Industry, employment, economics and trade theory with focus on the forest sector Peter Lohmander

Industry Employment Economics Trade theory The forest sector

The optimal combination of forest industry investments, forest industry production and forest production may be determined.

The employment is strongly dependent on the activities in the forest sector. Such dependences may be expressed via constraints in a forest sector model.

The economic result of all activities in the forest sector may be optimized.

Trade theory Is one way to investigate how the activitites in different countries are linked and influence each other.

Trade theory As presented by: Colin Danby.

The first purpose of trade theory is to explain observed trade. That is, we would like to be able to start with information about the characteristics of trading countries, and from those characteristics deduce what they actually trade, and be right. That’s why we have a variety of models that postulate different kinds of characteristics as the reasons for trade. Colin Danby.

Secondly, it would be nice to know about the effects of trade on the domestic economy.

A third purpose is to evaluate different kinds of policy. Here it is good to remember that most trade theory is based on neoclassical microeconomics, which assumes a world of atomistic individual consumers and firms. The consumers pursue happiness (“maximizing utility”) and the firms maximize profits, with the usual assumptions of perfect information, perfect competition, and so on. In this world choice is good, and restrictions on the choices of consumers or firms always reduce their abilities to optimize. This is essentially why this theory tends to favor freer trade.

Here you may study trade theory and the international forest sector: NA0061 The Forest Sector from an International View, 7.5 ECTS Skogssektorn i ett internationellt perspektiv

Industry, employment, economics, trade and the forest sector Can we optimize all of these things?

Observation: The raw material stock has been increasing for a very long time. Central Question: What is the optimal stock level when we consider the total present value of the forest sector, employment and the environment ?

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”.

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.

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.

The same method applied to a smaller problem of the same type: Såg och Massabolaget: -Ett praktikfall i Skogsindustriell Ekonomi - - Peter Lohmander

! SMB2; ! Peter Lohmander ; Max = TProf; TProf = - InkK - IntKostn + ForsI; InkK = PKTi*KTimmer + PKMav*KMav + PKFlis*KFlis + PReturpL*KReturpl + PReturpI*KReturpI; IntKostn = AvvK*Avv + TPKostTI*ETimmer + TPKostMA*EMav + CSV*ProdSV + CLiner*ProdLin; ForsI = PSV*ProdSV + PLiner*ProdLin + PSTi*STimmer + PSMav*SMav + PSFlis*SFlis; !Marknadspriser för råvaror samt ev. råvarurestriktioner ; PKTi = 380; PSTi = 330; PKMav = 200; PSMav = 120; PKFlis = 250; PSFlis = 150; PReturpL = 50; PReturpI = 730; [LRetP] KReturpL <= 100;

!SMBs egen skog och avverkning ; AvvK = 70; AvvKap = 570; TimAndel =.5; [KapAvv] Avv <= AvvKap; !SMAs egen virkestransport ; TPKostTI = 60; TPKostMa = 70; !SMBs eget sågverk ; PSV = 1500; CSV = 300; SVKap = 80; TTimmer = ETimmer + KTimmer; ProdSV =.5*TTimmer; ProdFl =.8*ProdSV; ProdSp =.2*ProdSV; [KapSV] ProdSV <= SVKap;

!SMBs råvarubalanser gällande egna producerade råvaror och halvfabrikat ; EMav = (1-TimAndel)* Avv - SMav; ETimmer = Timandel*Avv - STimmer; EFlis = ProdFl - SFlis; !SMBs egen linerfabrik ; PLiner = 4900; CLiner = 1200; LinerKap = 400; TRetP = KReturpL + KReturpI; TFiber = EMav + EFlis + KMav + KFlis; ProdLin =.25*TFiber +.95*TRetP; [FFiberK] TFiber/TRetP >= 4; [KapLiner] ProdLin <= LinerKap; end

