A Model for the Forest Sector

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A

MODEL FOR THE FORE%

SECTOR

Markku Kallio

I n t e r n a t i o n a l I n s t i t u t e f o r A p p l i e d S y s t e m s A n a l y s i s , L a x e n b u r g , A u s t r i a a n d H e l s i n k i School of E c o n o m i c s , H e l s i n k i , F i n l a n d

Anatoli Propoi

I n s t i t u t e f o r S y s t e m s S t u d i e s . Moscow, USSR

Risto Seppala

F i n n i s h F o r e s t R e s e a r c h I n s t i t u t e . H e l s i n k i , F'inland

RR-85-4 March 1985

INTERNATIONAL INSTITWE FOR APPLIED SYSTEMS ANALYSIS Laxenburg. Austria

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International Standard Book Number 3-7045-00783

Research Reports, which r e c o r d r e s e a r c h conducted a t IIASA, a r e independently reviewed b e f o r e publication. However, t h e views a n d opinions t h e y e x p r e s s a r e not n e c e s s a r i l y t h o s e of t h e I n s t i t u t e o r t h e Natlonal Member Organizations t h a t s u p p o r t i t .

Copyright O 1985

I n t e r n a t i o n a l I n s t i t u t e f o r Applied Systems Analysis

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Cover design by Martin Schobel P r i n t e d by Novographic. Vienna, Austrla

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This r e p o r t d e s c r i b e s a dynamic linear programming model f o r studying long- range development alternatives f o r f o r e s t r y and forest-based industries a t t h e national and regional level. The Finnish f o r e s t s e c t o r i s used t o illustrate t h e pro- c e s s of implementation and to provide numerical examples. The model is composed of two subsystems, t h e f o r e s t r y and t h e industrial subsystems, which a r e linked through t h e timber supply. The f o r e s t r y submodel d e s c r i b e s t h e development of t h e volume and age distribution of d i f f e r e n t tree species within t h e nation o r regions c o n c e r n e d . The industrial submodel considers various production activi- t i e s , such a s t h e saw mill industry, t h e panel i n d u s t r y , and t h e pulp and p a p e r i n d u s t r y , a s well a s secondary processing of primary products. For e a c h individual p r o d u c t , a l t e r n a t i v e technologies may b e employed. Thus, t h e production pro- c e s s is d e s c r i b e d by a small Leontief model with substitution. In addition t o con- s t r a i n t s r e l a t e d t o t h e supply of timber a n d t h e demand f o r f o r e s t products, production i s r e s t r i c t e d through t h e availability of labor, production c a p a c i t y , and financial r e s o u r c e s . The production activities a r e grouped into financial units and investments a r e made within t h e financial r e s o u r c e s of such units.

The model is designed f o r multicriteria analysis. Objective functions r e l a t e d to G N P , balance of payments, employment, wage income, stumpage earnings, and industrial profit have been formulated. End conditions a r e proposed, which can b e determined through a n optimal solution of a s t a t i o n a r y model f o r t h e whole f o r e s t s e c t o r .

The s t r u c t u r e of t h e i n t e g r a t e d forestry-forest industry model is given in t h e canonical form of dynamic linear programs f o r which special solution t e c h - niques may b e employed. A version of t h e Finnish f o r e s t s e c t o r model has been

~inplemented using SESAME, a n interactive mathematical programming system, and

;: :lumber of numerical r u n s a r e p r e s e n t e d t o illustrate possible uses of t h e model.

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FOREWORD

Dynamic linear programming models have been extensively used a t IIASA t o examine t h e long-term consequences of various economic policies and scenarios.

Applications have included e n e r g y supply p r o s p e c t s , alternative p a t h s f o r regional development, and t h e planned improvement of agricultural production.

This r e p o r t develops t h e methodology f u r t h e r and p r e s e n t s an applicatior, t o t h e s t u d y of f o r e s t r y and t h e forest-based industries; t h e Finnish f o r e s t r y s e c t o r is used as an illustrative example.

ANDRZEJ WIERZRTCKT Chairman, l.9'79-04 System and Decision Sciences

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The a u t h o r s wish t o t h a n k William Orchard-Hays f o r his h e l p in implementing o u r f o r e s t s e c t o r model, a n d J a r i Kuuluvainen (The Finnish F o r e s t R e s e a r c h Insti- t u t e ) , Heikki Seppala (Industria!ization Fund of Finland Ltd.), and Margareta Soismaa (Helsinki School of Economics) f o r d a t a collection. T h e work h a s bene- f i t e d from discussions with George B. Dantzie (Stanford University), t o whom we e x p r e s s o u r s i n c e r e g r a t i t u d e . T h e a u t h o r s a r e also g r a t e f u l t o two anonymous r e f e r e e s f o r most valuable comments a n d suggestions.

P a r t i a l financial s u p p o r t f o r t h i s work was received from t h e Academy of Fin- land a n d t h e Yrjo Jahnsson Foundation.

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A MODEL FOR THE FORE= SECTOR

Markku Kallio

I n t e r n a t i o n a l I n s t i t u t e f o r Applied S y s t e m s A n a l y s i s , L a x e n b u r g , A u s t r i a a n d H e l s i n k i School of Economics, H e l s i n k i . F i n l a n d

Anatoli Propoi

I n s t i t u t e for S y s t e m s S t u d i e s , Moscow, USSR

Risto Seppala

F i n n i s h Forest R e s e a r c h I n s t i t u t e , H e l s i n k i , F i n l a n d

A s is t h e c a s e with several o t h e r natural r e s o u r c e s , wood i s undergoing a transition from being a n ample t o a s c a r c e r e s o u r c e in many regions of t h e world.

In addition, t h e f o r e s t s e c t o r plays an important role in t h e economies of a number of countries. T h e r e f o r e , long-term policy analysis f o r t h e f o r e s t s e c t o r , i.e. for- e s t r y and t h e f o r e s t industries, is becoming a n important issue f o r those coun- t r i e s .

W e c o n c e n t r a t e h e r e on two basic a p p r o a c h e s t o t h e analysis of t h e long- range development of t h e f o r e s t s e c t o r : simulation and optimization. Simulation techniques (e.g. system dynamics) h e l p us t o u n d e r s t a n d and quantify basic rela- tionships influencing t h e development of t h e f o r e s t s e c t o r (see R a n d e r s 1976, J e g e r e t a l . 1978, Seppala e t al. 1980). Using a simulation technique w e c a n evalu- a t e t h e consequences of a specific policy. However, if o n l y simulation is used i t c a n b e difficult t o identify a n " a p p r o p r i a t e " (or in some s e n s e efficient) policy.

