v(m1) - v(xmin) = v(xmax) - v(m1)

38. Bisection method The value at m1 is:
Value measurement techniques
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) · v(xmax) = 0.5
v(m2) = 0.5·v(xmin) + 0.5·v(m1) = 0.25 v(m3) = 0.5·v(m1) + 0.5·v(xmax) = 0.75

39. Value measurement techniques: Bisection method
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) = 0 v(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

40. Value measurement techniques: Bisection method
Example (continued)
Define the midpoint m2 between 2500 and m1 in similar manner. Let’s state m2 = v(2620) = 0.5·v(2500) + 0.5·v(2900) = 0.25
The midpoint m3 between m1 and 3500 is defined to be m3 = 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.

41. Value function for the “Expected salary in 3 years” attribute
Value measurement techniques: Bisection method
Value function for the “Expected salary in 3 years” attribute
Assessing the form of value function
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42. Difference standard sequence
Value measurement techniques
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

43. Difference standard sequence
Value measurement techniques
Difference standard sequence
Normalise the values: where n is the number of attribute levels

44. Value measurement techniques: Difference standard sequence
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.

45. 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 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.

46. Value measurement techniques: Difference standard sequence
A linear approximation of the value function for the “weekly working hours” attribute

47. Value measurement techniques: Difference standard sequence
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.

48. Value function for the “weekly working hours” attribute
Value measurement techniques: Difference standard sequence
Value function for the “weekly working hours” attribute

49. Direct rating 1) Rank the alternatives
Value measurement techniques
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

50. 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.

51. Direct rating with Web-HIPRE
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
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52. The category estimation method
Value measurement techniques
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

53. Value measurement techniques: Category estimation
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.
Category
Salary range
Poor
Satisfactory
Good
More than 2500€ €
Less than 2100€

54. Values for the salary categories
Value measurement techniques: Category estimation
Values for the salary categories

55. Ratio estimation Choose one of the alternatives as a standard
Value measurement techniques
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

56. 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 Institute
Consulting Firm
Large Corporation
Small IT Firm 20
160
100 30
Alternative
Business Travel
(days a year)

57. 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

58. Values for different levels of “business travel” attribute
Value measurement techniques: Ratio estimation
Values for different levels of “business travel” attribute

59. 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.

60. 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
0.6
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...

61. SMART 1) Assign 10 points to the least important attribute (objective)
Weight Elicitation Methods
SMART
1) Assign 10 points to the least important attribute (objective)
wleast = 10
2) Compare other attributes with xleast and weigh them accordingly wi > 10, i  least
3) Normalise the weights
w’k = wk/(iwi ), i =1...n, n=number of attributes (sub-objectives)

62. Weight Elicitation Methods: SMART
Web-HIPRE example
The weights for the attributes under the “Compensation” objective in the job selection problem are determined with the SMART method.

63. Weighting attributes under the “Compensation” objective
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
SMART
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64. SWING 1) Rank the attributes in the order of importance.
Weight Elicitation Methods
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.

65. Weight Elicitation Methods: SWING
Web-HIPRE example
The weights for the attributes in the “Social” category in the job selection problem are assessed with the SWING method.

66. Weighting attributes under the ”Social” objective
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 points.
points
normalised weights
SWING
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67. SMARTER 1) Rank the attributes in order of importance
Weight Elicitation Methods
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 Rj rank of the attribute j
3) Normalise the weights

68. Weight Elicitation Methods: SMARTER
Web-HIPRE example
Weights for the attributes in the “Professional” category in the job selection problem are assessed with the SMARTER method.

69. Weighting attributes under the ”Professional” objective
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.
SMARTER
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70. AHP Compare each pair of
Preference elicitation
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 jth objective (or attribute, or alternative)
Assign A(i,j) = rij A=

71. AHP Check the consistency measure (CM)
Weight Elicitation Methods
AHP
Check the consistency measure (CM)
If CM > 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.

72. Weight Elicitation Methods: AHP
Web-HIPRE example
Weights of the attributes under the “Compensation” objective in the job selection case are determined with the AHP method.

73. Weighting attributes under the ”Compensation” objective
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
AHP
The consistency index is  the comparisons are consistent enough
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74. Results & Sensitivity Analysis
Job Selection Case
Results & Sensitivity Analysis

75. 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

76. Used preference elicitation methods
Results & Sensitivity Analysis
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

77. Attributes, alternatives and corresponding value scores
Results & Sensitivity Analysis - Preference Elicitation Choices
Attributes, alternatives and corresponding value scores

78. Attributes‘ and objectives‘ weights
Results & Sensitivity Analysis - Preference Elicitation Choices
Attributes‘ and objectives‘ weights

79. Results & Sensitivity Analysis
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 and 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.

80. Scores of the alternatives by the first level objectives
Results & Sensitivity Analysis
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
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81. One-way sensitivity analysis
Results & Sensitivity Analysis
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

82. Changes in “working hours” attribute
One-way sensitivity analysis
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

83. Changes in “working hours” attribute
One-way sensitivity analysis
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.

84. Changes in the weight of the “Compensation” objective
One-way sensitivity analysis
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

85. Changes in the weight of “Professional” objective
One-way sensitivity analysis
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

86. Changes in the weight of “Social” objective
One-way sensitivity analysis
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
Sensitivity analysis
Varying the weight of the “Social” objective in Web-HIPRE
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87. Results & 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