Without substitute decision-maker, decision support system, through their components,can facilitate the work of decision-maker by providing useful clues to solving problems andidentifying opportunities. Choosing an optimal solution in case of complex decision makingprocesses, with a degree of uncertainty, involving a series of interdependent decisions, performed inseveral periods of time, can be achieved using decision trees. Suggestive and simple propertiespropel decision trees among the tools with a high degree of adoption and integration in electronicdecisional systems.tree, decision, risk, rollback, certainty

Dan Racovitan

Janetta Sirbu

Nicolae Marginean

English

Research Papers in Economics

Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
631 
 
DECISION TREES – A PERSPECTIVE OF ELECTRONIC DECISIONAL 
SUPPORT 
 
 
Nicolae Mărginean
 1 
Janetta Sîrbu
 2 
Dan Racoviţan
 3  
 
 
ABSTRACT: Without substitute decision-maker, decision support system, through their components, 
can  facilitate  the  work  of  decision-maker  by  providing  useful  clues  to  solving  problems  and 
identifying  opportunities.  Choosing  an  optimal  solution  in  case  of  complex  decision  making 
processes, with a degree of uncertainty, involving a series of interdependent decisions, performed in 
several periods of time, can be achieved using decision trees. Suggestive and simple properties 
propel decision trees among the tools with a high degree of adoption and integration in electronic 
decisional systems.    
 
Key words: tree, decision, risk, rollback, certainty 
 
JEL code: M15 
 
 
 Introduction 
 Decision  support  system  is  one  of  the  best  tools  to  assist  decision  making  at  the 
organizational  level,  in  today's  society,  characterized  by  high  complexity  of  business,  global 
competition,  information  explosion,  uncertainty,  pronounced  inconstancy  and  so  on  (Mărginean 
2006). For all these aspects of contemporary, instruments must be identified for an appropriate 
handling and control. Without substitute decision-maker, decision support system, through their 
components  useful  in  supporting  all  phases  of  decisional  process,  can  facilitate  the  work  of 
decision-maker by providing useful clues to solving problems and identifying opportunities.  
 
 Literature review 
 Choosing an optimal solution in case of complex decision making processes, with a degree 
of uncertainty, involving a series of interdependent decisions, performed in several periods of time, 
can be achieved using decision trees. According to Wikipedia, a tree is a decision making tool that 
uses tree graphs in modeling decisions together with their consequences. In analyzing the decision, 
a decision making tree is a visual tool used to support decision making through computing expected 
values of all decision alternatives in order to identify the best solution. 
 A decision tree consists of multiple nodes connected by edges. Nodes of a decision tree can 
be of three kinds:  
·  decision nodes represented by squares; 
·  event nodes represented by circles; 
·  terminal nodes represented by triangle or vertical line.. 
                                                           
1 “Bogdan Vodă” University, Gr. Alexandrescu  no. 26A, Cluj-Napoca, România, marginean.nicu@yahoo.com 
2 “Bogdan Vodă” University, Gr. Alexandrescu  no. 26A, Cluj-Napoca, România, sjanetta2002@yahoo.com 
3 “Bogdan Vodă” University, Gr. Alexandrescu  no. 26A, Cluj-Napoca, România, ubv@ubv.ro Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
632 
 