This is because t h e f o r e s t s e c t o r is in f a c t a large-scale dynamic system, calling f o r policies t h a t satisfy a large number of conditions and requirements. To solve t h i s problem w e need a n optimization technique, o r more specifically, multiobjective optimization. Because of t h e complexity of t h e system in question, linear programming (Dantzig 1963) is considered t o b e t h e most a p p r o p r i a t e technique. It is worth noting t h a t t h e optimization technique itself should b e used on some s o r t of simulation basis; i.e. d i f f e r e n t numerical r u n s based on d i f f e r e n t assumptions a n d objective functions should b e c a r r i e d out t o help in t h e selection of a n appropri- a t e policy. Specific a.pplications of s u c h an a p p r o a c h t o t h e planning of an i n t e g r a t e d system of f o r e s t r y and f o r e s t industries have been r e p o r t e d , f o r instance, b y Jackson (1974) a n d Barros and Weintraub (1979).

Because of t h e n a t u r e of f o r e s t growth, any model used must necessarily b e dynamic. In t h i s r e p o r t w e consider a dynamic linear programming (DLP) model f o r t h e f o r e s t s e c t o r . Using t h i s a p p r o a c h t h e overall planning horizon (e.g. a 50-year

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period) is partitioned into a finite number of shorter periods (e.g. of five years each); for each of these shorter periods we consider a static linear programmine model. A dynamic linear program thus comprises a number of static models, inter- linked via various state variables (i.e. different types of "inventories," such as the amount of wood in the forests, production capacity, assets, liabilities, e t c . , at the end of a given period are equal to those a t the beginning of the following period).

In our forest-sector model, each static model comprises two basic submodels:

a forestry submodel and an industrial submodel of production, marketing and financing. The forestry submodel also describes ecological and land availability constraints for the forest, as well as labor and machinery constraints on harvesting and planting activities. The industrial submodel is a small input-output model of both mechanical (e.g. sawmill and plywood) and chemical (e.g. pulp and paper) production activities. Secondary processing of t h e primary products is also included in this submodel, particularly because of the expected importance of such activities in the future.

The r a t e of production is constrained by wood supply (which is one of the major links between t h e submodels), by final demand for forest products, by labor supply, by the availability of production capacity, and finally, by financial considerations.

The evaluation of alternative policies for t h e forest sector is very much a multiobjective procedure: while selecting a reasonable long-term policy, the preferences or needs of different interest groups (such as government, industry.

labor, and forest owners) have to be taken simultaneously into account. It should also be noted that the forestry and forest industry submodels have different tran- sient times: a forest normally requires a growing period of a t least 40-60 years, whereas a major structural change in the forest industry may occur within a much shorter period. Because of the complexity of the system, it is sometimes desirable first to consider forestry and t h e forest industries fairly independently, and only then to analyze an integrated model (see Kallio et aL. 1979).

It is also important to take into account all the uncertainties that can affect the forest and related sectors over such a long period. A stochastic model might a t first seem to be more appropriate for this purpose. However, the high input- data requirements of such a model and t h e difficulties of applying stochastic solution techniques led us to the conclusion that t h e dynamic linear programming approach suggested would be more realistic.

This report consists of two main parts. In the first (Sections 2-4). we describe t h e methodological approach followed. In the second (Section 5), we present a specific implementation for the Finnish forest sector and illustrate this with several hypothetical, numerical examples.

2. THE F'OREnRY SUBSYSTEM

Mathematical programming has been widely applied in forestry for operations management and planning (e.g. Wardle 1965, Navon 1971, Dantzig 1974, Newnham 1975, Williams 1976, Kilkki et aL. 1977). In this section we follow a traditional method of formulating forest t r e e population as a dynamic linear programming (DLP) system. We describe the forestry submodel, where the decision variables

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(control activities) are harvesting and planting activities, and where t h e state of t h e forests is represented b y t h e volume o f trees (m3) in d i f f e r e n t species and age groups. Because t h e model is formulated in t h e DLP framework, we will examine in detail t h e following elements: ( i ) state equations, which describe t h e development o f t h e system, (ii) constraints, which restrict t h e feasible trajectories for forest development, and (iii) t h e planning horizon.

2.1. State Equations

Each t r e e in t h e forest is assigned t o a class specifying its age and species.

A t r e e belongs t o age group a ^{( a}= 1,2,. . . , N

-

1 ) i f its age is at least ( a - 1 ) A but less than a A. where A is a given time interval ( f o r example, five years). In the highest age group, a = N , all trees are included that have an age of at least ( N - 1 ) A. (Instead o f age groups, we might alternatively assign trees to size groups specified b y diameter or volume.) We denote by wsa ( t ) t h e number of trees o f species s (e.g. pine, spruce, birch, e t c . ) in age group a at t h e beginning o f period

t

( t = 0 , 1 , . . . , T ) . Index s might also be extended to r e f e r t o region, soil class, or forest management strategy.

Let a:, , ( t ) denote t h e proportion o f trees of species s and age group a that will proceed to age group a ' during period t . We shall consider a model formula- tion where t h e length o f each period is A. Therefore, we may assume that a z a , ( t ) is independent o f

t

and equal t o zero, unless a' is equal t o a

+

1 (or a for t h e highest age group). We t h e n denote a;,,(t) = a: with 0 c a: c 1. The ratio 1 - a,S may be viewed as t h e attrition rate corresponding t o time interval A and species s in age group a . We introduce a subvector w , ( t ) = [wsa ( t ) {, specifying t h e age distribution o f trees (number o f t r e e s ) for each species s at t h e bepinning of period

t

. Assuming neither harvesting nor planting take place at t h e end of t h e period, t h e age distribution o f trees at t h e beginning o f t h e n e x t period, t

+

1 , will t h e n be given b y a S w s ( t ) , where a s is t h e square N x N growth matrix, which describes t h e removals due t o thinning and death o f trees from natural causes.

From our definition, this takes t h e form

Introducing a vector w

(t

) = [ w s (t ) j = [wsa ( t )

1,

describing t r e e species and age distribution, and a block-diagonal matrix a with submatrices a s on i t s diago- nal, t h e species and age distribution at t h e beginning o f period t

+

1 will be given b y aw ( t ).

We denote b y u + ( t ) and u - ( t ) t h e vectors o f planting and final harvesting activities for period t . The state equation describing t h e development of t h e forest will t h e n b e

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w h e r e m a t r i c e s q a n d w s p e c i f y activities in s u c h a way t h a t QU +(t ⁾and - o u -(t ⁾ a r e t h e i n c r e m e n t a l c h a n g e s in numbers of t r e e s r e s u l t i n g from planting and h a r - vesting a c t i v i t i e s , r e s p e c t i v e l y .

I t should b e n o t e d t h a t t h e growth r a t e of t h e t r e e s is in f a c t d e p e n d e n t upon t h e number of t r e e s growing p e r unit a r e a . Hence, i n s t e a d of ( 1 ) we should really u s e a nonlinear equation, b u t t h i s would complicate t h e problem c o n s i d e r - ably. T h e r e f o r e , i t seems more p r a c t i c a l t o u s e t h e l i n e a r approximation ( 1 ) with some a v e r a g e figures in t h e m a t r i x a. I t is possible t o c h e c k t h e s e figures a f t e r t h e solution h a s b e e n o b t a i n e d a n d t o u p d a t e t h e m if n e c e s s a r y .

