Managing forest plantations: long term models, tactical ...

Symposium on Models and Systems in Forestry – Chile 2002

Problem Area:

Managing forest plantations: long term models, tactical decisions, and

operational scheduling.


“Modeling supply chain integration in a forest company.

Ignacio Carrasco G. and Jorge Vera A.

Dpto. Ing. Industrial y Sistemas, Escuela de Ingeniería Pontificia Universidad Católica de Chile. Vicuña Mackenna 4860, Santiago, CHILE

tel: 56-2-686-4272 e-mail: [email protected]

The Problem Integrated Supply Chain management is an important subject in many industries, and in particular, in the forest industry. In this work we analyze the production planning problem of a forest industry formed by a forest division, a mill division, both of them under the control of the same parent company, together with pulp plants and export ports. In the current situation, each division makes decisions in a separated non-integrated manner, a setup which can generate inefficiencies when one looks at the global corporate objectives. Moreover, given the current incentives and the relations between both divisions, the production assignments can be sub optimal. In particular, one typical situation is that the mills receive logs of different characteristics to the ones under which the production planning would be carried out. This is due to lack of integration as well as limited information on the forest inventory. Methodology In this work, we have modeled the problem using a mathematical programming model which considers the production decisions in both divisions and their interaction. The objective of each company is to maximize profit within a one year horizon, with monthly decisions. The model considers the forest, mills, pulp plants as well as exports through ports. We consider the cases of decentralized decisions in each division, a case of decentralized decision, but with the additional constraint for the forest division of satisfying the mill requirements, and a fully centralized model where decisions are integrated toward maximizing corporate profit. We have considered various cases for both: fictitious and real situation of a forest company in Chile. Also conducted simulations for many price and demand situations was carry out. Our objective has been to understand an eventually quantify the value of integrated decisions in a vertically integrated company. We also addressed the problem of determining possible transfer prices for the products between divisions. Finally we give some elements on the analysis of the value of information together with integrated decisions, if better estimates of the forest inventory were available.


“Addressing computational complexity of large scale eucalypt forest management problems”

André O. Falcão Departamento de Engenharia Florestal

Instituto Superior de Agronomia Tapada da Ajuda, 1349-017 Lisboa, Portugal

e-mail: [email protected]

José G. Borges Departamento de Engenharia Florestal

Instituto Superior de Agronomia Tapada da Ajuda, 1349-017 Lisboa, Portugal


Howard M. Hoganson North Central Experiment Station

1861 Hwy 169 East, Grand Rapids, MN 55744-3396, USA e-mail: [email protected]

Forest managers are currently required to address complex problems (e.g. integration of planning levels, transportation considerations and concerns with the spatial arrangements of harvests). Model solving, in the case of such complex problems is crucial for adequate processing of all pertinent data. Specific solution techniques referenced in the literature include linear programs (LP) model decomposition (e.g. Hoganson and Rose 1984, Gunn and Rai 1987 and Lappi 1992), integer programs (IP) and mixed integer programs (MIP) (e.g. Kirby 1980, Covington et al. 1988, Jones et al. 1991, Hof and Joyce 1993, Murray and Church 1995b and Snyder and ReVelle 1997). Other authors used heuristic techniques to approximate optimal solutions to forest management scheduling problems. (O'Hara et al. (1989), Clements et al. (1990) and Nelson and Brodie (1990), Murray and Church (1995a), Weintraub et al. (1994), Weintraub et al. (1995), Lockwood and Moore (1993), Dahlin and Sallnas (1993), Murray and Church (1995a), Tarp and Helles (1997), Murray and Church (1995a), Bettinger et al. (1998), Boston and Bettinger (1999) Mullen and Buttler (1997), Hoganson and Borges (1998), Borges et al. (1999), Falcão and Borges (2001) ) The specificity of large scale eucalypt forest management problems, suggests the evolvement of appropriate model solving techniques. This paper discusses a two stage modeling approach to address the computational complexity of such problems. The first stage involves the design of an adequate data structure. The second stage, builds on the data structure to evolve an efficient solution technique. This modeling approach will be used to solve a large eucalypt management problem with the following structure:


Max NPV = x c ijij

M

j=1

N

=1i

i

∑∑ (1)

subject to,

x ij

M

j=1

i

∑ = 1, i∀ (2)

D xv kptijijpt

M

1=j

N

1=i

i

=∑∑ , T1,2,...,=t P1,2,...,=p ∧ and k=1,2….K (3)

0 = x 1 = x ijij ∨ , i∀ , M1,...,=j i∀ (4) where,

N = the number of management units. Mi= the number of alternatives (involving simultaneous harvest and transportation decisions) for management unit i. P = the number of products T = the number of planning periods K= the number of markets xij= binary variable that is set equal to 1 if alternative j is chosen for management unit i and to 0 otherwise. cij= net present value associated with alternative j for management unit i. It includes the value of the ending inventory. vijpt= yield of product p in period t that results from assigning alternative j to management unit i. dpt= deviation allowed from target volume level of product p in period t.

Vpt= target volume level of product p in period t. Equation (1) expresses the management objective of maximizing the forest net present value (NPV). Equation (2) ensures that one and only one alternative is assigned to each management unit. Equations (3) ensures that the demand levels for each product are met in each period and in each market. Equation (4) expresses the binary requirement on the decision variables. In general, this combinatorial optimization problem involves very large numbers of variables and constraints. This paper reports results from the application of this two-stage modeling approach. Keywords: Forest management; management models; computational complexity; Heuristics.


