Advanced Engineering Project Management Dr. Nabil I. El Sawalhi Assistant professor of Construction Management

Transcription

1 Advanced Engineering Project Management Dr. Nabil I. El Sawalhi Assistant professor of Construction Management 1

2 Decision trees Decision trees are tools for classification and prediction. 2

3 Decision Trees The Payoff Table approach is useful for a non-sequential or single stage. Many real-world decision problems consists of a sequence of dependent decisions. Decision Trees are useful in analyzing multi-stage decision processes. 3

4 DECISION TREES Used when: Single stage decision-making is required; Multi-stage decision-making is required; Schematic representation is useful. Consists of: Nodes; commonly represented by squares Branches; represented by lines Chances; represented by circles Probability estimates; Payoffs. End nodes - represented by triangles 4

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6 Decision nodes require a conscious decision on which branch to choose, typically shown as a square. Chance nodes show different possible events that can confront a chosen strategy, typically shown as a circle. Decision Branches represent a strategy or course of action, sometimes shown as two parallel lines. 6

7 Chance Branches represent a chancedetermined event, sometimes shown as a single line. Terminal Branches mark the end of the decision tree. Decision trees can be deterministic or probabilistic (stochastic). 7

8 DETERMINISTIC DECISION TREE Example 1. Excavator replacement decision The site manager for Droflas Construction has three alternative choices relating to the replacement of a mechanical excavator. They are shown in the payoff matrix: 8

9 Profit or Payoff ( ) Strategy Year 1 Year 2 Total S 1 : Replace Now S 2 : Replace after 1 year S 3 : Do not Replace

10 Draw the appropriate decision tree and identify the appropriate solution Decision Tree DN#1 Replace now Do not replace 5000 Replace DN#2 Do not replace First year AEPM Second L11 year 10

11 Example 2 A manager has developed a table that shows ($000) for future store. The payoffs depend on the size of the store and the strength of demand: Small Large The manager estimate that the probability of low demand is equal to the probability of high demand. The manager could request that a local research firm conduct a survey (cost $2000) that would better indicate wither demand will be low or high. In discussion with the research firm the manager has learned the following about the reliability of survey conducted by the firm. 11

12 » Actual results» Low high Survey showed low high a. if the manager should decide to use the survey, what would the revised probabilities be demand and what probabilities should be used for survey results (i.e. survey shows high demand) B. construct a tree diagram C. determine the EMV 12

13 A. the following are revised probabilities if survey shows low demand Actual demand Conditio nal p Prior p Joint p Revised p low 0.9 x 0.5 =.45.45/.6=.75 high 0.3 x 0.5 =.15.15/.6=.25 13

14 A. the following are revised probabilities if survey shows low demand Actual demand Condition al p Prior p Joint p Revised p low 0.1 x 0.5 =.05.45/.4=.125 high 0.7 x 0.5 =.35.15/.4=

15 Low p.6 Small d Survey Large.25 d1 HD p d No Survey

16 No Survey d1 Small d4 Large

17 Example 3 The Metal Discovery Group (MDG) is a company set up to conduct geological explorations of parcels of land in order to ascertain whether significant metal deposits (worthy of further commercial exploitation) are present or not. Current MDG has an option to purchase outright a parcel of land for 3m. If MDG purchases this parcel of land then it will conduct a geological exploration of the land. Past experience indicates that for the type of parcel of land under consideration geological explorations cost approximately 1m and yield significant metal deposits as follows: 17

18 manganese 1% chance gold 0.05% chance silver 0.2% chance Only one of these three metals is ever found (if at all), i.e. there is no chance of finding two or more of these metals and no chance of finding any other metal. If manganese is found then the parcel of land can be sold for 30m, if gold is found then the parcel of land can be sold for 250m and if silver is found the parcel of land can be sold for 150m. 18

19 MDG can, if they wish, pay 750,000 for the right to conduct a three-day test exploration before deciding whether to purchase the parcel of land or not. Such three-day test explorations can only give a preliminary indication of whether significant metal deposits are present or not and past experience indicates that threeday test explorations cost 250,000 and indicate that significant metal deposits are present 50% of the time. If the three-day test exploration indicates significant metal deposits then the chances of finding manganese, gold and silver increase to 3%, 2% and 1% respectively. If the three-day test exploration fails to indicate significant metal deposits then the chances of finding manganese, gold and silver decrease to 0.75%, 0.04% and 0.175% respectively. 19

20 What would you recommend MDG should do and why? A company working in a related field to MDG is prepared to pay half of all costs associated with this parcel of land in return for half of all revenues. Under these circumstances what would you recommend MDG should do and why? Below we carry out step 1 of the decision tree solution procedure which (for this example) involves working out the total profit for each of the paths from the initial node to the terminal node (all figures in '000000). 20

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22 Step 1 path to terminal node 8, abandon the project - profit zero path to terminal node 9, we purchase (cost 3m), explore (cost 1m) and find manganese (revenue 30m), total profit 26 ( m) path to terminal node 10, we purchase (cost 3m), explore (cost 1m) and find gold (revenue 250m), total profit 246 ( m) path to terminal node 11, we purchase (cost 3m), explore (cost 1m) and find silver (revenue 150m), total profit 146 ( m) path to terminal node 12, we purchase (cost 3m), explore (cost 1m) and find nothing, total profit -4 ( m) 22

23 path to terminal node 13, we conduct the three-day test (cost 0.75m m), find we have an enhanced chance of significant metal deposits, purchase and explore (cost 4m) and find manganese (revenue 30m), total profit 25 ( m) path to terminal node 14, we conduct the three-day test (cost 0.75m m), find we have an enhanced chance of significant metal deposits, purchase and explore (cost 4m) and find gold (revenue 250m), total profit 245 ( m) path to terminal node 15, we conduct the three-day test (cost 0.75m m), find we have an enhanced chance of significant metal deposits, purchase and explore (cost 4m) and find silver (revenue 150m), total profit 145 ( m) 23