A planting a c t i v i t y n may b e s p e c i f i e d t o mean t h e planting of o n e tree of s p e c i e s s t h a t e n t e r s t h e f i r s t a g e g r o u p ( a = 1 ) d u r i n g p e r i o d t . Thus, m a t r i x q h a s o n e unit column v e c t o r f o r e a c h s p e c i e s . T h e nonzero element of s u c h a column falls in t h e row of t h e f i r s t a g e g r o u p f o r s p e c i e s s in equation ( 1 ) .

A h a r v e s t i n g a c t i v i t y h i s s p e c i f i e d b y variables u h - ( t ) , which d e t e r m i n e t h e level of t h i s a c t i v i t y . T h e c o e f f i c i e n t s w i h of matrix w a r e d e f i n e d s o t h a t o i h u h - ( t ) i s t h e number of trees of s p e c i e s s from a g e g r o u p a h a r v e s t e d when a c t i v i t y h i s applied a t level u h ( t ) . Thus, t h e s e c o e f f i c i e n t s show t h e a g e a n d s p e c i e s d i s t r i b u t i o n of t r e e s h a r v e s t e d when a c t i v i t y h o c c u r s .

2.2. Constraints

Land. L e t H ( t ) b e t h e v e c t o r of t o t a l a c r e a g e of t h e d i f f e r e n t soil t y p e s d available f o r f o r e s t s a t period t . Let G i d b e t h e a r e a of soil t y p e d r e q u i r e d b y o n e tree of s p e c i e s s a n d a g e g r o u p a . W e assume t h a t e a c h s p e c i e s uses only o n e t y p e of soil; i.e. only o n e of t h e elements G&, d

=

1 . 2 , .

. .

^,i s nonzero. Thus, if we c o n s i d e r more t h a n o n e land t y p e , t h e n t h e i n d e x s may also refer t o t h e soil.

Defining t h e m a t r i x G = ( G l d ) , we h a v e t h e land availability r e s t r i c t i o n

I n t h i s formulation we assume t h a t t h e land a r e a H ( t ) i s exogenously given.

Alternatively, we may endogenize v e c t o r H ( t ) b y introducing a c t i v i t i e s a n d a s t a t e equation f o r changing t h e a r e a s of d i f f e r e n t t y p e s of land. S u c h a formulation would b e justified if c h a n g e s i n soil t y p e o v e r time w e r e c o n s i d e r e d o r if o t h e r land-intensive a c t i v i t i e s , s u c h a s a g r i c u l t u r e , w e r e included in t h e model.

Besides s t r a i g h t f o r w a r d land availability c o n s t r a i n t s , s p e c i f i c r e q u i r e m e n t s f o r land allocation (such a s p r e s e r v i n g t h e f o r e s t a s a w a t e r s h e d o r r e c r e a t i o n a l a r e a ) may b e s t a t e d i n t h e form of inequality ( 2 ) . In s u c h c a s e s ( t h e negative of) a component of H ( t ) would d e f i n e a lower bound o n s u c h a n allocation, while t h e left-hand s i d e would yield ( t h e negative of) t h e land allocated in a solution of t h e model.

Sometimes c o n s t r a i n t s o n land availability may b e given in t h e form of equali- t i e s requiring t h a t all land made available t h r o u g h h a r v e s t i n g in a given p e r i o d b e u s e d d u r i n g t h e same p e r i o d f o r planting new trees of a t y p e a p p r o p r i a t e f o r t h e soil. F o r e s t laws in many c o u n t r i e s e v e n r e q u i r e explicitly t h a t t h i s t y p e of pro- c e d u r e b e followed.

Labor a n d Other Resources. Harvesting a n d planting a c t i v i t i e s r e q u i r e r e s o u r c e s s u c h a s machinery a n d labor. L e t R;+,(t) a n d R g i ( t ) b e t h e usage of r e s o u r c e g a t unit levels of planting a c t i v i t y n a n d h a r v e s t i n g a c t i v i t y h ,

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respectively. Defining t h e matrices ~ ' ( t )

=

t ~ & ( t ) { a n d R - ( t ) = tR$(t)j, a n d also t h e v e c t o r R ( t )

=

tRg ( t ) j of available r e s o u r c e s during period t , w e may write t h e r e s o u r c e availability c o n s t r a i n t a s follows

~ + ( t ) u + ( t )

+

R - ( t ) u - ( t ) S R ( t ) (3) A more s a t i s f a c t o r y way of r e p r e s e n t i n g r e s o u r c e availability is t o use supply functions f o r which piecewise-linear approximations may b e employed.

Wood S u p p l y . The requirements f o r wood supplied b y f o r e s t r y t o t h e f o r e s t industries c a n b e given in t h e form

where v e c t o r y ( t ) = t y k ( t ) { specifies t h e requirements f o r d i f f e r e n t timber a s s o r t m e n t s k (e.g. pine logs, s p r u c e pulpwood, e t c . ) ; matrix S ( t ) transforms quantities of h a r v e s t e d t r e e s of d i f f e r e n t s p e c i e s a n d ages into t h e volumes of dif- f e r e n t timber assortments, while Vw ( t ) a c c o u n t s f o r thinning activities. Note t h a t t h e volume of a n y given tree being h a r v e s t e d is assigned in (4) between logs a n d pulpwood in a proportion t h a t d e p e n d s on t h e s p e c i e s a n d a g e group of t h e tree.

For e a c h s p e c i e s , s e v e r a l classes of log size may b e specified. T h e possibility of using a n y size of log a s pulpwood may also b e included in t h e model: in t h i s way t h e size distinction between logs a n d pulpwood actually becomes endogenous.

2.3. Plan- Horizon

The f o r e s t system h a s a v e r y long t r a n s i e n t time: one complete rotation of t h e t r e e s in t h e f o r e s t may, in e x t r e m e conditions, r e q u i r e more t h a n o n e h u n d r e d y e a r s . Naturally, various u n c e r t a i n t i e s make i t difficult t o plan f o r s u c h a long time horizon. On t h e o t h e r hand, if t h e planning horizon c h o s e n i s too s h o r t , i t is impossible t o t a k e i n t o account all t h e longer-term consequences of activities implemented a t t h e beginning of t h e planning horizon. In o r d e r t o s e t a n e n d condition f o r t h e f o r e s t s , i.e. a condition t o b e a t t a i n e d b y t h e e n d of t h e period o r planning horizon in question, w e shall employ t h e s t a n d a r d c o n c e p t of sustainable yield.

To analyze a s t a t i o n a r y regime f o r t h e f o r e s t s , we s e t w ( t

+

1 ) = w ( t ) = w , f o r all t

.

The s t a t e equation (1) c a n t h e n b e r e s t a t e d a s

Imposing c o n s t r a i n t s (2) through (4) on variables w , u + , a n d u -, w e c a n solve a s t a t i c linear programming problem t o find a n optimal s t a t i o n a r y s t a t e w* of t h e f o r e s t (and corresponding harvesting a n d planting activities). The solution of a dynamic linear program with e n d c o n s t r a i n t s

yields t h e optimal transition t o t h i s sustainable yield s t a t e .