“Harvest planning”

Jenny Karlsson and Mikael Rönnqvist

Division of Optimization

Linköping University 58183 Linköping

e-mail: [email protected], [email protected] The problem we consider is harvesting planning from the perspective of Swedish forestry companies. In comparison with competitors on the international market, Sweden has large costs due to the infrastructure. This fact force the provision of forest products to be both efficient and customer oriented. Large forest firms own a considerable part of the forest. Larger forest companies have an organisation where the operations are divided into smaller regions, which may be composed of one or several districts. At each district harvesting plans are made for both long term and short term. On a tactical level an overall plan for one year are made. Through a central planning, the annual industrial demand for paper-, pulp- and sawmills are distributed on a monthly level for each district. On an operative level a more detailed plan are made for a couple of weeks. On a short time horizon the industrial demand are determined on a weekly level. The plans are continuously updated. The harvesting planning include decisions on which areas to harvest and when to harvest so that the industries receive required amount of assortments. It also includes decisions to buy additional areas from smaller forest owners, contracting of harvest teams and planning opening of roads that are necessary for harvesting and transportation. As there are many restrictions and a huge amount of information that is used, it is often difficult to get a clear overview of the overall planning situation. There are most often a limited number of persons that make the plans, and they spend a large amount of time to come up with qualitative plans. Decision support systems based on optimization are a key part to make it possible to model the complex connections and many restrictions that must be considered. We have developed a mathematical model for the harvesting planning problem at a district, on both tactical and operative levels. We have done this in a hierarchical structure where tactical and operative harvesting plans are made by two different models. The tactical model gives data to the operative. The harvesting plans are made start from a pool of areas possible to harvest. When tactical plans are made the pool of areas corresponds to at least 1,5 years harvesting. For each month harvesting areas should be chosen so that the industries demand can be fulfilled. When short-term plans are made an overall plan should be available, describing suitable areas for the specific planning period. One of the basic ideas is to take into account the varying demand at industries and ensure a smooth production. Each harvest area is unique with particular properties. Areas are of varying size with supplies between 100 and 1000 cubic meters and the composition of assortments is different. Each area is either fully harvested or thinned. Once it is harvested it produces a given amount of assortments. The produced amount per day is depending on middle size of the trees. Harvesting planning include decision of which harvest team to use for each area. Each team has different skills. That means the teams have equipment suitable for thinning or final


felling. There is a limit on their capacity concerning middle size on the trees. The teams have different production capacities. Another important thing to consider is the road network. The harvesting planning includes decision about opening of roads connecting the areas to public roads to make harvesting and transportation possible. In winter there are costs for opening roads due to snow removal. During break frost period restoring can be necessary to make some roads accessible. To control when and which roads that must be open an overall transportation plan are made. The planning problem also includes control of storage levels in forest, at terminals and industries. A significant cost is due to quality deterioration of products stored outdoors at harvest areas or at terminals. At the industries the storage capacity are limited. In the annual planning all decisions are taken on a monthly level. Harvesting areas are chosen for each month. Their relative order are not considered, which means that costs connected to moving equipment can not be taken into account. The cost due to value decrease of products stored outdoors is considered and estimated per month. The weather and road conditions are varying a lot during one year and affect the annual plan. The accessibility to areas and roads during the different time periods are of vital importance. Certain roads can not be used during some time periods and others should be avoided. Some areas can not be harvested during break frost periods due to loose ground. The short-term planning includes the same aspect as the annual planning, with a few differences. The total planning period of five weeks contains decision on a weekly level. It is not necessary to consider the accessibility of areas and roads, as the possible areas are assumed to be suitable for the particular planning period. The actual sequence for each harvesting team is defined. The costs associated with moving equipment are taken into account. In a more detailed planning on an operative level it is of vital importance to take in consideration the storage level and the age of the harvested timber. The quality deterioration cost increase for each week of storing. In the short term planning both storage and age are estimated on a weekly level. We have developed two mathematical models, one for tactical planning and one for operative planning. Both models are linear, mixed integer large scale problems. In the annual planning problem with a pool of areas consisting of 1,5 year harvesting, the number of possible areas is about 400. The number of permanent working teams at the district are 5, there are 5 assortments, 5 industries and 12 time periods. That gives a problem with 25 000 binary variables, 220 000 continuous variables and 60 000 constraints. It is not possible to solve the problem directly to optimality within reasonable time limit using some commercial program. We have developed a heuristic that gives high quality integer solutions in one day. The operative model involves about 40 possible harvesting areas, 6 working teams, 5 assortments, 5 industries, 5 time periods and 5 age classes of storage. We generate a limited number of harvesting sequences. That give a problem with 32 800 continuous variables, 6500 constraints and each possible sequence corresponds to a binary variable. With the number of harvesting sequences limited to 10 000 this model are directly solvable to optimality within distinct time limit.


“Managing the Future Forest Resource through Designer Trees”

CL Todoroki Forest Research, Sala St, Rotorua, New Zealand e-mail: [email protected]

SD Carson

Carson Associates Ltd, 82 Tihi Rd,, Rotorua, New Zealand e-mail: [email protected]

