Decision trees(basics)
Ing.J.Skorkovský, CSc,
Department of Corporate Economy
FACULTY OF ECONOMICS AND ADMINISTRATION
Masaryk University Brno
Czech Republic

Description
•Diagramming technique which uses :
–Decision points – points in time when decisions are made, squares called nodes
–Decision alternatives – branches of the tree off the decision nodes
–Chance events – events that could affect a decision, branches or arrows leaving circular chance
nodes
–Outcomes – each possible alternative listed
•

DT diagrams
•Decision trees developed by
–Drawing from left to right
–Use squares to indicate decision points
–Use circles to indicate chance events
–Write the probability of each chance by the chance (sum of associated chances = 100%)
–Write each alternative outcome in the right margin
•
1

DT-Example I
•A restaurant owner has determined, that he needs to expand his facility. He has two alternatives.
One is one large expand now and risk smaller (lower) demand later or the second alternative is to
expand on a smaller scale now knowing, that he might need to expand again in three years. Which
alternative would be most attractive?
1
2
164000
225000
High demand (0,70)
High demand (0,70)
Low demand (0,30)
Low demand (0,30)
80 000
300 000
150 000
200 000
Expand
Do not expand
Expand  small
Expand  large
164000
225000
200000
Expected value
     analysis
[0,30..0,70]
Probability of occurrence
[50 000 , 80 000, 150 000, 200 000, 300 000  …]
Chance event outcomes
50 000
Calculation of these figures will be
 shown on the next slide
200 000

DT-Example I
•Decision tree analysis utilizes Expected Value Analysis (EVA), which is a weighted average of the
chance events :
–Probability of occurrence * chance event outcome
•
•
1
2
164000
225000
High demand (0,70)
High demand (0,70)
Low demand (0,30)
Low demand (0,30)
80 000
300 000
50 000
150 000
200 000
Expand
Do not expand
At
2
we do have
200 000 >150 000
So EXPAND !!!
Expand  small
Expand  large
Calculated (Expected Value) is : EVA small =0,3*80 000+0,7*200 000=164 000
Calculated (Expected Value) is : EVA large =0,3*50 000+0,7*300 000=225 000

At decision point 1 we have got clear result
Choose Expand Large   ->225000>164000
despite the fact, that  there is 30 %  chance , that
this might be worst decision!
[50 000 , 80 000, 150 000, 200 000, 300 000  …]
Chance event outcomes
200 000

DT-Example II
•Project to sell candies or lemonade. At the first sight it is clear : Candy !!
Resource: MBABullshit.com
0,5*100+ 0,5*(-30)=35 USD
0,5*90+ 0,5*(-10)=40 USD

DT-Example II
•So now it would be better to choose lemonade business ! So we have chosen bigger EVA. But..
Resource: MBABullshit.com
0,5*100+ 0,5*(-30)=35
0,5*90+ 0,5*(-10)  =    40
Decision based on EVA? Does this mean, that
if you do Lemonade project, you will earn 40? NO !
If you did the IDENTICAL Lemonade project
very many times (in exactly the same situation), then your
 average earnings  will be probably 40 per time.
This means that you will not get 40 US each time  !!
Because EVA(x) =å p(xi)xi for=1 to n,
Where Xi = outcome i and p(xi) is a probability
of event outcome i

Text related to the next example (sequential decision tree)
•
•The Southern Textile company is considering two alternatives: to expand its existing production
operation to manufacture a new line of lightweight material or to purchase land on which to
construct a new facility in the future.
•
•Each of these decision has outcomes based on product market growth in the future that results in
another set of decisions  (during a 10-Years planning horizon . as shown in the following figure of
the sequential decision tree.
•
•Nodes represent decisions, and the circle nodes reflect the different status of nature and their
probabilities
•
•So the first decision facing the company is whether to expand or buy land.
•
•

DT-Example III
Resource: Russel and Taylor  Operation management pages 66-67
1
Decision point
Chance event
(see Excel file with calculations !!!!!)
Payoff= contribution-benefit ->not in parentheses and sign is plus
Cost of ventures (-USD 200 000 and so on are in parentheses- cost are represented by minus sign )

DT-Example III
1
Decision point
Chance event

Decision tree calculation
Outcome
Probability
EVA
Expand

3 000 000,00
0,80



700 000,00
0,20
2 540 000,00







2 540 000,00

1 740 000,00
-800 000,00

1 740 000,00
0,60



790 000,00
0,40
1 360 000,00







1 360 000,00

1 160 000,00
-200 000,00

1 290 000,00

490 000,00
-800 000,00

Thanks for your attention
my dear decision makers !