mill, ton
3 1 ~ Mechanical p u l p
Runl: - R u e :
X - . - - *Run3:
+ - - +F i g u r e 3. A n n u a l p m d u c t i o n o f p u l p ( i n m i l l i o n s o f t o n p e r y e a r ) .
m i l l ,
m i l l . t o n ,
Converted 81 , P , ,
C
1 products
2020 year
2020 y e a r
F i g u r e 4. Annual p m d u s t i o n o f oaper and converted paper products ( i n m i l l i o n s o f t o n p e r year)
mill.
ton
5
4
Runl: -
R u e :
x - - - - .1980 2000 2020 year
F i g u r e 5. Paper export ( i n millions of ton p e r ear)
Run1 : -
R u e :
a . - - - xRun3:
c---0 '
1980 20gO 2020 year
F i g u r e 6. I n d u s t r i a l p r o f i t ( i n m i l l i o n s of d o l l a n p e r d ear).
mill.
rn
3 60
4 0 -
Runl: -
R u e :
& - - - x1980 2000 2020 year
F i g u r e 7. I n d u s t r i a l u s e o f round wood ( i n m i l l i o n s of m 3 p e r )tear).
The use of wood has been shown in Figure 7. At the be- ginning the industrial use of wood increases from about 4 0
3 3
million m /year to the level of 4 5 million m /year and stays rather steadily there. According to Figure 6, the industrial profit increases from the annual level of . 2 billion dollars towards the end of the planning horizon to around . 5 billion dollars per year.
For the secondrun we have chosen the discounted sum of the increments of the forest sector to gross nationalproduct as an objective function. The results have been illustrated using dotted lines in the same Figures 2 through 7.
Compared with the previous case, there is no significant difference in the production of sawn goods, panels and converted paper products for which export demand again limits the produc- tion. However, there is a significant difference in pulp and paper production. Pulp (both mechanical and chemical) is now produced to satisfy fully the demand for export. Paper produc- tion is now steadily increasing from 5 million ton/year to nearly 9 million ton/year. Paper export is still declining again due to increasing use for the converting processes of paper products.
Therefore, the export demand for paper is not fully exploited.
The bottleneck for paper production now is the biological capacity of the forests to supply wood. The use of round wood increases from about 4 0 million m3/year to the level of 6 5
million m /year. The increase in the yield of the forests may 3 be explained by the change in the age structure of the forests during the planning horizon. Such change over the period 1 9 8 0 -
2 0 1 0 has been illustrated in Figure 8 .
We notice a significant difference in the wood use between these first two runs. We may conclude that in the first run
(the profit maximization) the national wood resources are being used in an inefficient way; i.e., under the assumed price and cost structure the poor profitability of the forest industry results in an investment behavior which does not make full use of the forest resources.
bill. o f trees i n age group
age i n years
+ I L 1
0 20 40 60 80 1 0 0
F i g u r e 8. Age d i s t r i b u t i o n o f trees i n 1 9 8 0 a n d i n 2 0 1 0 a c c o r d i n g t o Run2.
The third run is the same as the first one except that the larger version of the model was used and pulp import was allowed to be used in paper mills. The production of sawn goods and con- verted paper products, as described by broken lines in Figure 2, still meet the export demand. However, panel production is
declining and it fallswell below the level of the previous runs.
The reason is that panel production is now considered as a sepa- rate financial unit which cannot afford to keep up its production capacity. Thus, an increase in panels production appears to be possible only if it is supported from other product lines.
Similarly, the use of spruce for mechanical pulp appears unprofit- able so that its .production is declining. Production of Si-pulp
(for which spruce pulpwood is used) grows steadily from 5 million ton/year to about 10 million ton/year. No spruce is used for Sa-pulp but both the use of pine and birch for Sa-pulp increase over time so that the total production of chemical pulp increases from about 3.5 million ton/year to the level of 7 million ton/
year during the planning horizon. Thus chemical pulp production somewhat exceeds the amount produced in the first run.
Paper production in this third run exceeds the level ob- tained in both previous runs. The reason is that imported pulp is now allowed to be used in paper mills. (Note that in the second run, the raw wood supply was the limiting factor for paper production.) As a consequence, total paper production increased from 5 million ton/year to above 1 1 million ton/year.
The share of newsprint is about one fifth and the share of
printing paper one quarter. Only paperboard production appears to decline.