With today’s tree improvement technology coupled with knowledge of the influence of site, silvicultural and other forest management practices on tree growth and log quality, it is possible to manipulate tree form to engineer designer trees with specific characteristics. Theoretically, at least, we have the ability to create stands and portfolios of forests to optimise suitability for different end uses. We could design Structural Forests to optimise the quality of lumber for building materials, for furniture and mouldings markets (Long Clear Forests), for fingerjoint markets (Short Clears Forests) or for pulp and paper industries (PulpWood Forests). This begs a question: “Can we significantly increase product value by targeting forest management and tree improvement goals to a specific end-product?” The goal of this project is to examine methods for exploring the impact of manipulating tree characteristics through forest management and tree improvement on the value of the final end-product. This will be done by extending the forest resource forward to the wood product, and providing linkage back to forest management and genetic selection of parent stock, whether it be seed, clones, or specific genes. In this paper effort is concentrated on the LongClears and ShortClears Forests. We attempt to identify those important tree and branching characteristics that could be manipulated to optimise production of specific lumber products. The range within which the relevant characteristics can be manipulated by silviculture and genetics is defined and the impact that this range has on the value of lumber suitable for furniture, joinery, and remanufacturing markets is quantified. Quantification of the impact of targeting management and breeding of trees to specific end-uses is achieved through a methodological approach whereby we model a range of logs with different branch structures successively propagate the logs to model multitudes of internodal spacing variations between whorls that can be achieved by manipulating silviculture and genetics; and use a combination of mathematical programming and operations research techniques to calculate wood product outturn and value.


“Optimal diameter distributions in forest stand optimisation”

O.Chikumbo The Swedish University of Agricultural Sciences,

Department of Forest Resource Management and Geomatics, Umeå S-901 83, Sweden

I.M.Y. Mareels

Department of Electrical and Electronic Engineering, The University of Melbourne, Victoria 3010, Australia

O. Eriksson

The Swedish University of Agricultural Sciences, Department of Forest Resource Management and Geomatics,

Umeå S-901 83, Sweden

B.J. Turner School of Resources, Environment and Society, The Australian National University,Canberra,

ACT 0200, Australia

A combined optimal and parameter selection problem for predicting an optimal silvicultural regime and an initial planting density, is formulated for Eucalyptus nitens forest stands. The problem consists of a cost functional, state equations which describe the dynamics of forest growth, constraints, and a system parameter which is a decision parameter independent of time. The dynamics of forest growth are described by dynamical models, where the first-order average stand diameter equation is integrated with a Weibull distribution function, making it possible to account for the stand diameter distribution at each time instant. The formulation is based on the Pontryagin's maximum principle such that an exhaustive search is carried out at each decision stage. This same formulation is approximated by a constrained nonlinear programming problem and therefore solvable by a sequential quadratic programming algorithm. 1. Introduction Formulating a stand optimisation (or optimal control) problem for predicting an optimal thinning strategy has been demonstrated using Pontryagin’s maximum principle (Chikumbo and Mareels, 1995, Chikumbo et al., 1997). In this formulation, competition mortality was not accounted for. This was based on an untested assumption that the modeled forest stands were intensively managed and therefore, less likely to be influenced by competition mortality. All initialisation parameters for the optimal control problem were assumed known prior to solving the problem. In this paper we attempt to solve a combined optimal control and parameter selection problem where one of the initialisation parameters is an unknown. This parameter was the initial stand density. The potential exists in the


formulation to estimate more than one parameter, as long as it fits the criterion of a one-off estimation problem at initialisation. The states in the combined optimal control and parameter selection problem, included 2 of the Weibull probability density function parameters, namely the threshold and scale parameters. Such information enabled us to account for the probabilities of diameter distributions and subsequently the frequencies of diameter classes at each time-step. This was made possible by integrating a first-order ‘dynamical model’ for average diameter growth, with a 3-parameter Weibull distribution function (Chikumbo et al., 1992). The Weibull modulus (or shape parameter) remained a constant in the integration and was therefore not included in the optimal control and parameter selection formulation. The analysis data used here, only reflected a thinning from below, which may not violate the constancy of the Weibull modulus. However, investigations on the behaviour of the Weibull modulus with respect to different thinning strategies, i.e. row thinning, thinning from below and thinning from above may need to be done, providing the appropriate data are available. The idea would be to include the Weibull modulus as one of the states in the optimal control and parameter selection formulation. Note however, that variations in the threshold and scale parameters still influence the shape of the Weibull distribution function (see Figures 1 and 2).


0 20 40 600

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mid-pt diameter (cm)

num

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aw = 1

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Figure 1. The Weibull distributions, where the number of trees, scale and modulus are held

constant at 1500, 50 and 3.5 respectively, whilst varying the threshold parameter, aw (1, 5, 10, 15).


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num

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f tre

esbw = 10

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Figure 2. The Weibull distributions, where the total number of trees, threshold and modulus are held constant at 1500, 10 and 3.5 respectively, whilst varying the scale parameter, bw (10,

20, 30, 40). Nomination of the Weibull distribution function for describing the diameter distribution was based on its mathematical convenience and familiarity of the function with most forest analysts (Little, 1976). Although the distribution function has its limitations in its representativeness of multi-modal distributions, it is still robust for unimodal distributions. In future, we will be looking at using the segmented form of the Weibull distribution function, i.e. a mixture of 2 Weibull distributions, that will easily represent bimodal distributions, thereby increasing the flexibility of our optimal control and parameter selection formulation.