Another way of introducing sustainable yield is t o consider a n infinite-period formulation a n d t o impose c o n s t r a i n t s w ( t ) = w (t

+

I ) , u -(t ) = u -(t

+

I ) , a n d u ⁺= u + ( t

+

I ) , f o r all t 2 T. If t h e model p a r a m e t e r s f o r period t a r e assumed i n d e p e n d e n t of time f o r all t 2 T, t h e n t h e dynamic, infinite-horizon, linear pro- gramming model may b e formulated a s a (T

+

1)-period problem, where t h e last

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k,cr.iod represents a stationary solution for periods t 2 T and t h e first T periods represent t h e transition from the initial s t a t e t o t h e stationary solution.

There is a certain difference between these two approaches t o handling t h e stationary s t a t e . In t h e f i r s t , we initially find t h e optimal stationary solution independently of t h e transition period, and t h e r e a f t e r we determine t h e optimal transition t o this stationary s t a t e . In t h e second approach, we link t h e transition period with t h e period corresponding t o t h e stationary solution. The linkage takes place in t h e stationary-state variables, which a r e determined in an optimal way taking into account both periods simultaneously.

3.

THE

INDUSL'RIAL SUBSYWEM

We will now consider t h e industrial subsystem of t h e forest sector. Again t h e formulation used is t h a t of a dynamic linear programming model. We discuss first t h e section related t o t h e production of and final demand for forest products.

a f t e r which we move t o financial considerations.

3.1. Production and Demand

Let z ( t ) b e t h e vector (levels) of production activities i for period t , for t

=

0: 1 , . .

.

, T

-

1. Such activities may include t h e production of sawnwood, panels, pulp, p a p e r , converted products, e t c . For each single product j t h e r e may exist several alternative production activities i , which may b e specified in terms of alternative uses of raw material, technology, e t c . Let U be t h e matrix of wood usage p e r unit of production activity, so t h a t t h e wood processed by industries during period t is given by vector U z ( t ) . Note t h a t matrix U has one row for each timber assortment k (corresponding to t h e components of t h e timber-supply vec- t o r y ( t ) in t h e forestry model). Some of t h e elements of U may be negative. For instance, saw milling consumes logs but produces raw material (industrial residu- als) for pulp mills; this by-product then appears as a negative component in matrix U. We denote by r ( t ) = t r k ( t ) I t h e vector of wood raw-material inventories a t t h e beginning of period t (i.e. wood harvested but not yet processed by industry). As above, let y ( t ) be t h e amount of wood harvested in different timber assortments, and z '(t ) and z -(t), respectively, t h e (vectors of) import and e x p o r t of different assortments of wood during period t . Then we have t h e following s t a t e equation for t h e wood raw-material inventory

In o t h e r words, t h e wood inventory a t t h e e n d of period t is t h e inventory a t t h e b e g i n n i n g of t h a t period plus wood harvested and imported less wood consumed and exported d u r i n g t h a t period. Note t h a t if t h e r e is no storage (change), and neither import nor export of wood, then (7) reduces t o y ( t )

=

U z ( t ) ; i.e. wocd harvested equals wood consumed. For imports and e x p o r t s of wood we assume upper limits ~ ' ( t ) and Z-(t ), respectively

'(t)

s

Z + ( t ) and z -(t) S Z-(t) (8)

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The production p r o c e s s may b e d e s c r i b e d b y a simple input-output model with substitution. Let A ( t ) b e an input-output matrix having one row for e a c h product j and one column f o r e a c h production activity i , s o t h a t A ( t ) z ( t ) is t h e vector of n e t production when production activity levels a r e given b y z ( t ) . Let m (t ) = fm, ( t ) and e (t ) = te, ( t ) j b e t h e vectors of import from a n d e x p o r t t o t h e f o r e s t s e c t o r , respectively, for products j. Then, ignoring a n y possible changes in t h e product inventory, w e have

Domestic consumption is included in e ( t ) . For e x p o r t s and imports w e assume e x t e r n a l l y given bounds, E (t ) and M (t ), respectively

Such c o n s t r a i n t s may b e s u b s t i t u t e d b y piecewise-linear e x p o r t and import functions in t h e model. The same applies t o t r a d e in timber.

Production activities a r e f u r t h e r r e s t r i c t e d through labor and mill capaci- ties. L e t L ( t ) b e t h e vector of d i f f e r e n t t y p e s of labor available f o r t h e f o r e s t industries. Labor may b e classified in d i f f e r e n t ways taking into account, f o r instance, t y p e s of production and t y p e s of responsibility in t h e production pro- c e s s (e.g. work f o r c e , management, e t c . ) . Let p(t ) b e a coefficient matrix such t h a t p ( t ) z ( t ) is t h e vector of demand f o r d i f f e r e n t t y p e s of labor given production activity levels z ( t ) . Thus w e have

Again, s u c h a c o n s t r a i n t may b e s u b s t i t u t e d b y a piecewise-linear supply function f o r labor.

We consider t h e production (mill) capacity h e r e as an endogenous s t a t e variable. Let q ( t ) b e t h e vector of t h e amount of different t y p e s of s u c h capacity a t t h e beginning of period t . Such t y p e s may b e distinguished by region (where t h e capacity i s located), b y product group f o r which t h e capacity is used, and b y t h e d i f f e r e n t technologies required o r available t o produce a given product. Let Q ( t ) b e a coefficient matrix such t h a t Q ( t ) z ( t ) is t h e vector of demand f o r t h e s e t y p e s of capacity. Such a matrix has nonzero elements only when t h e region-product- technology combination of a c e r t a i n production activity matches t h a t of t h e t y p e of capacity available. The production capacity r e s t r i c t i o n is t h e n given as

The development of t h e capacity over time is given b y a s t a t e equation

where 6 is a diagonal matrix accounting f o r (physical) depreciation a n d v ( t ) is a vector of investments (in physical units). Capacity expansions a r e r e s t r i c t e d through financial resources. We d o not consider possibie c o n s t r a i n t s arising from o t h e r s e c t o r s , such a s machinery o r construction, whose capacity may b e employed in f o r e s t - s e c t o r investment.

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We now turn our attention t o t h e financial aspects. We partition t h e set o f production activities i into financial units (so that each activity belongs uniquely t o one financial unit). Furthermore, we assume that each production capacity is assigned t o a financial unit so that each production activity employs only capaci- ties assigned t o t h e same financial unit as t h e activity itself.

Production capacity in (14) is given in physical units. For financial calcula- tions (such as determining taxation) we define a vector { ( t ) of fixed assets. Each component o f this vector determines fixed assets (in monetary units) for a finan- cial unit related t o t h e capacity assigned t o that unit. Thus, fixed assets are aggregated according t o the grouping o f production activities into financial units.

for instance, b y region, b y industry, or b y group o f industries.