From the production curves of the primary uses of wood, i.e., sawn goods, panels and pulp, we may conclude (comparing with the second run) that wood resources are again being used inefficiently. It appears that, under the assumed price and cost structure, fiber (pulp in particular) import to be used as raw material in paper mills is more profitable than the use of domestic wood raw material.
6. SUlNMARY AND POSSIBLE FURTHER RESEARCH
We have formulated a dynamic linear programming model of a forest sector. Such a model may be used for studying long- range development alternatives of forestry and forest based
industries at a national and regional level. Our model comprises of two subsystems, the forestry and industrial subsystem, which are linked to each other through the raw wood supply from forest- ry to the industries. We may also single out static temporal submodels of forestry and industries for each interval (e.g., for each five year period) considered for the planning horizon.
The dynamic model then comprises of these static submodels which are coupled with each other through inventory-type of variables; i.e., through state variables.
The forestry submodel describes the development of the
volume and the age distribution of different tree species within the nation or its subregions. Among others, we account for the land available for timber production and the labor available for harvesting and planting activities. Also ecological con- straints, such as preserving land as a watershed may be taken into account.
In the industrial submodel we consider various production activities, such as saw milling, panel production, pulp and paper milling, as well as further processing of primary products. For a single product, alternative production activities employing, for instance, different technologies, may be included. Thus, the production process is described by a small Leontief model with substitution. For the end product demand an exogenously given upper limit is assumed. Some products, such as pulp, may also be imported into the forest sector for further processing. Be- sides biological supply of wood and demand for wood based pro- ducts, production is restricted through labor availability, pro- duction capacity, and financial resources. Availability of
different types of labor (by region) is assumed to be given.
The development of different types of production capacity depends on the initial situation in the country and on the investments which are endogeneous decisions in the model. The production
a c t i v i t i e s a r e g r o u p e d i n t o f i n a n c i a l u n i t s t o w h i c h t h e r e s p e c -
However, because of somewhat hypothetical data used for some key parameters, no conclusions based on these runs should be made on the Finnish case.
The purpose of this work has been the formulation, imple- mentation and validation of the Finnish forest sector model.
Natural continuation of this research is to use the model for studying some important aspects in the forest sector. For in- stance, the influence of alternative scenarios of the energy price and the world market prices for wood products would be of interest. Furthermore, the studies could concentrate on employ- ment and wage rate questions, on labor availability restrictions and productivity, on new technology for harvesting and wood
processing, on the influence of inflation and alternative tax- ation schemes, on land use between forestry and agriculture, on site improvement, on ecological constraints, on the use of wood as a source of energy, etc. Given the required data, such studies can be carried out relatively easily.
Further research requiring a larger modeling effort may con- centrate on regional economic aspects, on linking the forest sector model for consistency to the national economic model, and on studying the inherent group decision problem for controlling the development of the forest sector. The first of these three topics requires a complete revision of our model generating pro- gram and, of course, the regionalized data. The second task
may be carried out either by building in the model a simple input- output model for the whole economy where the non-forest sectors are aggregated up to ten sectors. Alternatively, our current model may be linked for consistency to an existing national economic model. The group decisioc problem has been proposed to be analyzed, for instance, using a multicriteria optimization approach (Kallio, Lewandowski, and Orchard-Hays forthcoming) which is based on the use of reference point optimization
(Wierzbicki 1979)
.
APPENDIX: N O T A T I O N
I n d i c e s
a g e g r o u p o f t r e e s ( r a n g e 1 ,
...,
N )t y p e o f f o r e s t l a n d
t y p e o f r e s o u r c e f o r f o r e s t r y a c t i v i t i e s h a r v e s t i n g a c t i v i t y
p r o d u c t i o n a c t i v i t y ( o f t h e f o r e s t i n d u s t r i e s ) i n d u s t r i a l p r o d u c t
t i m b e r a s s o r t m e n t p l a n t i n g a c t i v i t y t r e e s p e c i e s
t i m e p e r i o d ( r a n g e 1 , .
