Peter Lohmander Professor of Forest Management and Economic Optimization

1. Optimal Forest Management Under RiskInternational Seminars in Life SciencesUniversidad Politécnica de Valencia Thursday 2007-02-22 Peter Lohmander Professor of Forest Management and Economic Optimization SLU, Swedish University of Agricultural Sciences Umea, Sweden http://www.Lohmander.com Version 2007-02-18

2. Schedule of Peter Lohmanderfrom Claudio Benavent,International Officer ETSMRE - ETSIA Thursday 2007-02-22 10:30 Welcome at ETSMRE 10:45-13:45 Visits on campus and interviews with UPV Colleagues 14:00 Lunch on campus offered by ETSMRE 16:30 Conference in International Seminars 19:30 Free programme Friday 2007-02-23 10:30 Interview with Prof. Penny McDonald, Coordinator of the course "Preparation for International Study" 11:00-12:15 Institutional Presentation of your home Institution 12:30-13:30 International Office ETSMRE 14:00 Lunch on campus offered by ETSMRE 15:30 Free programme Location: ETSMRE International Office (Avda. Blasco Ibáñez, 19-21).

3. AMBITION Research that leads to economically profitable and practical solutions and at the same time leads to new discoveries of methods and practical general approaches to problems in operations research in general and to forest economics. “Environmentally friendly” solutions are sometimes discovered also to be economically optimal!

4. Stochastic Dynamic Optimization The future state of the world is hard to predict perfectly. Some decisions must be made before the future is perfectly known. Stochastic Dynamic Programming is the relevant approach.

5. The unpredictable world and the decision problems

6. Figure 1.The real (inflation adjusted) stumpage price in Sweden. Source: Swedish Board of Forestry, Yearbook of Forest Statistics, 2000. We may regard the stumpage price as a stochastic processes. There is no method available which can predict future prices without error.

7. Stochastic prices and optimal adaptive harvest decisions

8. Stochastic windthrows and optimal adaptive spatial harvest

9. Optimal initial species mix and optimal adaptive selective thinnings

10. Stochastic spatial forest fires and optimal adaptive planning

11. Stochastic fungi damages and optimal adaptive harvesting

13. Stochastic spatial harvesting and economies of scale

14. Stochastic Price

15. Stochastic Price

16. Low Correlation between Energy Prices and Pulp Prices (Source: Statistics Sweden)

17. Low Correlation between Energy Prices and Pulp Prices

18. Low Correlation between Energy Prices and Pulp Prices • It has been proved that the expected marginal capacity value of a production plant increases with price variation when different products are produced with the same type of raw material and the correlation between product prices is less than 1. (Lohmander 1989)

19. Low Correlation between Energy Prices and Pulp Prices • As a consequence, the most profitable investment level in production capacity, for instance a power plant, is higher with prices that are not perfectly predictable than according to what you find with traditional calculation.

20. Joint probability density function with correlation 0.25 (which corresponds to the prices of electricity and kraft paper)

21. Stochastic dynamic example with heating and pulp plants P2 Time P2 P2 P1 P1 P1 The prices of electricity and kraft paper are not known many years in advance.

22. Stochastic dynamic example with heating and pulp plants Time Stock level The stock level can be changed over time. The most profitable extraction (harvest) in a particular period is affected by the prices of kraft paper and energy. This is one reason why it has to be sequentially optimized, based on the latest price information from the markets.

23. Stochastic dynamic example with heating and pulp plants P2 Time P2 P2 P1 P1 Time P1 Stock level

24. The stochastic dynamic optimization problem We maximize the expected present value of all future production. The production of electricity and kraft paper in future periods is affected by the product prices and the stock of resources. The stock of resources is dynamically optimized.

25. The stochastic dynamic optimization problem The optimal expected present value, f, as a function of time, the stock level and the prices electricity and kraft paper.

26. The stochastic dynamic optimization problem The profit in a particular period, t, as a function of the production levels of electricity and kraft paper, time, the stock level and the prices of electricity and kraft paper.

27. The stochastic dynamic optimization problem The cost of the stock in a period as a function of time, the stock level and the production levels of electricity and kraft paper. (The production in period t affects the stock level in period t and in period t+1.)

28. The stochastic dynamic optimization problem The production of electricity and kraft paper in a period, t, is constrained by the production capacities in the kraft paper mill and the energy mill in that period and the entering resource stock level.

29. The stochastic dynamic optimization problem The expected optimal objective function value of period t+1 is discounted to period t. The probabilities of reaching different market state combinations at t+1 in the electricity market and in the kraft paper market are conditional on the prices in these markets at t.

30. The stochastic dynamic optimization problem The total optimization problem is found above. Now, we will illustrate this with a numerical program!

31. General illustration why the marginal value of production capacity increases with price risk (and connection to heating plants) X2 Production capacity 1 Production capacity 2 Total wood supply X1

32. The economic optimization problem Along the iso profit line we have:

33. X2 Production capacity 1 Production capacity 2 Total wood supply Isoprofit line X1

34. X2 Production capacity 1 Production capacity 2 Total wood supply Isoprofit line X1

35. X2 Production capacity 1 Production capacity 2 Total wood supply Isoprofit line X1

37. Link to the software: • http://www.lohmander.com/CDP5L.htm

46. Results: • The expected economic value of one more unit of heating plant capacity is 17551 – 16461 = 1090. The economically optimal decision is this: If the investment cost of an extra unit of capacity is less than 1090: Build this extra heating plant capacity! No other investment calculation method would give the correct rule.

47. Conclusions from the numerical model: • It is possible to adaptively optimize all decisions over time including production of electricity, kraft paper and resource extraction. • The approach makes it possible to determine the expected value of production capacity investments in heating plants and paper mills. • The approach can be expanded to cover the complete energy and forest sector.

48. Already in 1981 • World Bank Model” to study the Swedish forest sector. (Nilsson, S.) • In the model, timber, pulp wood and fuel wood could be produced and harvested in all regions. • The energy industry was considered as an option in all regions. It was possible too burn wood, not only fuel wood but also “pulp wood”.

49. Capacity investments • The existing capacity in the saw mills, pulp mills and paper mills was investigated and used in the model. It was possible to invest in more capacity of different kinds in the different regions.

50. Structure in 1981 • The forest sector of Sweden was modelled as a linear programming problem. • The total economic result of all activities in the forest sector of Sweden was maximized. • The wood based part of the energy sector was considered as a part of this forest sector.