Financial and physical depreciation may d i f f e r from one another, for instance when t h e former is specified b y law. We define a diagonal matrix (I

-

$ t ) ) such that (I - 6 ( t ) ) q ( t ) is t h e vector of fixed assets l e f t at t h e end o f period t when investments are not taken into account. Let K ( t ) be a matrix in which each com- ponent determines the increase in fixed assets o f a certain financial unit per (physical) unit of an investment activity. Thus t h e components of vector K ( t ) v ( t ) determine t h e increase in fixed assets (in monetary units) for t h e financial units when investment activities are applied (in physical units) at a level determined b y vector v ( t ). Then we have t h e following state equation for fixed assets

For each financial unit we consider external financing (long-term d e b t ) as an endogenous state variable. Let l ( t ) be t h e vector o f initial balance o f external financing for d i f f e r e n t financial units in period t . In this notation, t h e state equa- tion for long-term debt is as follows

l ( t

+

1 ) = l ( t )

+

l + ( t )

-

1 - ( t ) (16) We restrict t h e total long-term debt through a measure that may be con- sidered as t h e market value of a financial unit. This measure is a given percentage o f t h e total assets, less short-term liabilities. Let p ( t ) be a diagonal matrix of such percentages, and let b ( t ) be the endogenous vector of total stockholders' equity (including cumulative profit and stock). Then t h e upper limit on loans is given as

(I - p ( t ) ) I ( t ) < ~ ( t ) b ( t ) (17)

Alternatively, external financing may be limited, for instance, t o a percen- tage o f a theoretical annual revenue (based on available production capacity and on assumed prices o f products). Note that no repayment schedule has been intro- duced in our formulation, because an increase in repayment can always be compen- sated b y an increase o f withdrawals in t h e state equation (16).

Next we will consider t h e profit (or loss) over period t

.

^Let^p^{' ( t}⁾^and^p^-(t⁾

be vectors whose components indicate profits and losses, respectively, for t h e financial units. By definition, profit and loss cannot be simultaneously nonzero for any financial unit. For any given solution o f t h e model, this condition is usually fulfilled t h r o u ~ h t h e choice of objective function.

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Let P ( t ) be a matrix o f prices for products (with one column f o r each pro- duct and one row for each financial unit) such that t h e vector o f revenue ( f o r d i f - f e r e n t financial units) from sales e ( t ) outside t h e forest industry is given b y P ( t ) e ( t ) . Let C ( t ) be a matrix o f direct unit production costs, including, for instance, timber, energy, and direct labor costs. Each row o f C ( t ) r e f e r s t o a financial unit and each column t o a production activity. The vector o f direct pro- duction costs for financial units is t h e n given b y C ( t )z ( t ).

The fixed production costs may be assumed proportional t o t h e (physical) production capacity. We define a matrix F ( z ) such that t h e vector F ( t ) q ( t ) yields t h e fixed costs over period t for each o f t h e financial units. According t o t h e notation introduced above, (financial) depreciation is given b y t h e vector - a ( t ) @ ( t ) . We assume that interest is paid on t h e initial balance o f d e b t . Thus, i f

~ ( t ) is t h e diagonal matrix o f interest rates, t h e n t h e vector o f interest paid ( b y t h e financial units) is given b y ~ ( t )l ( t ) . Finally, let D ( t ) be a vector o f exo- genously given cash expenditure covering all other costs. Then t h e profit (loss) b e f o r e t a x is given as follows

The stockholder equity b ( t ) , which was introduced above, now satisfies t h e following state equation

b ( t

+

^{1 )}= b ( t )

+

( I

-

r ( t ) ) p + ( t )

+

^{B ( t )} (19) where ~ ( t ) is a diagonal matrix for taxation and B ( t ) is t h e (exogenously given) amount o f stock issued during period t

.

Finally, we consider cash (and receivables) for each financial unit. Let c ( t ) be t h e vector of cash at t h e beginning o f period t . The change in each during period t is due t o t h e profit (loss) a f t e r t a x , depreciation (i.e. noncash expendi- t u r e ) , debts incurred, repayments, and investments. Thus we assume that t h e pos- sible change in cash due t o changes in accounts receivable, in inventories (wood.

end products, e t c . ) , and in accounts payable cancel each other out (or that these quantities remain unchanged during t h e period). Alternatively, such changes could be taken into account b y assuming, for instance, that t h e accounts payable and receivable, and t h e inventories, are proportional t o t h e annual sales of each financial unit.

Using our earlier notation, t h e state equation for cash is now

3.3. Initial and Final State Conditions

In our industrial model, we now have t h e following state vectors: wood raw material inventory T ( t ). (physical) production capacity q ( t ), fixed assets q ( t ), long-term debt I ( t ), cash c ( t ), and total stockholders' equity b ( t ) . For each o f them we have an initial value and possibly a limit on t h e final value. We shall r e f e r t o these initial and final values b y superscripts 0 and *, respectively; thus we

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write t h e given initial s t a t e a s

r ( 0 ) = r O , q ( 0 ) = q 0 , Q ( 0 ) = i 0 1 ( 0 ) = 1 ° , c ( 0 ) = c O , b ( 0 ) = b O

The initial s t a t e is d e t e r m i n e d b y t h e s t a t e of t h e f o r e s t i n d u s t r i e s a t t h e beginning of t h e planning horizon. The final s t a t e may b e d e t e r m i n e d a s a s t a t i o n a r y solution, in a manner similar t o t h a t d e s c r i b e d above f o r t h e f o r e s t r y model.

4. THE INTEGRATED -16

We now c o n s i d e r t h e i n t e g r a t e d f o r e s t r y - f o r e s t i n d u s t r i e s model. F i r s t we p r e s e n t a g e n e r a l discussion on possible formulations of objective functions f o r s u c h a model. Then we summarize t h e model in t h e canonical form of dynamic linear programming. A t a b u l a r r e p r e s e n t a t i o n of t h e s t r u c t u r e of t h e i n t e g r a t e d model is also given.

4.1. Objectives

The f o r e s t s e c t o r may b e viewed a s a s y s t e m controlled b y s e v e r a l i n t e r e s t groups o r p a r t i e s . Any given p a r t y may have s e v e r a l objectives t h a t a r e in conflict with e a c h o t h e r . F u r t h e r m o r e , t h e objectives of a n y o n e p a r t y may c l e a r l y b e in conflict with t h o s e of a n o t h e r p a r t y . F o r i n s t a n c e , t h e following p a r t i e s might reasonably b e t a k e n i n t o account: r e p r e s e n t a t i v e s of i n d u s t r y , government, labor, a n d t h e f o r e s t owners. Among t h e objectives of i n d u s t r y , a major c o n c e r n may b e t h e development of t h e profitability of d i f f e r e n t financial units. Govern- ment may b e i n t e r e s t e d in t h e contribution of t h e f o r e s t s e c t o r t o gross national p r o d u c t , t h e balance of payments, a n d employment. T h e labor unions a r e i n t e r e s t e d i n employment a n d t o t a l wages e a r n e d in f o r e s t r y a n d in d i f f e r e n t i n d u s t r i e s within t h e s e c t o r . T h e objectives of t h e f o r e s t owners may b e t o i n c r e a s e t h e i r income from selling a n d harvesting wood. Such objectives r e f e r t o d i f f e r e n t p e r i o d s t (within t h e overall planning horizon) a n d possibly also t o dif- f e r e n t p r o d u c t lines. W e will now give simple examples of how s u c h objectives may b e formulated a s linear objective functions. Nonlinear objectives may also b e employed.