2. Data and state equations The data used for the model development came from the North Forests Burnie’s Eucalypt Tree Farm growth plots for three species, courtesy of North Forest Products, Tasmania, Australia. In this paper we only concentrated on Eucalyptus nitens growth plots. The combined optimal control and parameter selection formulation was based on control theory, where the forest stand system possesses internal energy, hence dynamic. Any control of such a system induces internal energy shifts that influence its outcome. To effectively account for the effects of the control actions of such a system, we need to have a defined objective, over a sufficient time scale where the likelihood of unforeseen events is minimal, and models that simulate the internal reactive-changes that influence all the possible outcomes. These models define the state of the system and we used dynamical models to represent these state equations. The state equations/dynamical models, which are stand growth models, respond to a control input and interact to give a combined effect on the outcome. The sequence of control actions (i.e. thinning at specified times) is what we predict in the optimisation problem, for any desired outcomes. Dynamical models are common building blocks in control models in disciplines such as Systems Engineering and Control Theory. What we present here is not an entirely new venture but an adoption of a well-founded research area. We introduce the thinking to stand forest management as an extension of an engineering methodology that has been used for many years to resolve practical problems. A discrete-time dynamical model has a mathematical structure where its response at t, is a summation of its regressed value of the previous response at time t-1, and a control input. Time is implicit in the function and is used as an integer to indicate equidistant observations (Ljung, 1987). Models are expressed in terms of orders of magnitude of their previous values. For example, a second-order model would have its current response at time t, expressed in terms of the regressed response variables at times t-1 and t-2. Application of dynamical models to forest growth has been demonstrated in the past 10 years for different types of forests (Chikumbo et al., 1996, Chikumbo et al., 1999, Chikumbo, 2001). The state equations were as follows:

sph(t) = [a1*sph(t-1) + a2*sph(t-2) + a3*sph(t-3) + a4*sph(t-4) + a5*sph(t-5) + b1(sph)] – u(t-1), (1) sba(t) = a6(el,si,sph)*sba(t-1) + b2*(1-a6(el,si,sph)), (2) mdh(t) = a7(el,sph)*mdh(t-1) + a8(a7)*mdh(t-2) + b3*(1-a7(el,sph)), (3) aw(t) = a9(el,si,sph)*aw(t-1) + b4*(1-a9(el,si,sph)), (4) bw(t) = a9(el,si,sph)*bw(t-1) (5)

where t = discrete-time (years), u = number of trees removed at thinning, sph = stand density (stems ha-1) sba = stand basal area (m2h-1), mdh = mean dominant height (metres), aw = Weibull threshold parameter, bw = Weibull scale parameter, el = elevation in metres, si = site index in metres, a1 = 1.2589, a2 = -0.7856, a3 = 0.4462, a4 = -0.173, a5 = 0.0248, a6 = -1.816e-5*sph + 7.3817e-8*el*sph – 1.0118e-6*si*sph – 3.575e-6*el*si + 0.9985,


a7 = 2.3775e-4*sph – 3.3146e-7*el*sph + 7.5876e-4*el + 1.381, a8 = -0.914*a7 + 0.8342, a9 = 3.3e-5*sph – 1.4e-5*el – 7.77e-4*si + 0.9572, b1 = -3.526e-4*sph2 + 1.032876*sph – 466.247, 900>∀sph ,

b1 = 8.5e-5*sph2 + 0.11*sph + 11, 900≤∀sph , b2 = 75, b3 = 50, b4 = 45.

Equation (1) that updates the number of standing trees in the combined optimal control and parameter selection formulation includes a fifth-order, tree survival model. Equations (1) and (2) are the first-order stand basal area and second-order predominant mean height respectively. Integration of the Weibull probability density function and a first-order dynamical model (Chikumbo, 1992) resulted in equations (3) and (4). The parameters in equations (1)-(4), i.e. a1, a2, a3, a6, a8, a9, and b1 are themselves predicted from environmental variables and initial/residual stand density. Inclusion of stand density as an explanatory variable was strategic, such that growth dynamics resulting from thinning would be captured (Chikumbo et al., 1999). A model with 2 or more orders was represented in the combined control and parameter selection model as a series of first-order functions. Therefore, we had a total of 10 states for our formulation. 3. Combined optimal control and parameter selection formulation The combined optimal control and parameter selection formulation was based on Pontryagin’s maximum principle (PMP) making it possible to impose constraints on the formulation. This is made possible by the inclusion of the Hamiltonian in the formulation such that the first-order necessary condition for optimality is satisfied (Dixon, 1972). PMP does not suffer from the ‘curse of dimensionality’ (Bellman, 1957) because it breaks the problem into a sequence of sub-problems. By applying ‘control parameterisation’ the combined optimal control and parameter selection problem may be approximated by a constrained nonlinear programming problem solvable by standard mathematical programming algorithms (Teo et al., 1989). MISER control software (Jennings, 1990) that employs NLPQL (Schittkowski, 1985), a sequential quadratic programming algorithm for solving constrained nonlinear programming problems, was used for solving our combined optimal control and parameter selection problem. The cost functional was a value production one based on a volume function with a proxy for value that maximised trees with higher stand basal area. With sufficient costs and revenue for forest operations, we would replace this proxy with an economic value. The cost functional was as follows:

)()()(

)()(max

)(0 tsph

tsbatVtsph

tuuimise

uJT

t∑

=

= (6)

V(t) = 0.3512*sba(t)*mdh(t) (7) where T = terminal time, with inequality constraints,


