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 (rozhodovací uzly)
–Decision alternatives – branches of the tree off the decision nodes (alternativy řešení )
–Chance events – events that could affect a decision, branches or arrows leaving circular chance
nodes- (co může rozhodnutí ovlivnit)
–Outcomes – each possible alternative listed (výstupy, výsledky, závěry,…)
–Payoff-   (prospěch, výhoda výnos – využití v posledním příkladu)
•
1

DT diagrams
•Decision trees developed by
–Drawing from left to right (kreslí se zleva doprava)
–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%) (součet
pravděpodobností všech možností)
–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 demand later or the second alternative is 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
200000
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
renovace po
 částech
Expand  large
rozšíření hospody
najednou
164000
225000
200000
Expected value
     analysis= EVA
[0,3..0,7]
Probability of occurance
[50 000 , 80 000 …300 000]
Chance event outcomes
50 000

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
200000
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  !
Despite the fact , that  there is 30 %  chance , that
this might be worst decision  !

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 USD each time  !!
Because EVA(x) =å p(xi)*xi for=1 to n,
Where Xi = outcome i and p(xi) is a probability
of outcome i

Example III
•The first decision facing the company is whether to expand or buy land. If the company expands,
two states of nature is possible. Either the market will grow (probability 0,6) or it will not grow
(probability 0,4). •Either state of nature will result in a payoff. On the  other hand, if company
chooses to purchase land, three years in the future another decision will have to be made regarding
the development of the land

DT-Example III
Resource: Russel and Taylor  Operation management pages 66-67


DT-Example III



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


2 540 000 – 800 000 =1 740 000
1 740 000*0,6 + 790 000*0,4=1 360 000
1 360 000-200 000= 1 160 000
1 290 000-800 000=490 000

3 000 0000 * 0,8 + 700 000 *0,2=2 540 000

Final decision
•Expand  : 129 000-800 000= 490 000
•Land :        1 360 000-200 000 = 1 160 000
•Payoff of purchasing land is 1,16 milions

Thanks for your attention
my dear decision makers !