Industrial P r o f i t . The v e c t o r of p r o f i t s f o r t h e industrial financial units was d e f i n e d above a s (I

-

~ ( t ) ) p '(t ) - p -(t ) f o r e a c h p e r i o d t . If we wanted t o distinguish between d i f f e r e n t financial u n i t s , t h e n actually e a c h component of s u c h a v e c t o r could b e c o n s i d e r e d a s a n objective function. However, f o r p r a c t i - c a l p u r p o s e s we f r e q u e n t l y aggregate s u c h objectives, f o r i n s t a n c e summing discounted p r o f i t s o v e r all p e r i o d s , summing o v e r financial u n i t s , o r summing over b o t h p e r i o d s and financial units.

C o n t r i b u t i o n to G r o s s N a t i o n a l P r o d u c t . TO define t h e contribution of t h e f o r e s t s e c t o r t o GNP, we consider t h e s e c t o r a s a "profit c e n t e r , " where no wage is paid t o t h e employees within t h e s e c t o r , where no p r i c e is paid f o r raw

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materials originating from t h i s s e c t o r , and where n e i t h e r i n t e r e s t nor t a x e s a r e paid. The contribution t o GNP i s t h e n simply t h e profit f o r such a unit.

C o n t r i b u t i o n to t h e B a l a n c e of P h y m e n t s . The contribution of t h e f o r e s t s e c t o r t o t h e balance of payments may b e e x p r e s s e d b y an amended version of t h e expression f o r GNP. The necessary changes a r e a s follows: first, multiply t h e components of t h e p r i c e vector b y t h e s h a r e of e x p o r t s in t o t a l sales; second, multiply t h e components of t h e c o s t vectors b y t h e s h a r e of imported inputs in e a c h c o s t t e r m ; t h i r d , multiply by t h e s h a r e in foreign d e b t s (among all long-term d e b t s ) of t h e financial unit concerned; and finally, r e p l a c e t h e depreciation function b y investment e x p e n d i t u r e s on imported goods.

Employment. Total employment (in man-years) f o r each period t , f o r dif- f e r e n t t y p e s of labor in different activities and regions, has already b e e n included in t h e left-hand sides of inequalities (3) a n d (12).

Wage Income. For e a c h subgroup of t h e work f o r c e , t h e wage income f o r period t is obtained b y multiplying t h e expressions f o r employment (given above) b y t h e average annual salary within each s u c h subgroup.

S t u m p a g e E a r n i n g s . Besides t h e wage income f o r f o r e s t r y (which we already defined above), and an aggregate profit (as e x p r e s s e d in (6)), w e may also wish t o t a k e into account stumpage earnings, i.e. t h e income r e l a t e d t o t h e p r i c e of wood p r i o r t o harvesting. This income may b e readily obtained f o r a given timber assortment if t h e components of t h e h a r v e s t yield vector y ( t ) a r e multi- plied b y t h e r e s p e c t i v e prices of t h e d i f f e r e n t t y p e s of wood.

4.2. The Integrated Model

The i n t e g r a t e d forestry-forest industry model is illustrated in Figure 1. The interactions between t h e f o r e s t r y and industrial subsystems o c c u r via roundwood consumption. Both subsystems also i n t e r a c t with t h e general economy (which in o u r model is exogenous). This l a t t e r subsystem determines t h e supply (in terms of prices and quantities) of capital, labor, e n e r g y , and land. Domestic consumption and e x p o r t demand (import supply) a r e also determined b y t h e general economy subsystem.

W e will now summarize t h e i n t e g r a t e d f o r e s t r y - f o r e s t industry model in t h e canonical form of dynamic linear programming ( s e e e.g. Pr-opoi and Krivonozhko 1978). Denote b y X ( t ) t h e vector of all s t a t e variables (defined above) a t t h e beginning of period t . The components of t h i s vector include t h e number of t r e e s of e a c h t y p e in t h e f o r e s t , d i f f e r e n t t y p e s of production capacity in t h e industry.

wood inventories, e x t e r n a l financing, e t c . Let Y ( t ) b e t h e nonxegative vector of all control activities f o r period t , t h a t is, t h e vector of all decision variables, such a s levels of harvesting o r production activities. An u p p e r bound vector for Y ( t ) is denoted b y ? ( t ) (some of whose components may b e infinite). W e assume t h a t t h e objective function t o b e maximized is a linear function of t h e s t a t e vectors X ( t ) and t h e c o n t r o l vectors Y(t), and we denote b y y ( t ) and h ( t ) t h e coefficient vec- t o r s f o r X ( t ) and Y(t ), respectively, f o r s u c h an objective function. This function may b e , f o r instance, a linear combination of t h e objectives defined above. For rnulticriteria analysis y ( t ) and h ( t ) a r e matrices. The initial s t a t e X(0) is denoted b y

x',

a n d t h e final requirement f o r X(T) b y

X .

Let r ( t ) and h ( t ) b e t h e coeffi- c i e n t matrices f o r X(t ) and Y(t ), respectively, and l e t ( ( t ) b e t h e exogenous

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Forest Industry Submodel: General Economy :

Production and investment (exogenous)

Consumption and trade Capital supply

Resources: capital, labor Labor s u ~ ~ l v

Timber Supply

t ^'

Land suddli

Energy supply Domestic demand Export demand

Forestry Submodel:

Forest dynamics Forest management

Resources: capital, labor, land

.

FIGURE 1 Integration of forest-sector submodels.

right-hand side vector in t h e s t a t e equation f o r X ( t ) . Let @ ( t ) and R ( t ) b e t h e corresponding matrices and @ ( t ) t h e right-hand side vector f o r t h e constraints.

Then t h e integrated model can b e s t a t e d in t h e canonical form of dynamic linear programming a s follows:

find Y ( t ) for 0 S t S T - 1 , and X ( t ) f o r 1 S t S T , suah a s t o T -1

maximize ( 7 ( t ) X(t )

+

7 ( t ) Y ( t ))

+

7 ( T ) X(T)

t =O

subject t o

O S X ( ~ ) , O S Y ( ~ ) S ? ( ~ ) f o r all t with t h e initial s t a t e

a n d t h e final requirement X ( T ) S X *

The notation f o r t h e constraints a n d t h e final requirement r e f e r s e i t h e r t o

=, t o ^{S ,}o r t o ^{2 ,}s e p a r a t e l y f o r e a c h constraint. The coefficient matrix (corresponding t o variables X ( t ) , Y ( t ) , and X ( t

+

1 ) ) and t h e right-hand side vec- t o r of t h e i n t e g r a t e d forestry-forest industry submodel of period t a r e given a s

respectively. Their s t r u c t u r e is illustrated in Figure 2, using t h e notation introduced in Sections 2 a n d 3.