. . ,
T )S t a t e a n d c o n t r o l v a r i a b l e s
b ( t ) s t o c k h o l d e r s e q u i t y a t t h e b e g i n n i n g o f p e r i o d t b O = b ( 0 ) i n i t i a l l e v e l o f s t o c k h o l d e r s e q u i t y
c a s h ( a n d r e c e i v a b 1 e s ) a t t h e b e g i n n i n g o f p e r i o d t
c" = c ( 0 ) i n i t i a l amount o f c a s h
c * t e r m i n a l r e q u i r e m e n t f o r c a s h
e ( t ) = { e . ( t ) e x p o r t ( a n d s a l e s o u t s i d e t h e f o r e s t s e c t o r ) o f 3 f o r e s t p r o d u c t s d u r i n g p e r i o d t
Parameters
ratio of trees of species s and in age group a that will proceed to age group a' during period t
tax factors for the industries during period t
R+(t) =
ii+
(t) )Barros, 0.1 and A. Weintraub (1979) Planning for Vertically Integrated Forest Industry. Presented at Tenth Inter- national Symposium on Mathematical Programming, Wontreal.
Dantzig, G. (1963) Linear Programming and Extensions. Princeton, N.J.: Princeton Univ. Press.
Dantzig, 2. (1974) Determining Optimal Policies for Ecosystems.
Technical Report 74-11. Stanford, California: Department of Operations Research, Stanford University.
Jackson, B. (1974) Forest Products in the United Kingdom Economy.
Fh.D. thesis, Ijepartn~ent of Forestry, Oxford University.
Gegrt K - I E - Miller, and K. Thompson (1978) PAPRISIM 1
-
A Dynamic idodel of the Canadian Pulp and Paper Industry.Pointe Clair, P.Q.: Pulp and Paper Research Institute of Canada.
Kallio, M., W. Orchard-Hays, and A. Propoi (1 973) Linking of Opti~nization i-lodels. WP-79-83. Laxenburg, Austria:
International Institute for Applied Systems Analysis.
Kallio, M., and iv. Orchard-Hays (1979) Experiments with the Reduced Gradient Xehtod for Linear Programming. WP-79-84.
Laxenburg, Austria: International Institute for Applied Systems Analysis.
Kallio, M., A. Lewandowski, and W. Orchard-Hays (1980) Applica- tion of a 14ulticriteria Optimization Xethod Using Reference Objectives. Laxenburg, Austria: International Institute
for Applied Systems Analysis. Forthcoming.
Kilkki, P., K. Kuusela, and 14. Siitonen(1977) Timber production programs for the forestry board districts of southern
Finland. Folia Forestalia 307, The Finnish Research Institute (in Finnish).
Newnham, H. (1975) LOGPLAN, A idode1 for Planning Logging Opera- tions. Information Report FMR-77. Ottawa: Forest Manage- ment Institute, Canadian Forestry Service.
Navon, Daniel I. (1971) Timber RAbI--A Long Range Planning Plethod for Commercial Timberlands Under i4ultiple-Use Management.
Orchard-Hays, W. (1978) Anatomy of a mathematical programming system. Design and Implementation of Optimization Soft- ware, edited by H. Greenberg. Netherlands: Sijthoff and Noordhoff.
Propoi, A., and V. Krivonozhko (1978) The Simplex Method for Dynamic Linear Programs. RR-78-14. Laxenburg, Austria:
International Institute for Applied Systems Analysis.
Randers, J.(1976) A System Dynamic Study of the Transition From Ample to Scarce Wood Resources. Hanover, N.H.: Publications of Resource Policy Center, Dartmouth College.
Rorres, C. (1978) A linear programing approach to the optimal sustainable harvesting of a forest. Journal of Environmental Management 6.
Seppala, H., J. Kuuluvainen, and R. Seppala. The Finnish Forest Sector at the Turning Point .(in Finnish). Forthcoming.
Steuer, R. and A. Schuler (1978) An interactive multiple-objective linear programming approach to a problem in forest manage- ment. Operations Research 26.
Wardle, P. (1965) Forest management and operational research:
a linear programming study. 14anagement Science 1 1 .
Ware, G., and J. Clutter (1977) A mathematical programming system for the management of industrial forests. Forest Science, 17.
Weintraub, A., and 3. Navon (1976) A forest management planning model integrating silvicultural and transportation acti- vities. Management Science 22.
Wierzbicki, A. (1 979) A i.lethodolcqica1 Guide to Plultiobjective Optimization. WP-79-122. Laxenburg, Austria: ~nternational
Institute for Applied Systems Analysis.
Williams, D. (1976) Integrating Stand and Forest i3odels for Decision Analysis. Ph.D. thesis, Department of Forestry, University of British Columbia.
Yearbook of Forest Statistics 1977/1978. O f f i c i a l Statistics of Finland XVII A:10, The Finnish Forest Research Institute.