MCDA in natural resources management PART II

1. MCDA in natural resources managementPART II Jouni Pykäläinen, D.Sc.(For.) Metsämonex Ltd

2. Brief introduction to MCDA methods • mathematical programming • MAUT ”family” • voting methods

3. Mathematical programming • linear programming, LP • goal programming, GP • multi-objective linear programming, MOLP

4. Linearity and additivity assumptions in mathematical programming • NRE management goals defined with linear goal and constraint equations (linearity assumption) • values of the goal(s) and constraints calculated as sums or means of the calculation units (additivity assumption)

5. Standard linear programming, LP • one objective function at a time • other goals defined with constraints • does not serve multi-criteria planning in the best possible way • interactive use of linear programming allows multi-criteria planning

6. Goal programming, GP • weighted sum of the deviations from the target values of the goal variables are minimized • corresponds to the idea of multi-criteria planning better than the standard linear programming • both prior and progressive articulation of preferences have been used in the applications of GP • varying the weights of deviations from the target levels is a common way to use GP interactively

7. Multi-objective linear programming, MOLP • attention to the technical efficiency of the solutions • solution gradually improved • Interactive articulation of preferences • travelling on the efficient frontier of the alternative solutions • constraints of feasible solutions, the weights, trade-offs or aspiration levels of the goal variables used for defining the goals • #A# lot of different algorithms

8. Multi-attribute utility theory, MAUT • MAUT evaluates decision alternatives by comparing the utilities produced by them • it is assumed that the DM selects a plan that maximizes #THE# #POIS:his# expected utility • the applications of MAUT often use explicit utility functions

9. Additive utility function • most commonly used form of utility functions • sums up the weighted sub-utilities attained by producing different goals • generally speaking, an additive formulation of the utility function best describes the DM's real preferences

10. Sub-utility functions Criteria/sub-criteria have different values in different alternatives Sub-utility functions transform values of the criteria measured in their own units into subjective sub-utility values [0-1].

11. Calculating the total utilities produced by the alternatives • rescaled (weighted) sub-utilities are summed up where ui(qi) is a sub-utility function for criteria i qi is the value of criteria i ai is the weight of criteria i n is the number of criteria

12. MAUT and heuristic optimization • heuristic algorithms needed when searching the best alternative from a very large mass of decision alternatives • heuristics allow a versatile and flexible problem formulation without a remarkable loss in the efficiency of the computing stage • many goals of heuristic optimization, e.g. spatial goals in forest planning, cannot be easily included in mathematical programming • mostly been used according to the principle of prior articulation of preferences • can be applied in interactively due to improved computing capacity

13. Analytic hierarchy process • widely applied MAUT application • decision criteria and alternatives compared #pairwise# in relation to the upper level elements in a decision hierarchy • local and global priorities calculated based on the results of the paired comparisons • AHP also allows qualitatively measured criteria • pairwise comparisons of the decision alternatives must be done separately for every set of alternatives • it is suggested that the number of alternatives be limited #TO# under 10, since otherwise the amount of the pairwise comparisons becomes too large

14. Uncertainty related to outcomes of the alternatives explicitly in utility functions • Alternative approaches • uncertainty as a separate criterion • estimating sub-utility functions for different outcome levels of the criteria (e.g. for the worst, expected and the best levels) and giving weights for these sub-utility functions • probabilities of different outcome levels must be known • weighting criteria according to uncertainty related to outcomes of them

15. Uncertainty as a criterion

16. Including different realization levels of the criteria into the utility function Weights for the sub-criteria worst, expected and the best income according to the DM’s risk behaviour. Probabilities of different outcomes are known. #A RISK# #POIS:Risk# seeker gives strong weight for the best income and a risk avoider gives strong weight for the worst income. A risk neutral person gives a strong weight for the expected income.

18. Voting methods • Cumulative voting • Borda count • Multi-criteria approval

19. Cumulative voting • every voter is given as many votes as there are candidates in the election • each voter can cast his votes according to his preferences • a common modification: each voter distributes 100 points among the candidates according to his preferences

20. Borda count –method • takes into account the voters’ preference ordering for candidates • in the case of n candidates, each voter gives n votes for the most preferred candidate • n-1 for the second preferred candidate • finally one vote for the least preferred candidate • candidate receiving the most votes is the winner

21. #Multi-criteria# approval -voting • multi-criteria decision making • approval borders first set for the criteria • in the basic version of MA, the average values of the criteria are selected for the approval borders • alternatives into approved and disapproved cateqories in relation to each criterion • depending on whether the criterion value in the specific alternative is better or worse than the corresponding approval border • alternatives ranked based on this classification and the importance order of the criteria • can be used for group decision making as long as the decision makers agree on the order of importance and the approval borders for the criteria

22. Voting results in MA • unanimous: one and only one of the alternatives is approved in relation to all the criteria • majority: one alternative is approved in relation to the majority of the most important criteria (selected by the decision maker(s)) that other alternatives are not • ordinally dominant: an alternative is approved and is better than the other candidates in relation to the order of importance of the criteria • deadlocked: two or more alternatives do as well in relation to the criteria in their order of importance • indeterminate: no alternative can be judged to be the best one on the basis of the criteria’s ordinal importance order, and instead more information is needed