sph(t) ≥ 0, sph(t) ≥ sph(t-1), (8) sph(t-1) ≥ sph(t-2), sph(t-1) ≥ sph(t-3), sph(t-3) ≥ sph(t-4), sph(t-4) ≥ sph(t-5), initial states, sph(t0) = z(1), sba(t0) = 14, (9) mdh(t0) =4.8, mdh(t0+1) = 0.7 + 1.19*mdh(t0), aw(t) = 1, bw(t) = 50, where z(1) = initial stand density estimated in the control and parameter selection model, t0 = initial time, lower and upper bounds on the control, 0 ≤ u(t) ≥ 300 ∀t ∈ [5,40] (10) and, lower and upper bounds for system parameter, 900 ≤ z(1) ≥ 1500 (11) The site index and elevation were fixed at 20m and 400m respectively. 4. Results and discussion Though we employed PMP that would ensure that we avoid the curse of dimensionality, we created other problems because of too many states, and that is ill-conditioning. Ill-conditioning implies that there exists widely varying solutions that satisfy the criteria for acceptance as the optimal solution. Despite running the combined optimal control and parameter selection problem in MISER with different initial guesses, it was difficult to find a convergence to a true solution. There was one initialisation, where the constraints were met satisfactorily, even though the optimality of the Kuhn-Tucker condition was still to be satisfied. This meant that the current solution was close to the true solution and for practical purposes is acceptable as the optimal solution (Jennings, 1990). The solution had an initial stand density of 1359 stems ha-1 and thinning was concentrated in the years 21, 24, 28 and 32 at the rates of 102, 126, 121 and 128 stems ha-1. One way to guarantee local optimality would be to look closely at the survival model in equation (1) with the hope of reducing the order of the model. Investigations may also be carried out for the mean dominant height model to see whether a first-order dynamical model would be statistically sufficient in predicting height instead of the second-order model in equation (3). Reduction of orders would mean a less number of states leading to lesser likelihood of ill-conditioning, and greater possibility of satisfying both the constraints and the Kuhn–Tucker conditions for optimality. We noted that a combined optimal control and parameter selection formulation with 8 states (excluding the Weibull parameters) convergenced to an optimal solution without ill-conditioning problems. We could not at this stage validate the diameter distributions with available re-measurement data, given this research work was initiated by the desire of North Forests Wood Products to explore alternative silvicultural strategies. Measurements from thinning experiments that can be simulated with our combined optimal control and parameter selection model would be ideal for validation. Figure 3 shows some plots of diameter distributions, where the maximum possible diameter at each time step were guessed to the best of our knowledge. Our preferred position in the future would be to base such kind of guesses on measurement data. However, it interesting to note how the distributions still change in shape despite the Weibull modulus being kept constant. A worthwhile exercise would be to investigate the adequacy of the Weibull distribution, whether or not it adequately represents the diameter distributions of these intensively managed eucalypt forest stands.


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Figure 3. Solution plots of diameter distributions from the combined optimal control and

parameter selection problem where the Weibull modulus is a constant at 3.5. 5. Conclusion The diameter distributions from the combined optimal control and parameter selection model need to be validated with re-measurement diameter distribution data. Our work has served the purpose of demonstrating the feasibility of tracking diameter distributions in a stand optimisation model. There is a need of reducing the number of states to reduce the likelihood of ill-conditioning. However, we have provided a mechanism that, following rigorous diameter distributions validation, can be used as a basis for predicting alternative silvicultural strategies for E. nitens. Such capability is not yet available for North Forests Products.


Literature cited Bellman, R.E., 1957. Dynamic Programming. Princeton, NJ, Princeton University Press. Chikumbo, O., 2001. A basal area model responsive to thinning for a plantation forest.

Environment International 27(2001), 1-4. Chikumbo, O., James R.N., I.M.Y. Mareels, Turner B.J., 1996. Mortality simulations in

Pinus radiata plantations in the Tarawera valley regimes trial. Ecological Modelling 86, 253-258.

Chikumbo, O., Mareels, I.M.Y., 1995. Optimal thinning strategies based on dynamical models and the maximum principle. In: Bren, L., Greenwood, C., (Eds.), Application of New Technologies in Forestry, Ballarat, Victoria. Institute of Foresters of Australia, 1, pp. 239-245.

Chikumbo, O., Mareels, I.M.Y., Turner, B.J., 1999. Predicting stand basal area in thinned stands using a dynamical model. Forest Ecology and Management 116 (1999), 175-187.

Chikumbo, O., Mareels, I.M.Y., Turner, B.J., 1992. Integrating the Weibull into a dynamical model to predict future diameter distributions. In: Wood, G.B., Turner, B.J., (Eds.), Integrating Forest Information over space and Time. The Australian National University, ANUTECH Pty Ltd, pp. 94-102.

Chikumbo, O., Mareels, I.M.Y., Turner, B.J., 1997. A stand optimisation model developed from dynamical models for determining thinning strategies. In: Vasievich, J.M., Fried, J.S., Leefers, L.A., (Eds.), Seventh Symposium on Systems Analysis in Forest Resources, Traverse City, MI. Gen. Tech. Rep. NC-205, St. Paul, MN: U.S. Department of Agriculture, Forest Service, North Central Research Station, pp. 355-360.

Dixon, L.C.W., 1972. Nonlinear Optimisation. The English Universities Press Ltd., Bell & Ban Limited, Glasgow, UK.

Jennings, L.S., Fisher, M.E., Leo, K.L., Goh, C.J., 1990. MISER3 Optimal Control Software: Theory and User Manual. EMCOSS PTY Ltd., WA, Australia.

Little, S.N., 1976. The Weibull function as a diameter distribution model for mixed stands of Douglas-fir and western hemlock. Master of Science thesis, Pennsylvania State University.

Ljung, L., 1987. System Identification: Theory for the User. Englewood Cliffs, New Jersey 07632, Prentice Hall, Inc.

Schittkowski, K., 1985. NLPQL: A FORTRAN subroutine for solving constrained nonlinear programming problems. Annals of Operations Research, 5, 485-500.

Teo, K.L., Wong, K.H., Goh, C.J., 1989. Optimal maintenance of a system of machines with the weakest link dependence performance. Optimal Control Methods and Application, 10, 113-127.


