Use of Stochastic Compromise Programming to develop forest management alternatives for ecosystem services

Transkriptio

1 Use of Stochastic Compromise Programming to develop forest management alternatives for ecosystem services Kyle Eyvindson Forest Science Department / Kyle Eyvindson 3/26/2014 1

2 Overview Introduction of Compromise programming through an example simulated forest, managing opinions and timber Moving towards integrating uncertainty through Stochastic programming

3 What is Compromise programming? An Operations Research tool which finds a solution to a problem which requires limited preference information from a decision maker. All that is required is that the DM identifies Criterion which are important

4 The CP formulation: Compromise programming: (Yu,1973) The standard formulation:

5 Visualization L 1 metric minimizes the aggregated distance to the ideal point, L 2 metric minimizes the euclidean distance, L minimizes the maximum distance. (Miettinen, 1999)

6 What is the meaning behind the distances? In a general perspective, L 1 -solution provides the maximum aggregated (average) achievement between the different goals. The most efficient solution L - solution minimizes the maximum disutility (disagreement) or what is equivalent to the maximization of the balance between the levels of achievement of the different The most equitable solution (Baltiero et al. 2013)

7 The CP formulation? This formulation minimizes the distance for all Criterion using the same measurement metric. For cases in forestry, this may not necessarily be appropriate. We may want to treat economic goals according to a philosophy of efficiency, whereas ecological goals may be better served according to equity

8 Modified Compromise Programming General modified formulation: weighs the different distance metrics Normalizes different distance metrics

9 Formulation of Problem A simplified yield and growth table was used. For each time period, the forest would develop 1 step. thinning was allowed for middle aged, mature and old stands, providing timber of 100, 250 and 300 m3 respectively clear-cutting was allowed for mature and old stands, providing timber of 500 and 600 m3. The problem then is to maximize the opinions, while maximizing the timber provided

10 Aggregation of Opinions Aggregated both comprehensively and based on group membership. Group 1 Group 2 Group 3 Complete aggregation Clear Cut New Stand Young Spruce Mid-aged Spruce Mature Spruce Old Spruce Young Pine Mid-aged Pine Mature Pine Old Pine Young Birch Mid-aged Birch Mature Birch Old Kyle Birch Eyvindson

11 Formulation of Problem General modified formulation:

12 Formulation of Problem and could be subject to the constraint: Which is a sustainability constraint, ensuring that the value for the criterion does not decrease over time

13 Formulation of Problem Justification: Why segregate into partitions? In this case we have clearly economic Criterion, and clearly non-economic Criterion. One metric provides balances (L ) minimizes the maximum deviation. One provides efficiency (L 1 ) minimizes the aggregate deviation

14 Results With Aggregated preferences

15 Results With Grouped preferences

16 Results Differences in treatments top aggregated, bottom grouped

17 Moving towards Stochastic Compromise programming? Briefly about Stochastic Programming: A method for including uncertainty into the optimization process One method is to represent the uncertainty is through creating a representative set of possible scenarios. So where the non-stochastic version solves the problem for one scenario, the stochastic version solves the problem for many possible scenarios

18 The optimization matrix: Standard CP Stand 1 Stand 2 deviations Schedule 1 Schedule 2 Schedule 1 Schedule 2 Schedule 3 Critierion 1 XX XX XX XX XX 1 = Y1 Critierion 2 XX XX XX XX XX 1 = Y2 Critierion 3 XX XX XX XX XX 1 = Y3 Area constraint 1 1 = = 1 Solution Z1 Z2 Z3 Z4 Z5 Z6 to Z9 Kyle Eyvindson

19 The optimization matrix: Stochastic CP Stand 1 Stand 2 Deviations Schedule 1 Schedule 2 Schedule 1 Schedule 2 Schedule 3 Iteration 1 Criterion 1 XX XX XX XX XX 1 = Y1 Criterion 2 XX XX XX XX XX 1 = Y2 Criterion 3 XX XX XX XX XX 1 = Y3 Iteration 2 Criterion 1 XX XX XX XX XX 1 = Y1 Criterion 2 XX XX XX XX XX 1 = Y2 Criterion 3 XX XX XX XX XX 1 = Y3 Iteration 3 Criterion 1 XX XX XX XX XX 1 = Y1 Criterion 2 XX XX XX XX XX 1 = Y2 Criterion 3 XX XX XX XX XX 1 = Y3 Area constraint 1 1 = = 1 Solution Z1 Z2 Z3 Z4 Z5 Z6 to Z15 Kyle Eyvindson

20 Complications by introducing stochasticity Increasing problem size Need to compare similar results Development of formulations which take advantage of the estimates of uncertainty

21 References Birge, J.R. and F. Louveaux, Introduction to stochastic programming. Springer-Verlag. Diaz-Balteiro, L., González-Pachón, J., & Romero, C. (2013). Goal programming in forest management: customising models for the decision-maker's preferences. Scandinavian Journal of Forest Research, 28(2), Miettinen, K. (1999) Nonlinear Multiobjective Optimization. Klower s Academic Publishers. Dordrecht, The Netherlands. Yu P A class of solutions for group decision problems. Management Science 19(8):