# Mini intro to Value Tree Analysis - Aalto

Introduction to Value Tree Analysis eLearning resources / MCDA team Director prof. Raimo P. Hmlinen Helsinki University of Technology Systems Analysis Laboratory http://www.eLearning.sal.hut.fi Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Contents About the introduction Basic concepts A job selection problem Problem structuring Preference elicitation Results and sensitivity analysis Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

About the introduction This is a brief introduction to multiple criteria decision analysis and specifically to value tree analysis After reading the material you should know basic concepts of value tree analysis how to construct a value tree how to use the Web-HIPRE software in simple decision making problems to support your decision Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Basic concepts Objective is a statement of something that one desires to achieve for example; more wealth

Attribute indicates the level to which an objective is achieved in a given decision alternative for example by selecting a certain job offer you may get 3000 /month Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Basic concepts Value function Value function v(x) assigns a number i.e. value to each attribute level x. Value describes subjective desirability of the corresponding attribute level. For example:

value value 1 1 Size of the ice cream cone Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Working hours / day Basic concepts Value tree In a value tree objectives are organised hierarchically overall objective sub-objectives attributes alternatives Top speed Driving

Citroen Acceleration Ideal car VW Passat Price Audi A4 Economy Expenses Each objective is defined by sub-objectives or attributes There can be several layers of objectives Attributes are added under the lowest level of objectives Decision alternatives are connected to the attributes Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Basic concepts Phases of value tree analysis The aim of the Problem structuring is to create a better understanding of the problem Decision context is a setting in which the decision occurs In Preference elicitation DMs preferences over a set of objectives is estimated and

measured The aim of the Sensitivity analysis is to explore how changes in the model influence the recommended decision Note: Only the highlighted parts are covered in this mini intro Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA A job selection 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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Problem structuring Hierarchical organisation of objectives 1) Identify the overall objective. 2) Clarify its meaning with more specific sub-objectives. Add the subobjectives to the next level of the hierarchy. 3) Continue recursively until an attribute can be associated with each lowest level objective. 4) Add the decision alternatives to the hierarchy and link them to the attributes.

5) Iterate the steps 1- 4, until you are satisfied with the structure. Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Problem structuring The objectives hierarchy for the job selection problem Overall objective Decision alternatives Sub-objectives Attributes Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Video Clip: Structuring a value tree in Web-HIPRE with sound (.avi 3.3MB) no sound (.avi 970KB ) animation (.gif 475KB) Problem structuring Consequences Attribute Research Institute Consulting Firm Large Corporation

continuing 3 3 1 education starting salary/ 1900 2700 2200 expected salary 2500 3500 2800 in 3 years/ hours / week 37.5 55 40 atmosphere 3.2 2.5 3.7 travelling days / 20 160 100 year Small IT Firm

2 2300 3000 42.5 4.5 30 Video Clip: Entering the consequences of the alternatives in Web-HIPRE with sound (.avi 1.33 MB) no sound (.avi 230 KB) animation (.gif 165 KB) Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Preference elicitation: an overview The aim is to measure DMs preferences on each objective. Value elicitation First, single attribute value functions vi are determined for all attributes Xi. Weight elicitation 1/4 1/8 3/8 1/4

Value 1 vi(x) [0,1] Attribute level Second, the relative weights of the attributes wi are determined. Finally, the total value of an alternative a with consequences Xi(a)=xi n is calculated as V ( x1 , x2 ,..., xn ) wi vi ( xi ) i 1 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA (i=1..n) Preference elicitation 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. Possible ranges for the working hours/d attribute 2) Estimate value functions for attributes Assessing the form of value function Direct rating Bisection Difference standard sequence Category estimation Ratio estimation AHP Note:

Methods used in this case are shown in bold Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Preference elicitation Setting attributes ranges No new job offers expected Analysis is used to compare only the existing alternatives small ranges are most appropriate Attribute Research Institute Consulting Firm Large Corporation Small IT Firm Range continuing 1-3 3 3 1 2 education starting 1900 - 2300 1900 2700 2200 2300

salary/ expected salary in 3 2500 - 3500 2500 3500 2800 3000 years/ hours / week 37.5 - 55 37.5 55 40 42.5 atmosphere 2.5 - 4.5 3.2 2.5 3.7 4.5 travelling days 20 - 160 20 160 100 30 / year

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Preference elicitation Assessing the form of value function Value scale Is the value function increasing or decreasing? linear? Is an increase at the end of the attribute scale more important than a same sized increase at the beginning of the scale? You can use Bisection method to ease the assessment. More about the Bisection method (optional) Attribute level scale In the following video clip the Bisection method is used to estimate a point from the value curve. Web-HIPRE uses exponential approximation to estimate the rest of the value function. Video Clip: Assessing the form of the value function with bisection method in Web-HIPRE with sound (.avi 1.69 MB) Systems Analysis Laboratory no sound (.avi 303 KB) Helsinki University of Technology eLearning / MCDA animation (.gif 180 KB)

Preference elicitation 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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Video Clip: Using direct rating in WebHIPRE with sound (.avi 1.17 MB) no sound (.avi 217 KB) animation (.gif 142 KB) Preference elicitation About weight elicitation In the Job selection case hierarchical weighting is used. 1) Weights are defined for each hierarchical level... 0.6 2) ...and multiplied down to get

the final lower level weights. 0.6 0.4 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... Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Preference elicitation 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 wk = wk/(iwi ), i =1...n, n=number of attributes (subobjectives)

Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Video Clip: Using SMART in WebHIPRE with sound (.avi 1.12 MB) no sound (.avi 209 KB) animation (.gif 133 KB) Preference elicitation AHP 1) Compare each pair of sub-objectives or attributes under an objective 2) 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 3) Check the consistency measure (CM)

If CM > 0.20 identify and eliminate inconsistencies in preference statements A= r11 ... ... rn1 ... ... ... rnn Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA r1n Video Clip: Using AHP in Web-HIPRE with sound (.avi 1.97 MB) no sound (.avi 377 KB) animation (.gif 204 KB) Results & sensitivity analysis Used preference elicitation methods

The job selection value tree with used preference elicitation methods shown in Web-HIPRE: Direct rating SMART AHP Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Assessing the form of the value function (Bisection method) Note: Only the highlighted methods are covered in this introduction. 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 0.407 and 0.405 respectively) Research Institute is clearly the least preferred alternative (total value of 0.290) Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Solution of the job selection problem in WebHIPRE. Only first-level objectives are shown. Video Clip: Viewing the results in WebHIPRE with sound (.avi 1.58 MB) no sound (.avi 286 KB) animation (.gif 213 KB) 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 alternative increase to 50 h/week or the salary in the Research Institute rises to 2900 euros/month? In other words, how sensitive our solution is to changes in the objective weights, single attribute value functions or attribute ratings In one-way sensitivity analysis one parameter is varied at time 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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Results & 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 Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA Results & sensitivity analysis Changes in working hours attribute Changes in the weekly working hours in Large corporations 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 Institutes

job offer dont have any effect on the solution or on the preference order of rest of the alternatives. Video Clip: Sensitivity analysis in Web-HIPRE with sound (.avi 1.60 MB) no sound (.avi 326 KB) animation (.gif 239 KB) Systems Analysis Laboratory Helsinki University of Technology eLearning / MCDA

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