“Modeling the effects of forest management on carbon sequestration in a loblolly pine plantation”

Michael P. Spinney and Stephen P. Prisley

Virginia Tech Department of Forestry 319 Cheatham Hall

Blacksburg, VA 24061 United States

tel: 540-231-2493 e-mail: [email protected]

Global warming from increased atmospheric concentrations of greenhouse gases (GHG) may cause extensive damage, although considerable uncertainty surrounds the extent of the impact. Carbon dioxide is the most important greenhouse gas because it accounts for 80% of total US GHG emissions and 61% of the enhanced absorption. Forests have the ability to alleviate the impact through carbon sequestration. Forest based mitigation is economically efficient because forests have market and non-market value, and economic investment in management can be recovered. Forest management controls the annual harvested volume and the end-use disposition category of wood products. Shorter rotations tend to produce a large amount of short-lived wood (and paper) products, while longer rotations produce more long-lived wood products such as building materials. Determining optimal carbon based management regimes is essential to management of forests as carbon sinks. A general framework for trading emission permits has been established by the Kyoto Protocol. A change in management that increases storage of carbon (C) earns credit equal to the difference between current storage and baseline. Our model addresses the following questions in the context of tradable emission permits. What would the value of a C permit need to be to change management from baseline to scenarios storing more C? Can a shorter rotation sequester more C than a longer rotation such that income from selling credits provides income beyond forest products? Our model has two goals. The first is to track standing timber and residual wood product volume and carbon for 50 years under each of six management scenarios. Second, we compare the C storage of modeled scenarios to a baseline to determine how a tradable C emission permits scheme can affect forest management. Analysis will be limited to relative differences among modeled regimes. The model scenarios have rotation lengths ranging from 20 to 40 years with thinnings scheduled as soon as year 17 and as late as year 30. Initial stand conditions are equal for all scenarios. All stands are planted at 726 trees per acre. Site index is assumed to be constant throughout the rotation at 60 feet at base age 25. Residual basal area of thinnings is 70ft2/ac. The two main components of the model are that harvested timber is made into wood products then those wood products decompose. The decomposition rate depends on the classification of the wood product as sawtimber or pulpwood. Our model utilizes the growth rate, timber harvest volumes and merchantability proportions of Tauyield, a regional


loblolly pine growth and yield model, and decomposition assumptions from the US forest sector carbon model (FORCARB). The initial age class distribution of an existing loblolly pine plantation is subjected to area regulation, where annual harvested area equals total area divided by rotation length. The oldest age classes are harvested first, and harvested volume is merchandized into either pulpwood or sawtimber. The net present value (NPV) of the baseline is compared to other scenarios. An initial goal of this analysis is to examine tradeoffs between timber production and C storage. Preliminary results indicate that these objectives are compatible in most of the modeled scenarios. It is possible to increase NPV and C storage simultaneously. Cumulative wood products volume accounts for a substantial amount of the C stored by a forest management regime. Only the shortest scenario has less NPV than baseline, but all sequester more C than baseline.


“Forwarding at harvest areas”

M. Forsberg The Forestry Research Institute of Sweden


P. Flisberg Division of Optimization, Linköping University


M. Rönnqvist The Forestry Research Institute of Sweden

Division of Optimization, Linköping University e-mail: [email protected]

The cost of raw material in Sweden is among the highest in the world. It is therefore important to keep all costs in the entire wood-flow chain as small as possible. A general opinion in Swedish forestry today, is that the potential lies in improved integration between different parts of the wood-flow chain. The information flow together with improved transportation planning are important components. Furthermore, customer orientation is at the center of attention. The idea is that the correct quality and amount of raw materials should be delivered to the customer at the right time. By this, the customer has the opportunity to improve on the utilization of the raw material as well as in production planning. Hereby, both a decrease in processing costs as well as an increase in product value may be achieved. Customer orientation will dramatically increase the demands put on the logistics system in Swedish forestry. The number of assortments will increase as well as the need and request for timed deliveries. Storage must be reduced since maintaining the inherent quality of the raw material until it is delivered, is one of the basic ideas of customer orientation. An important operative problem is to extract roundwood from actual felling points to forest roads. Once at the pickup point, logging trucks collect it for further secondary transportation to saw- and pulp-mills. The actual extraction problem is to move logpiles in as short time as possible from the felling piles to the pickup point. Harvesting of full trees are mechanized and there are two types of vehicles operating in the forest. The vehicle which actually fell and buck trees is the harvester. The harvester puts the bucked logs in small piles based on assortment as it moves around. These piles are then collected by a forwarder and moved to larger piles adjacent to forestry roads. In principle all sawlogs are extracted by a forwarder for the first distance. The overall cost for this operation is estimated to be $US 200-250 million. A small increase in efficiency may obviously have a large impact on operational costs. The trend is also that the number of assortments i.e. the number of different piles is increasing, making operations both increasingly difficult and more costly. In this paper we report on a system that combine a geographical information system (GIS) and operations research techniques to establish routes. The purpose has been to verify earlier results, improve the optimisation procedures and to develop a system that use information


gathered by a harvester, use real time GPS information, automatic routing and mobile communication in an onboard computer in the forwarder. An harvester is used to collect information online. A combination of optimization and heuristics is used to construct routes within distinct time limits. Tests performed at a major Swedish forest company show savings of about 5-10%.