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5. APPLICATION TO THE FINNISH

FOREST SECTOR

5.1. Implementation

A version of t h e integrated model was implemented using an interactive mathematical programming system called SESAME (Orchard-Hays 1978). The model generator is written using SESAME'S data management extension, called DATAMAT.

Each particular model is specified by t h e data tableaux of t h e generator programs. The example described h e r e was specifically designed for t h e Finnish forest sector. This model may have, a t most, t e n periods, each of which r e p r e s e n t s a five-year interval. The whole country is considered h e r e as a single region. Table 1 shows t h e dimensions of t h e model.

TABLE 1 Dimensions of the Finnish forest-sector model.

Characteristic Value

Number of periodsa

Length of each period in yearsn Number of regions

Number of t r e e species

Number of age groups for treesa Harvesting activitiesa

Soil types

Harvesting and planting resources Timber assortments

Production activities Types of labor in industry Types of production capacity Number of financial units

Number of rows in a ten-period LP 520 Number of columns in a ten-period LP 612 '~hese values may be specified by the model data. The

numbers show the aotual values used i n the Finnish model.

The seven product groups considered a r e sawnwood, panels, f u r t h e r processed (mechanical) wood products, mechanical pulp, chemical pulp, paper and board, and converted paper products. For each product group we specify a separate type of production capacity and labor force. All production has been aggregated into one financial unit. Just one type of t r e e r e p r e s e n t s all t h e t r e e species in t h e forests. The t r e e s a r e classified into 2 1 age groups. 'Thus, t h e age increment being five years, t h e oldest group contains t r e e s more than 100 years old. Two harvesting activities a r e possible within t h e model framework, and two timber assortments a r e considered

-

logs and pulpwood.

The data for t h e Finnish model were provided by the Finnish Forest Research Institute. They a r e partially based on t h e official forest statistics (Yearbook of Forest Statistics 1977/1978) published by t h e same institute. Valida- tion runs (which eventually resulted in the c u r r e n t formulation of t h e system) were carried out by contrasting model solutions with experience gained in t h e earlier simulation study of t h e Finnish forest s e c t o r carried out by Seppala e t al.

(1980).

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5.2. Scenario Ekamples

F o r illustrative p u r p o s e s we will now d e s c r i b e a few t e s t r u n s . Most of t h e d a t a u s e d in t h e s e e x p e r i m e n t s c o r r e s p o n d a p p r o x i m a t e l y t o t h o s e f o r t h e Finnish f o r e s t s e c t o r . This i s t h e c a s e , f o r i n s t a n c e , with t h e initial s t a t e ; i.e. numbers of trees i n t h e f o r e s t s , d i f f e r e n t t y p e s of production c a p a c i t y , e t c . More h y p o t h e t i - c a l s c e n a r i o s w e r e used, however, f o r c e r t a i n k e y q u a n t i t i e s , s u c h a s final demand.

a n d p r i c e a n d c o s t development. Thus, t h e r e s u l t s o b t a i n e d d o n o t necessarily r e f l e c t a n y s p e c i f i c , r e a l situation b u t a r e r a t h e r p r e s e n t e d in o r d e r t o i l l u s t r a t e possible u s e s of t h e model.

For e a c h t e s t r u n a t e n times five-year p e r i o d model was c o n s t r u c t e d . L a b o r c o n s t r a i n t s f o r b o t h i n d u s t r y a n d f o r e s t r y w e r e r e l a x e d . In t h i s s t a g e , just o n e a c t i v i t y f o r c o n v e r t e d p a p e r p r o d u c t s was c o n s i d e r e d , while b o t h imports a n d e x p o r t s of roundwood w e r e e x c l u d e d . T h e assumed demand f o r wood p r o d u c t s i s given in Table 2. Mechanical pulp i s assumed not t o b e e x p o r t e d . At t h e e n d of t h e planning horizon, we r e q u i r e t h a t , in e a c h a g e g r o u p , t h e r e e x i s t a t l e a s t 80 p e r c e n t of t h e number of trees initially in t h o s e g r o u p s . F o r production c a p a c i t y a similar final requirement was set a t 50 p e r c e n t . Initial production c a p a c i t y i s given i n Table 3 a n d t h e initial a g e d i s t r i b u t i o n of t h e trees i s i l l u s t r a t e d i n Figure 3.

TABLE 2 Assumed annual demand f o r f o r e s t products.

Period Sawn-

wood

( 1 0 ~ ~ ~ )

Panels Chemical

pulp ( l o 6 ton)

P a p e r and board ( l o 6 ton)

4.8 5.8 7.0 8.3 9.8 11.6 13.2 15.1 17.1 19.2

Converted paper ( l o 6 ton)

TABLE 3 Annual production capacity a t the beginning of the planning horizon in 1980 and in 2010 according t o Scenario A.

Product 1980 2010

Sawnwood

L l o 6

m3) ^7.0 ^10.2

Panels (10 m3) 1.7 3.6

Mechanical pulp ( l o 6 ton) 2.2 1.9

Chemical pulp ( l o 6 ton) 4.0 4.3

P a p e r and board ( l o 6 ton) 6.2 6.2 Converted paper products ( l o 6 ton) 0.5 2.9

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0.0

- ,

0 20 40 60 80 100 Age (years)

FIGURE 3 Age distribution of trees in 1980 and in 2010 according to Scenario B.

5.2.1. Scenario A: Base Scenario

For the first run the discounted sum of industrial profits (after tax) was chosen as an objective function. Such an objective should reflect a t least approximately the forest industry's behavior in response to changes in cost structure and price developments. The resulting production trajectory is illustrated in Fig- ure 4. Mechanical processing activities a r e limited almost exclusively to the assumed demand for sawnwood and panels. The same is true for converted paper products. However, chemical pulp produced is almost entirely used in paper mills, and therefore the potential demand for export has not been tapped. Neither have the possibilities for exporting paper been fully exploited. Paper exports decline sharply from an initial level of 5 million ton yr-l and approach zero toward the end of the planning horizon. This is due to the strongly increasing production of converted paper products. The corresponding structural change in the production capacity of the forest industry over the 30-year period from 1980 to 2010 is shown in Table 3 .

5.2.2. Scenario B:

GNP

Fbtential

For t h e second run we chose as an objective function the discounted sum of the contributions of the forest sector to gross national product. Compared with Scenario A, there is no significant difference in the production of sawnwood.

panels, or converted paper products, for which export demand once again sets limits on production. However, there is a significant difference in pulp and paper production. Pulp is now produced to satisfy fully the demand for export. Paper production now steadily increases from 5 million ton yr-l to nearly 9 million ton yr-I by t h e end of the planning horizon. Paper exports still decline, again due to

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A

-

A

Sawnwood ;I

C

r 4

.- 0 _Y⁰

2 Year 2

n n

Chemical pulp

1980 2000 2020

3

Year 2

n

Converted + paper products -

board

Year FIGURE 4 Production in the Finnish forest industry under Scenario A .

t h e increasing uses f o r c o n v e r t e d p a p e r products. Therefore, t h e e x p o r t demand f o r p a p e r is not fully exploited.

