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 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 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 Expand large 164000 225000 200000 Expected value analysis [0,30..0,70] Probability of occurence [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 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 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 !