“Logistics optimization of the production chain in forestry by means of simulation software”

Anne-Katrin Bruchner Dep. of Forest Work Science TUM

Am Hochanger 13, 85354 Freising, Germany tel. (49) 8161 – 71 47 57

e-mail: [email protected] Introduction The annual cut in the German forest industry amounts to 40 Mio cbm. Two thirds of the harvested roundwood are delivered to saw mills. Enterprises in the forest sector, today, have to compete for a position on a global timber market. To fulfill the requirements of their customers and to meet international timber prices it is necessary to reduce operation and transport costs in the timber harvesting process. Improved organisation and planning of harvesting operations in forestry have been identified as a means of optimizing the disposition of log assortments for timber and paper markets. The timber industry as well as pulp and paper mills require roundwood from local forest enterprises in constant quantity and high quality. The challenge for forestry, today, is a market orientated timber supply and to become a proactive industry instead of a reactive one. Harvesting operations are still mostly planned due to silvicultural regimes, but in the future with growing investments into machines economical aspects are going to be very important for the positioning of an enterprise in a global timber market. Low operational costs and a high technical productivity of the machinery will become more and more decisive for forest operations. An improvement of the integral logistics management can only be achieved by taking a close look on all elements of the production chain. The main aim of forest logistics in Germany is to manage the material flow in all segments of the wood supply chain from felling to mill. In order to be able to respond on the industrial dynamics it is important for the forest enterprises to know exactly their production layout and stand inventory at any time. Planning processes within the operational system that are based on an up-to-date inventory of the raw material can be optimized by using supporting tools like simulation software.


Figure 1. Production environment for harvesting operations.Anne-Katrin Bruchner

Simulation Software as a Planning Tool in Forestry Simulation software is a common tool in several different industrial branches for optimizing internal production and logistics and is designed for analysing, planning and controlling material handling systems. Simulation software is also already applied in the wood supply chain in the paper industry.

Figure 2. Possible application of simulation software in the wood supply chain

Simulation can be used for analysing large and complex real-world situations that can not be solved by mathematical operations research models. A large number of variables, parameters and also functions can be handeled. An advantage of modelling is that it does not disturb the real system, and various decision-making scenarios can be tested without interfering. The system can be run in a short period of time because of the possibility of compressing time in computer simulations. Therefore, simulated data are much cheaper to collect than similar data from the real-world system. A computer based simulation model describes the operation of the system and its individual components whose behaviour can be predicted. This feature allows a study of the interaction between individual processes in the system.


In comparison to other industries timber production is part of a very complex system and is performed in a sensitive environment. German forestry has to deal with the management of a “plant area” with an average size of about 10.000 ha and has special production conditions such as inhomogenous stands and changing weather conditions. Standard simulation software has to be adapted to special requirements in forestry. Required parameters for implementation of simulation software in forestry: • topographical information: Digital forest maps with position of logging roads and

extraction lines, digital 3 D models for slope information • information about the “storehouse capacity”: quantity of trees, distribution of tree

species, classification of the stands according to alternatives of silvicultural management • quality of raw material: tree species, diameter at breast height dbh), length and volume

of each single tree • produced log assortments: tree species, short wood/long wood, quality/dimension

(diameter) • information about the production: charakteristics of alternative silvicultural treatment

(removal, time of removal, produced assortments) • information about harvesting and transport operations: data of efficency rate, cost rate

and expenditure Research Methodology and Applied Simulation Technique The first step in our research study was to evaluate software which could be adapted to complex systems such as the production chain in forestry. Eight different software packages were tested in a multiple goal analysis by means of a catalogue of criteria containing several specific forest requirements. The results showed that it is possible to apply simulation software for material handling systems for operational planning in the forest sector. For modelling different timber harvesting scenarios it is necessary to create a virtual enterprise which provides basic informations of stand characteristics, logging roads and machinery data. Our software study proved that only four programms out of eight due to variuos reasons could be used for material flow planning in forestry. In the next step of this research one software package is going to be intensively investigated. Within this discrete simulation a material handling system can be defined with all its physical components in an edit environment in which also the logic is programmed. The simulation can then be run in a simulation environment in which a detailed 3 D real-time visualisation of the system is generated. The development of the forest model is divided into five phases: 1. Definition of the problem the model should solve 2. Construction of the model 3. Simulation runs 4. Verification and Validation of the model 5. Implementation of the results in the real-world system The simulation of the current research is concentrating on one forest estate located in Southern Germany. The stand data are results of detailed research work of the Chair of Yield Science and the Chair of Silviculture of the Technical University Munich and are provided for the model. At the beginning of the simulation harvesting operations will be modelled and analysed on stand level. The number and combinations of different operations will be extended with time.


After the implementation of these basics it is possible to build different operational scenarios. The user of the software can call up statistics for every single step of each operation at any time of the running simulation. Results of the Application of Simulation Software in Forestry The aim of the research is to identify the most effective and efficient machine combination(s) for the timber production and to optimize possible harvesting operations which simultaneously lead to reduced process costs. Simulation statistics give detailed realtime information about the harvesting and transport processes as shown below: Simulation software allows the following statistical parameters in forestry : • machine hour rate (pmh) • work volume • degree of utilization of the timber growing stock • costs: staff costs, pmh-costs (productive machine hour), fixed costs, profit contribution • efficiency rate • max. energy consumption • total driving distance of the machines (harvester, forwarder) during the operation • distribution of machines on logging roads and extraction lines • payload of the machines The advantages of a computer based simulation model for forest enterprises are: • optimizing and reducing costs in all steps of the production • increasing product quality and improving forecasting of available timber supply quantity • improve service output for their costumers List of literature available on request.