 Decision node represents the point where decision-maker is able to choose one of several 
possible variants. Edges that start from this node represent decision alternatives or options. The 
decision nodes and edges represent the controllable factors of decision making. 
 An event or chance node represents a point of uncertainty in decision making where can 
occur more events. Edges that start from such a node represent possible events that can occur at that 
point. Through event nodes are represented uncontrollable factors of decision making. 
 Each  edge  of  the  decision  tree  has  attached  a  label  with  her  meaning  and  a  value 
representing the cost or benefit that is obtained by choosing the action attached to the edge in 
question. In addition, event type edges have attached the probability of occurrence for events they 
represent. 
 Terminal nodes are the final paragraphs of the decision tree and represent the outcome of a 
sequence  of  decisions  and  events.  Each  terminal  value  is  obtained  by  summing  all  the  values 
attached to the edges found on the unique path from the initial node of the decision tree to the 
current terminal node. Thus it can say that the final value of a node quantifies a scenario to consider 
for identifying the optimal solution. 
 In the context of decision tree "roll back" algorithm determines the optimal sequence of 
decisions and events. Firstly, it is calculated the optimal decision at the last decision point, after 
optimal  mathematical  expectation  criterion.  Then  it  is  proceeded  the  decision  selection  for  the 
following  decision  point  upstream,  thus  going  step  by  step  up  to  the  initial  decision  point 
(Stănciou.1998). In other words, the algorithm "roll back" are applied on the decision tree going 
through  the  terminal  toward  the  initial  node,  where  for  each  node  are  computed  the  so-called 
rollback value of certainty. This value is positioned in the lower left of each node and is calculated 
based on the decision-maker attitude towards risk. 
 The essence of decision making is a complex process that often involves a less or greater 
uncertainty.  One  way  to  quantify  the  uncertainty  is  based  on  the  probability  theory.  Each 
uncontrollable event can occur in a certain given situation and has attached some probability of 
occurrence,  computed  on  the  basis  of  existing  statistical  data,  collected  over  time.  Thus,  to 
characterize the uncertainty of a one situation, it is used the probability distributions that synthesize 
all possible events associated with their likelihood. A synthetic view of a probability distribution for 
a certain situation is given by the expected value. Expected value is a criterion for choosing a 
decision in conditions which it is taken account all possible outcomes and their likelihood. Expected 
value of economic actions is given by the sum of the values obtained by multiplication of the values 
(benefits or costs) associated to the events and their likelihood of occurrence.   
 
∑ = =
j
j j x x X P X E ) ( ) (                                               ………………………………..      (1) 
 In case the expected value is accepted by a decison-maker as a result of actions, it can speak 
about a position of neutrality towards risk. Decision-maker accept in the same time the possibility 
of winning and the possibility of loosing. For example, in situations where in a certain decision 
point  it  can  be  identified  two  variants,  a  gain  (100RON)  and  a  loss  (-50RON)  with  the  same 
probability, expected value is 100 * 0.5 -50 * 0.5 = 25RON. In the case of neutral attitude towards 
risk, decision-maker  has the same attitude both for the situation of certain alternative of 25RON 
equal to expected value and for situation of uncertain alternative described by a gain (100RON) 
with 50% probability and a loss (50RON) with the same probability.    
 In the case of neutral attitude towards risk and a maximization problem, for all nodes will be 
computed rollback values as follows: 
· for terminal node, Rollback values are equal to terminal value; 
· for event node, Rollback values are equal to expected value of that point ; Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
633 
 
· for decision nodes, Rollback values are equal to maximum of the rollback values situated 
to the immediately succesor nodes. 
  
 Bussiness  practice  proved  that  in  decisional  field  is  presented  the  phenomenon  of  risk 
aversion. It is prefered certain low benefits against uncertain high benefits. For previous scenario, 
decision-maker prefers to win an amount smaller than expected value (25RON) against to adventure 
him in the presented uncertain situation. In this case it is necessary to identify a new indicator that 
replace the expected value. If  expected value caracterizes sintetically the outcome of the uncertain 
situation with neutral attitude towards risk, certainty equivalent will caracterize the outcome of the 
uncertain situation with risk aversion. Firstly, the new indicator supposes adjusting the likelihood of 
the events with exponential utility function having the next form:  
 
                                                             ) / ( * ) ( RT x EXP B A x U - - =                                     (2) 
where: 
·  x – obtained outcomes 
·  RT  –  tolerance  to  risk  –  is  a  parameter  that  quantifies  the  attitude  towards  risk  of 
decision-maker, having a value equal with the maximum amount Y where decision-maker accepts 
the scenario  
                                              


 

 -
5 . 0 5 . 0
2 / Y Y
                                                                         .  (3) 
against to a certain null gain. 
·  The most unfavorable outcome(valmin) has the utility equal to 0. 
·  The most favorable outcome(valmax) has the utility equal to 1. 
·  A=EXP(-valmin/RT)/[EXP(-valmin/RT)-EXP(valmax/RT)] 
·  B=1/[EXP(-valmin/RT)-EXP(valmax/RT)]. 
 