24 path to terminal node 16, we conduct the three-day test (cost 0.75m m), find we have an enhanced chance of significant metal deposits, purchase and explore (cost 4m) and find nothing, total profit -5 ( m) path to terminal node 17, we conduct the three-day test (cost 0.75m m), find we have an enhanced chance of significant metal deposits, decide to abandon, total profit -1 ( m) path to terminal node 18, we conduct the three-day test (cost 0.75m m), find we have an reduced chance of significant metal deposits, purchase and explore (cost 4m) and find manganese (revenue 30m), total profit 25 ( m) 24

25 path to terminal node 19, we conduct the three-day test (cost 0.75m m), find we have an reduced chance of significant metal deposits, purchase and explore (cost 4m) and find gold (revenue 250m), total profit 245 ( m) path to terminal node 20, we conduct the three-day test (cost 0.75m m), find we have an reduced chance of significant metal deposits, purchase and explore (cost 4m) and find silver (revenue 150m), total profit 145 ( m) path to terminal node 21, we conduct the three-day test (cost 0.75m m), find we have an reduced chance of significant metal deposits, purchase and explore (cost 4m) and find nothing, total profit -5 ( m) 25

26 path to terminal node 22, we conduct the three-day test (cost 0.75m m), find we have an reduced chance of significant metal deposits, decide to abandon, total profit -1 ( m) Hence we can arrive at the table below indicating for each branch the total profit involved in that branch from the initial node to the terminal node. 26

27 Terminal node Total profit

28 We can now carry out the second step of the decision tree solution procedure where we work from the righthand side of the diagram back to the left-hand side. Step 2 Consider chance node 7 with branches to terminal nodes emanating from it. The expected monetary value for this chance node is given by (25) (245) (145) (-5) = Hence the best decision at decision node 5 is to abandon (EMV=-1). The EMV for chance node 6 is given by 0.03(25) (245) (145) (-5) =

29 Hence the best decision at decision node 4 is to purchase (EMV=2.4). The EMV for chance node 3 is given by 0.5(2.4) + 0.5(-1) = 0.7 The EMV for chance node 2 is given by 0.01(26) (246) (146) (-4) = Hence at decision node 1 have three alternatives: abandon EMV=0 purchase and explore EMV= day test EMV=0.7 Hence the best decision is the 3-day test as it has the highest expected monetary value of 0.7 ( m). 29

30 Sharing the costs and revenues on a 50:50 basis merely halves all the monetary figures in the above calculations and so the optimal EMV decision is exactly as before. However in a wider context by accepting to share costs and revenues the company is spreading its risk and from that point of view may well be a wise offer to accept. 30

31 STOCHASTIC DECISION TREES Example 4 Based upon the recommendations of their strategic planning group, Droflas Associates has decided to expand their present organisation. Having considered several alternatives, the following strategies were considered to be viable options: Strategy A: Build a large office with an estimated cost of 2M. 31

32 This alternative can face two states of nature (market conditions), high demand for surveying services with a probability of 0.7 or low demand with a probability of 0.3. If the demand is high, the company can expect to receive an annual cash flow of for 7 years. If the demand is low, the annual cash flow would be only because of the large fixed costs and inefficiencies caused by the small work load. 32

33 Strategy B: Build a small office with an estimated cost of 1M. This alternative also faces two states of nature, high demand with a probability of 0.7 and low demand with a probability of 0.3. The company expects to receive an annual cash flow of or if demand is high or low respectively. If the demand is low and remains low for 2 years the office will certainly not be expanded. 33

34 However, if initial demand is high and remains high for 2 years they will face another decision of whether or not to expand the office. It is assumed that the cost of expanding the office at that time will be 1.5M. Further, it is assumed that after this second decision, the probabilities of high and low demand will remain the same. If the decision to expand is made, the company then expects to receive an annual cash flow of or if the demand is high or low respectively. 34

35 Which is the optimal strategy? Elements needed to construct a decision tree: All decision and chance nodes; Branches that connect various decision and chance nodes; Payoff (reward or cost), if any, associated with branches emanating from decision nodes; Probability value associated with branches emanating from chance nodes; 35

36 Payoffs associated with each chance node; Payoffs associated with each terminal branch at the conclusion of each path that can be traced through various combinations that form the tree; Position values of chance and decision nodes; The process of rollback. 36

37 Some possible refinements: The sequence of decisions can involve a larger number of decisions; At each decision node, consider a larger number of strategies; At each chance node, consider a larger number of chance branches, or assume a continuous probability distribution at each chance node; 37

38 More sophisticated and more detailed projections of cash flows can be introduced; Discounted cash flows can be introduced; The quality of risk can be explicated by estimating the range or standard deviation of the payoff distribution for each path; Sensitivity testing and sensitivity analysis can be introduced. 38

39 2.66m CN#1 HD.7, cash.5m A1 Large office 2m LD.3 cash.1m 2 YEARS 5 YEARS A2 DN# HD.7, cash.6 B1 Small office, 1m HD.7, cash 0.3 Expand 1.5m DN#2 Not expand CN# LD.3, 0.1 HD.7, cash.3 B2 B3 CN#4 CN#2 LD.3, 0.15 m LD.3, 0.15 B4 B5 39

40 Large office EMV1=-2+0.7x.5x7+ 0.3x0.1x7 = 0.66m(best strategy) Small office expand after 2y DN #2 =.7x.3x5 +.3x.15x5=1.275m Small office Not Expand EMV2 = x.7 +.7x.3x2 +.3x.15x 2=0.402m 40