Job selection case eLearning resources / MCDA team Director prof. Raimo P. Hämäläinen Helsinki University of Technology Systems Analysis Laboratory http://www.eLearning.sal.hut.fi
Contents • About the case • The problem • Problem structuring • Preference elicitation • 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
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).
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 Salary You have also come up with the following estimates for the expected salaryin three years time. Table 2. Expected salaries in three years.
The problem 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
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.
Problem structuring • 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... • ... Example of a decision context
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 Possible objectiveswith their descriptions What other objectives might there be?
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.
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 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 structure The hierarchy requires further modification; • Networking may be difficult to measure and there is no real information available on it either. • According to the DM • Task diversity is not relevant; tasks are likely to change over time, and all job offers have some variability. • Facilities have only a minor importance. • Daily commuting may be neglected because it is almost the same for all jobs.
Problem structuring - Hierarchical organisation of objectives The final objectives hierarchy for the job selection problem Structuring a value tree • with sound (3.26Mb) • no sound (970Kb) • animation (480Kb) Objectives hierarchy after pruning.
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.
Problem structuring - Specifying attributes Attributes associated with the objectives - = No attribute associated with the objective. Direct rating is used when evaluating the preferences.
Problem structuring - Specifying attributes Constructed attributes
Problem structuring - Specifying attributes Consequences of the alternatives Entering consequences • with sound (1.4Mb) • no sound (200Kb) • animation (150Kb)
Job selection case Preference elicitation
Preference elicitation - contents • Overview • Single attribute value function elicitation • Weight elicitation • AHP
Preference elicitation Value Attribute level 1/4 1/8 3/8 1/4 Overview The 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 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 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 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 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 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 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” 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 • with sound (1.7Mb) • no sound (300Kb) • animation (180Kb)
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) = 0v(xmax) = 1 v(m1) - v(xmin) = v(xmax) - v(m1)
Value measurement techniques 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 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 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 for the “Expected salary in 3 years” attribute Assessing the form of value function • with sound (1.7Mb) • no sound (300Kb) • animation (180Kb)
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
Value measurement techniques Difference standard sequence • Normalise the values:where n is the number of attribute levels
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.
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.
Value measurement techniques: Difference standard sequence A linear approximation of the value function for the “weekly working hours” attribute
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.
Value measurement techniques: Difference standard sequence Value function for the “weekly working hours” attribute
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
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.