 Expected  utility  for  an  uncertain  situation  having  probabilistic  distribution  (x,P(x))  is 
computed according to the next formula: 
 
                                                                                                                                                (4) 
  
Once expected value is computed, the corresponding certainty equivalent will be computed 
using the next formula: 
 
                                                                                           …                                       (5) 
 
 In the case of risk aversion and maximization problem, for all nodes will be computed both 
rollback values and expected utilities. Thus: 
· for terminal node, rollback value is equal with terminal value; having terminal value, can 
be computed the corresponding utility;  
· for event node, it is computed expected utility and then rollback value is equal to certainty 
equivalent;  
· for decisional node, rollback value is equals to maximum of the rollback values situated in 
the immediately succesor nodes; having rollback value can be computed expected utility. 
Considering  that  the  only  decision  nodes  are  controllable  factors,  possible  strategies  for 
action, starting from a certain decision tree, are given by the sequence of all relevant options from 
decision nodes.  
∑ = = ) ( * ) ( x x i i U X P EU
] / ) [( * B EU A LN RT CE - - =Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
634 
 
After Rollback method was applied, identifying Rollback values of all nodes, the optimal 
strategy can be identified easily. Key decision-related variants that determine the optimal strategy is 
the  Rollback  values  located  around  to  decision  nodes.  Within  one  decision  node,  the  output 
decisional  variant  that  has  the  rollback  value  identical  with  the  Rollback  value  of  the  input 
decisional  variant  represents  one  component  of  the  optimal  strategy.  On  this  occasion,  within 
decision node, represented by a square, it will be placed the order number of decisional variant that 
satisfies the above condition so that optimal strategy will be identified easily by scrolling sequential 
decision  nodes  and  taking  the  decisional  variants  whose  sequence  number  is  presented  within 
decision nodes.   
 
Research methodology   
Solving a practical decisional problem by the usage of decision trees can emphasize their 
main characteristics in a clearer manner and their utility for decision-maker.  Let's consider the 
following situation (adapted from Middleton 2003): 
 A firm wants to develop a new product. Since the firm hasn’t experience in developing such 
products, it will be appealed to an external firm through the organization of an auction. Current firm 
X wants to sign up for the auction. In case the auction would have won, company X would have an 
income  of  200000EUR.    To  register  to  bid  and  to  elaborate  all  the  necessary  documentation, 
company X will spend 50000EUR. Management of Company X believes that chances of winning 
the auction are 50%. Company X has three ways to provide that product manufacturing: 
·  a manual way to guarantee getting a product as required by the beneficiaries and 
whose cost is 100000EUR  
·  a  semi-automatic  way  to  guarantee  getting  a  product  according  to  customer's 
requirements only in proportion of 50% and whose cost is 40000EUR  
·  a automatic way to guarantee getting a product according to customer's requirements 
only in proportion of  70% and whose cost is 70000EUR  
In case semiautomatic or automatic manufacturing way fails, it will be chosen the manual 
method. It is required to identify the optimal strategy both for neutral attitude towards risk and for 
risk aversion.  
Generation of decision trees and application of their algorithms is among the concerns of 
many  software  producers.  Software  packages  as  Lumenaut  Decision  Tree,  TreeAge  Software, 
Vanguard Software, TreePlan, GraphViz and so on, provide a range of tools that enable us to build 
easily and quickly decision tree models for many real life situations. Within these tools can find the 
Treeplan add-ins, a very useful extension of computer application Microsoft Excel, by which were 
automatically generated decision trees of the problem presented for both neutral version and variant 
of aversion risk.  Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
635 
 
 
Fig. no.1 - Decision tree in the case of neutral attitude towards risk 
 
 
Fig. no.2 - Decision tree in the case of risk aversion Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
636 
 
 
  For the first case (fig. no.1), the above decision tree highlights the optimal decision strategy 
that consist of choosing the first option - preparing documentation (1) - and choosing the second 
option - semi-automatic method for manufacturing process (2)- from the next decision node. 
  In the second case (fig. no.2), decision-maker manifests a risk aversion attitude, accepting to 
bet for a maximum gain having amount 200,000 with a probability of 50% or loss 100 000 with the 
same  probability.  The  decision  tree  indicates  that  with  such  a  profile  regarding  risk,  the  best 
solution is to not participate in the auction (2). 
  Sensitivity  analysis  method  applied  to  the  obtained  decision  tree  may  reveal  important 
aspects of its behaviour, regarding the model sensitivity to changes of different parameters of the 
problem. A good example in this regard is the identification of the decision-maker profile that joins 
the auction. Otherwise said, we study the model sensitivity to parameter changes in RT and we 
identify the point where the optimal variant is changing.  
 