Local optimal solution found at step: 10 Objective value: Variable Value Reduced Cost TPROF INKK INTKOSTN FORSI PKTI KTIMMER PKMAV KMAV PKFLIS KFLIS PRETURPL KRETURPL PRETURPI KRETURPI AVVK AVV

TPKOSTTI ETIMMER TPKOSTMA EMAV CSV PRODSV CLINER PRODLIN PSV PLINER PSTI STIMMER PSMAV SMAV PSFLIS SFLIS AVVKAP TIMANDEL SVKAP

TTIMMER PRODFL PRODSP EFLIS LINERKAP TRETP TFIBER

Row Slack or Surplus Dual Price LRETP KAPAVV KAPSV FFIBERK E KAPLINER

Wood for energy in 1981 Among these results, it was found that a large proportion of the “pulpwood” should be used to produce energy. This was particularly the case in the north, at large distances from the coast.

Surprise? Not really! The cost of transporting pulpwood large distances is very high. If energy can be produced from pulpwood, far away from the coast and the pulp industry, it is not surprising that this may be the most profitable alternative.

Relevant model in 1981? Of course, linear programming models are only models of reality. This is true with all models. Of course, linear programming models do not capture all nonlinear and other “real” properties of the real world such as risk and integer constraints. Better options exist today to handle nonlinearities, risk, integer constraints and all kinds of other properties of the real world.

Relevant result from 1981? The general finding that it may be optimal to use some of the wood for energy, still remains!

SVENSKA SKOGS- OCH MASSABOLAGET, SSM, Praktikfallsuppgift i Kostnads - Intäktsanalys med Optimering Peter Lohmander

SVENSKA SKOGS- OCH MASSABOLAGET, SSM, Praktikfallsuppgift i Kostnads - Intäktsanalys med Optimering Peter Lohmander Företaget står i begrepp att utforma en 10- årsbudget innefattande hela verksamheten inklusive avverkning, rundvirkestransport, massa- och pappersproduktion samt investeringar. Man har för avsikt att ekonomiskt optimera två femårsbudgetar simultant via lineär programmering.

Questions today (#1): Can we combine the forest sector and the energy sector in one modern optimization model for both sectors? The model should include relevant data for the heating and electricity plants and for all types of forest industry mills.

Necessary Model Properties: The model should be dynamic and include the options to invest in new production capacity. Such new capacity could, when it comes to investments in energy plants, have different properties with respect to technological choices, possible fuels and degrees of flexibility.

Why flexibility? Prices and the availability of different fuels are impossible to predict over horizons of the economic life time of a heating plant. That is why flexibility is valuable. In the old type of optimization models, such things could not be analyzed at all. Now, economic optimization of flexibility is possible.

Dynamic options In the model from 1981, one period was analysed. In a new dynamic model, the use of the forest resources can also be optimized over time. In the model from 1981, the capacities of different mills were constant. In the dynamic model, the capacity investments can be optimized over time.

The Option A new generation of optimization models is possible to construct. We should not hesitate to develop this generation!

Detailed long term forest planning is not optimal. Why should we make a detailed long term plan based on future prices and other conditions? Such things can not be perfectly predicted!

Stochastic Price

Economic Risk Management in Forestry and Forest Industry and Environmental Effects in a Turbulent World Economy

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

Low Correlation between Energy Prices and Pulp Prices Price of Electricity (li) Export Price of Kraft Paper and Kraft Board Price of Electricity (li) 10,2450 Export Price of Kraft Paper and Kraft Board 0,24501

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

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)

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.

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

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

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

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

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

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

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

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

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.

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.

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.

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.)

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.

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.

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

Link to the software:

Results: The expected economic value of one more unit of heating plant capacity is – = 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.

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.

Where do we focus on optimization in the forest sector? OR in the Forest Sector 2007 INFORMS International Meeting 2007 Puerto Rico

Industry, employment, economics and trade theory with focus on the forest sector may be optimized. It is our duty and pleasure to do that! Peter Lohmander