Decision Making: The Structuring

Transcription

1 ENGS 41 SUSTAINABILITY and NATURAL RESOURCE MANAGEMENT Decision Making: The Structuring Source: Decision Making in Natural Resource Management by M. J. Conroy & J. T. Peterson, 2013 (Chapter 6) Benoit Cushman Roisin February 2018 Influence Diagram: An influence diagram is a graphical representation of the decision process. Its elements are: contain uncertainties NODES Decision Variable Event Outcome Consequence Payoff LINKS utility Dependence, if leading to variable/event or outcome/consequence/payoff Sequence, if leading to a decision Not a flow chart Both causal and non causal influences No cycles! Easy to interpret; sometimes hard to draw. 1

2 Example Improve habitat? Decision Yes If information used in making decision size Affects size Variables (numbers, each with uncertainty) Leads to Outcome Consequence Payoff A root node is a node with no arrow leading to it (above: current size and decision in absence of information on current ). If the root node is a variable or event, it must be one that is independent of the decision maker (ex. a present state or future weather condition). An important distinction about information: Example: may be used as information to make the decision. But how well known is this information? Have the animals been actually counted? (comprehensive data) Or, has some inference been drawn from a few observations? (fragmented data + some reasoning) If one has very reliable data, we call that Perfect Information (PI). Most often, however, the number is the result of incomplete information. We call that Sample Information (SI). 2

3 Sample the? Improve habitat? Field sampling results size size Another example with 2 sequential decisions Restore Habitat? habitat habitat Reintroduce species? Species well being 3

4 Influence diagrams may not be cyclic, but there are time when repetition is needed. This is handled by repeating the portion of the influence diagram! Harvest? (at time t=1) Harvest? (at time t=2) Harvest? (at time t=3) Population size (at t=1) Population size (at t=2) Population size (at t=3) Harvest #1 Harvest #2 Harvest #3 Cumulative Harvest Implementing the cost relations Restore Habitat? habitat habitat Reintroduce species? Species well being $ $ 4

5 Direct and indirect effects: Streamflow Stream habitat Fish Forest fire Vegetation Bird Case of even more indirect relations: When linking complementary models Landscape model Precipitation Land use change? Soil disturbance fish Fish habitat model Streambed sediment Stream habitat fish 5

6 Exercise: Farmer with land, water and labor (each with its known limit) deciding whether to grow cotton, barley or both QUESTION for us: How do we represent the farmer s decision(s) with an influence diagram? Farm for another year or retire? Grow cotton? Grow barley? Total land available Land for cotton River Land for barley Water for cotton Total water available Town Water for barley Labor for cotton Total labor available Labor for barley Cotton sold Total sales Barley sold 6

7 Ascribing states to nodes: Improve Habitat? Yes / No habitat 0 33% / 33 67% / % habitat 0 33% / 33 67% / % / 0 50 / / > / / >100 Node states must be mutually exclusive and collectively exhaustive (all possibilities covered) Pro s and Con s of Influence Diagrams: Advantages of Influence Diagrams The omission of detailed node states leads to a clear overview even for rather complex decision problems. It is easy to combine influence diagrams into rather complex system models. Disadvantages of Influence Diagrams o Rather cumbersome to develop. o Lists of decision alternatives and node states have to be provided in addition to the diagram to show all information (or boxes get crowded). 7

8 From an influence diagram to a decision tree: Case of 3 levels Improve Habitat? Yes / No / / >100 Improve habitat > / >100 Note: The same outcome (ex. ) can be reached in multiple ways (6 ways here). Pro s and Con s of Decision Trees: Advantages of Decision Trees The consideration of node states leads to a visual graphical representation of the problem. For more complex problems, the procedure may be automated. Disadvantages of Decision Trees o Need to come up with probabilities of the different node states. o The tree can become very complicated in the case of many alternatives, outcomes, decisions or variable nodes. 8

9 Comparison of Influence Diagrams and Decision Trees: Influence diagrams and decision trees are isomorphic (not at all identical, but with one to one correspondence). Influence diagrams are preferred in the problem structuring phase. When the problem is complex, influence diagrams can still be drawn while decision trees get too large for presentation. Decision trees show more detail, hence are more useful for in depth understanding and sensitivity analysis. Another example: Case with 4 levels: Timber harvest? Yes / No Stream habitat Good / Poor Small / Large Socio economic Score 1 to 4 Small / Large Timber harvest Now adding probabilities Stream habitat Finally, adding utility s Utility

10 From the sequential probabilities, we can calculate utilities per branch: Stream habitat Utility Utility expectation = 0.35 x 0.80 x 0.30 x 2 = Timber harvest YES to timber harvest Stream habitat Utility expectation Good Small Small 0.35 x 0.80 x 0.30 x 2 Good Small Large 0.35 x 0.80 x 0.70 x 4 Good Large Small 0.35 x 0.20 x 0.10 x 2 Good Large Large 0.35 x 0.20 x 0.90 x 4 Poor Small Small 0.65 x 0.80 x 0.60 x 2 Poor Small Large 0.65 x 0.80 x 0.40 x 4 Poor Large Small 0.65 x 0.20 x 0.50 x 2 Poor Large Large 0.65 x 0.20 x 0.50 x 4 SUM: Now, do the same for the opposite case of NO timber harvest and compare: Stream habitat Utility expectation Good Small Small 0.35 x 0.80 x 0.30 x 2 Stream Good Small Large 0.35 x 0.80 x 0.70 x 4 Utility expectation habitat Good Large Small 0.35 x 0.20 x 0.10 x 2 Good Small Small 0.60 x 0.80 x 0.30 x 1 Good Large Large 0.35 x 0.20 x 0.90 x 4 Good Small Large 0.60 x 0.80 x 0.70 x 3 Poor Small Small 0.65 x 0.80 x 0.60 x 2 Good Large Small 0.60 x 0.20 x 0.10 x 1 Poor Small Large 0.65 x 0.80 x 0.40 x 4 Good Large Large 0.60 x 0.20 x 0.90 x 3 Poor Large Small 0.65 x 0.20 x 0.50 x 2 Poor Small Small 0.40 x 0.80 x 0.60 x 1 Poor Large Large 0.65 x 0.20 x 0.50 x 4 Poor Small Large 0.40 x 0.80 x 0.40 x 3 SUM: Poor Large Small 0.40 x 0.20 x 0.50 x 1 YES to timber harvest Poor Large Large 0.40 x 0.20 x 0.50 x 3 SUM: NO to timber harvest CONCLUSION: There is greater utility after timber harvest. DECISION: Go ahead with the timber harvest 10

11 Programmed on spreadsheet Decision harvest yes no.xlsx 11