 
Fig. no. 3 - Model sensitivity at the changing of RT parameter 
 
 In the above figure (fig. no.3) ID = 1 has as meaning the participation to the auction while 
ID=2 means the giving up to sign up for the auction. As it can see, in the current problem, a greater 
value of RT than 420000 means that decision maker is willing to sign up for the auction. In other 
words, decision maker will sign-up for the auction when he is willing to bet on a scenario within 
can earn maximum 420000RON with probability of 50% or can lose 210000RON with the same 
probability.   
 
 
 Conclusions 
 A decision tree provides a consistent picture of a decision situation through the alternatives 
that are figured, through potential consequences of these, by presenting the main uncontrollable 
external factors with their probabilities of occurrence and by presenting the output results of action 
strategies. In conditions of uncertainty represented by probabilities, applying algorithm Rollback on Annales Universitatis Apulensis Series Oeconomica, 12(2), 2010 
637 
 
the decision tree provides an optimal strategy to follow for a certain decision problems. The using 
of decision trees supposes mainly 4 steps: 
·  problem structuring in a decision tree form; 
·  attaching probabilities to event edges; 
·  assigning benefits/costs for the edges of decision tree; 
·  choosing  the  optimal  strategy  applying  Rollback  method  both  neutral  attitude 
regarding risk and risk aversion.   
There are many software packages that allow to decision-maker quickly to model real life 
decision processes and select the decision path that produces either the highest or lowest outcome, 
obtaining an optimum solution for their business. With an intuitive interface and graphical output 
these packages are practical for anyone - expert or not - to apply the analytical strengths of decision 
analysis to virtually any decision problem. As tool of electronic decisional support, decision trees 
meet the conviviality requirement of decision support system. Every decision maker can understand 
decision tree models after a previous short explanation. Suggestive graphical representation of a 
decisional situation using decision tree has all chances to be adopted and integrated among the 
working tools of many decision-makers.  
 Furthermore,  finding  a  solution  for  decisional  problems  using  decision  trees  supposes 
attending the main stages of decision making: analysis, modelling, the choosing a solution and its 
implementation. In other words, the software tools based on decision tree can provide support for 
all phases of decisional process.    
   Another  advantage  of  decision  trees  is  the  possibility  of  combining  them  with  other 
decision techniques. Net Present Value or making use of Monte Carlo type simulations are just two 
examples.  For  instance,  in  situations  where  certain  values  can  not  be  expressed  with  a  100% 
certainty,  Monte  Carlo  simulation  offers  a  solution  for  that  decisional  problem  in  probabilistic 
terms. 
As a final conclusion, for making decisions in a certainty or uncertainty economical context, 
the tools based on decision tree analysis technique can be applied with success to many different 
project management situations. 
  
 
References 
1.  Hullet D., 2006. “Decision trees analysis for the risk averse organization”, available on-line 
at http://www.projectrisk.com/Welcome/White_Papers 
2.  Kirkwood  C.,  2002.  “Decision  tree  primer”,  available    on-line  at 
http://www.public.asu.edu/~kirkwood/DAStuff/decisiontrees/index.html 
3.  Mărginean  N.,  2006.  Sisteme  informatice  de  asistare  a  deciziilor,  Ed.  Risoprint,  Cluj-
Napoca 
4.  Middleton M., 2003. Decision Modeling using EXCEL,University of San Francisco 
5.  Stăncioiu  I.,  Militaru  Gh.,  1998.  Management  -  Elemente  fundamentale.  Ed.  Teora, 
Bucure ti 
6.  ***, “Decision trees”, available online at http://en.wikipedia.org/wiki/Decision_tree 

Decision Modeling using EXCEL,University of San Francisco

Decision trees analysis for the risk averse organization”, available on-line at http://www.projectrisk.com/Welcome/White_Papers

Management - Elemente fundamentale.

Sisteme informatice de asistare a deciziilor,

DECISION TREES – A PERSPECTIVE OF ELECTRONIC DECISIONAL SUPPORT

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DECISION TREES – A PERSPECTIVE OF ELECTRONIC DECISIONAL SUPPORT

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