The bottleneck f o r p a p e r production is now imposed b y t h e biological capa- c i t y of t h e f o r e s t s t o supply wood. The annual use of roundwood i n c r e a s e s from about 40 million m3 t o 65-70 million m3 (see Figure 5a). The i n c r e a s e in t h e yield of t h e f o r e s t s may b e explained in terms of t h e change in t h e age s t r u c t u r e of t h e f o r e s t s during t h e planning horizon (see Figure 3 f o r t h e period u p t o 2010).

Notice t h a t t h e r e is a significant d i f f e r e n c e in wood use between Scenarios A and 0 . In Scenario A (based on profit maximization), national wood r e s o u r c e s a r e being used inefficiently; i.e. under t h e assumed p r i c e and c o s t s t r u c t u r e , t h e poor profitability of t h e f o r e s t i n d u s t r y r e s u l t s in investment behavior t h a t does not make full u s e of t h e f o r e s t resources.

5.2.3. Scenarios C and D: Variations in Product Price and Demand

The p r i c e s of f o r e s t products in Scenario C r e p r e s e n t average world market p r i c e s . The p r i c e s used in Scenario A a r e 10% above t h i s level (taking into account possible quality differences). Investment is now unprofitable. and t h e r e - f o r e , u n d e r t h e profit-maximization c r i t e r i o n , production declines a t t h e same r a t e a s c a p a c i t y depreciation. As illustrated in Figure 5 a , b y t h e y e a r 2020 wood r e s o u r c e utilization has fallen t o 50% of i t s level in 1980. The same is also t r u e f o r GNP.

In Scenario D, demand f o r all f o r e s t products is double t h a t of Scenario A.

Because of poor profitability, only p a r t of t h i s demand potential is, however, exploited. The resulting wood consumption i s showrl in Figure 5a. Compared with Scenario A, i t is about 1 0 p e r c e n t higher.

5.2.4. Scenario E: Inflation

Next, we modified t h e base scenario b y a n eight-percent annual r e a l inflation of all c o s t and p r i c e figures. This applies t o production c o s t f a c t o r s , s u c h a s wages, e n e r g y and wood c o s t s , investment c o s t s , and t h e r a t e of i n t e r e s t a s well a s t o f o r e s t p r o d u c t p r i c e s . In t h i s scenario, t h e inflation losses due t o taxation and t h e gains d u e t o a r e a l reduction in loan repayments approximately outweigh e a c h o t h e r , s o t h a t profit maximization r e s u l t s in roughly t h e same production figures as in Scenario A (see Figure 5b).

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~ l l l l l l l l l l , 0 1 ' " " 1 ~ " ,

1980 2000 2020 1980 2000 2020

Year Year

a. Variations in product b. Inflation, wage rates, and

A

price and demand

A

productivity

-

_I_L ⁶⁰

^-

⁶⁰

>-

FIGURE 5 Industrial consumption of roundwood for Scenarios A-K.

-

c. Energy cost increases 1, d. Variations in timber

5.2.5. S c e n a r i o s F a n d G: Wage R a t e s a n d P r o d u c t i v i t y

For Scenario F, a n annual r e a l i n c r e a s e of 2% was assumed in all wage c o s t s . The near-term e f f e c t is minor in comparison with Scenario A, whereas over t h e longer term such a n increase r e s u l t s in a significant reduction in production (see Figure 5b). On t h e o t h e r hand, a change in t h e opposite direction, i.e. a 2% annual i n c r e a s e in labor productivity, influences production significantly e a r l i e r . As shown b y Scenario G in Figure 5 b , wood consumption increases t o a level of 50 million m3 annually only 10-15 y e a r s a f t e r t h e beginning of t h e period studied.

m E G

w

- 5'

^40,

C D 40

0 E

.- ₊ A A

a

5

2 0 - 20 - F

S

^C

-

60

m E

w

K

-

z

J

-

^I

c 4 0 -

.- ₊0 _A _A

E a

^H

2 0 -

S

0 - 1 I I I I I I 1 I F

1980 2000 2020

Year Year

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5.2.6. S c e n a r i o s H a n d I: E n e r g y Cost I n c r e a s e s

In t h e next two scenarios, t h e energy costs of Scenario A were increased by 2.7% annually (i.e. by 15% over five years). Scenario H, illustrated in Figure 5c.

shows t h e resulting decrease in production, which is significant only in t h e long term. In Scenario I we assume, in addition, t h a t t h e price of wood as a primary energy source increases by t h e same r a t e of 2.7% annually. Around t h e year 2000 t h e use of wood f o r energy becomes competitive with industrial wood processing and from t h e n on t h e total consumption of wood s t a r t s to increase. The difference between Scenarios I and H in Figure 5c r e p r e s e n t s this use of wood as a source of energy.

5.2.7. S c e n a r i o s J a n d K: V a r i a t i o n s in T i m b e r Cost

Finally, two experiments were c a r r i e d out to study t h e sensitivity of consumption t o t h e price of wood. In Scenario J a 20% decrease was imposed a s compared t o t h e wood costs in Scenario A; in Scenario K t h e corresponding decrease was 2% annually. The impacts on wood consumption a r e shown in Figure 5d. The 20% decrease results in b e t t e r profitability and consequently a steady and immedi- a t e growth of t h e industry. The annual decrease of 2% results in significant change only a f t e r 1 0 years. However, t h e r e a f t e r forest industry growth is f a s t and reaches t h e biological limits of t h e forests (i.e. 60-70 million m3 of wood harvested annually) around t h e year 2000.

6 . SUMMARY AND DIRECTIONS FOR FVTURE RESEARCH

We have formulated and presented a dynamic linear programming model of t h e forest sector. Such a model may b e used to study long-range development alternatives for f o r e s t r y and t h e forest-based industries a t both national and regional levels. Our model comprises two subsystems, t h e f o r e s t r y and t h e forest industry subsystems, which a r e linked together through t h e supply of roundwood from for- e s t r y t o industry. We also have corresponding s t a t i c , temporal submodels of each subsystem for each interval (e.g. each five-year period) considered within t h e planning horizon. The dynamic model is then composed of a series of t h e s e s t a t i c submodels, coupled together through a number of inventory-type variables, i.e.

s t a t e variables.

The f o r e s t r y submodel describes t h e development over time of t h e volume and t h e age distribution of different t r e e species within a nation o r its regions.

Among t h e factors explicitly considered a r e t h e land available for timber production and t h e labor available for harvesting and planting activities. Ecological con- s t r a i n t s , such a s preserving land for use a s a watershed, may also be taken into account.

In t h e industrial submodel we consider various production activities, such as saw milling, panel production, and pulp and paper milling, as well a s t h e f u r t h e r processing of primary products. For each individual product, alternative production activities employing, for instance, different technologies, may be included.

Thus, t h e production process is essentially described by a small Leontief model with substitution. For end-product demand an exogenously given upper limit is assumed. Some products, such as pulp, may also be "imported" into t h e forest sec- t o r for f u r t h e r processing. Apart from t h e biological limits on wood supply and