“Logistics software implementation in Austrian forest and timber industries”

Peter Daxner University of Agricultural Sciences, Vienna

Institute of Forest and Mountain Risk Engineering Peter-Jordan-Str. 70/2, 1190 Vienna, Austria

tel. 0043 1 47654 4303 e-mail: [email protected]

1. Introduction In connection with increasing mechanization of timber harvesting systems technical optimisation of tree processing and transportation was the main task over the past years. Another main part of customer-oriented timber production, information interchange, is still in its infancy. According to experiences in other economic sectors it is estimated that further benefit can be generated by interface design. For that reason it is necessary to reduce process variability within and especially between different companies and to synchronize inter-entrepreneurial processes. At the moment many companies operate like a “black box” for their business partners – information (e.g. in the form of an order) is brought in and after some time output (e.g. information, material) is generated, but internal processes and mechanisms are obscure. To obtain goals like • better fulfilment of customer needs and improved quality management, • higher accuracy of planning, • reduction of cost as an effect of efficient information supply it is necessary to provide common structures and to integrate inter-entrepreneurial business processes. One possible way is the linkage of information systems and the automation of information flow. The project “Produktionskette Holz” was started to promote information interchange in mechanized timber harvesting systems by implementing GEOMAIL software in Austrian forest and timber industries. 2. Methodology 2.1 Logistics-software GEOMAIL GEOMAIL is a software tool to enhance data flow in timber production. It is based on a geographic information system (GIS) and therefore it allows to display information relevant for forest logistics on a basic map. The main technical features of GEOMAIL are: • Data processing via e-mail • Universal data standard XML • No database required, but possibility of database integration • Integration of Global Positioning System (GPS) • Connection to the Internet via mobile phone (GSM). The main advantages of GEOMAIL software are:


• up-to-date information and saving of time: for process partners the same level of information is available at any time • enhanced overview of the whole timber production chain from stand selection to trucking • improved orientation and routing for staff of forest companies, contractors as well as

truck drivers: most information is map-based; auxiliary information can be directly digitised in GEOMAIL

• reduction of timber losses through better overview of log piles • interoperability: integration of GEOMAIL into existing business software • improved controlling and quality management 2.2 Process management The general approach for logistics software implementation in Austrian timber production is based on the basic steps of process management (Figure 1).

Figure 1: Process management approach.

The first step of process management is survey and data collection. Activities within the business process of timber production are defined and documented. Available information is organized in the step of structuring. In the analysis step the different processes are determined, common attributes are filtered and the processes are mapped as models. On the basis of this data reference models are developed considering the business framework and environmental impacts. These reference models are evaluated and adapted in a modification step. The result are reference models for different kinds of processes which are implemented at the business partners. At this time the step of monitoring starts a continuous improvement of the business processes and useful information for subsequent process changes is gained. 3 Preliminary results 3.1 Data collection and process representation The survey of the present processes was carried out at 20 different companies. 11 of these companies are specialised in the production of sawlogs and pulpwood (mainly forest companies), 7 companies deal with sawmilling and pulp and paper and 2 companies work as forest contractors (harvesting and transportation). In the survey the following information was collected (Table 1):


Process representation was done in terms of LOV-Charts (“line-of-visibility”) according to Micrografx iGrafx Process methodology. 3.2 Rating of process steps Within process models single steps were differentiated according to their influence on business performance. Grouping was done on the basis of the following criteria: • influence on current and expected revenues • relevance on fulfilment of customer needs and expectations • contribution to other process steps • substitutability by technical solutions • necessary changes following process modifications • transferability to other process partners

3.3 Development of reference models The next step was to develop reference models. The realisation of optimisation potentials and minimisation of productivity gaps was based on process mapping, process analysis and rating of process steps as well as productivity ratings. Reference models were evaluated, tested and further modified with regard to functionality. At this phase the documentation and representation of business processes is another advantage of reference models. Reference models can be used for enhanced quality management.


Figure 2: Reference model for information interchange with GEOMAIL software.

3.4 Implementation and monitoring Process models were implemented in test runs. In preliminary workshops all partners were informed about the aims of the test, the implementation of reference models and the integration of existing business processes. All test runs were monitored and experiences were used to adapt the reference models. Hence it was tried to realize a systematic, continuous process refinement. 4 Conclusions The present investigation started with the aim to introduce GEOMAIL logistics software in Austrian forest and timber industries. The result of the implementation phase is the suitability of the software tool to fulfil the objectives of enhanced data flow. In detail the following results and open questions are to point out: • GEOMAIL is designed as an information system. In GEOMAIL software there are

presently no optimisation or controlling mechanisms included and therefore no controlling functions for optimising the timber production chain can be expected.

• Although handling of GEOMAIL software is quite user-friendly right now there should be further development to raise usability and user acceptance.

• Major problems were caused by the process implementation mainly in forest companies. For some participants it was quite difficult to adjust to new process structures and terminations. In some companies this problem was reinforced due to the first introduction of computers at lower management level.

• Some participants could hardly identify themselves with the continuous process of change. They expected to receive a practically finished solution for their business needs and problems and could not see themselves as a part of the implementation process.

5 Acknowledgements


Sincere thank to the Provincial Government of Lower Austria and the Austrian Federal Ministry of Agriculture, Forestry, Environment and Water Management for funding this research work.


“Models for forest operational decisions”

Rafael Esptein N. and Andrés Weintraub P.

Department of Industrial Engineering University of Chile

República #701, Santiago – Chile tel: (56-2) 678-4046

e-mail: [email protected], [email protected] Operational decisions in forest management involve location of harvesting machinery, short term harvesting and transportation. Forest firms in Chile are mostly vertically integrated and use pine plantations. We first describe models we have developed to support these decisions and algorithmic challenges derived from these problems. The machine location problem consists in determining how harvesting machinery should be deployed to harvest an area of say 500 hectares in the next several months. Skidders are used for flat areas and towers or cable logging for steep slopes. Roads need to be built to access the tower areas and skidder operations. A system was developed in joint work with John and Bren Sessions, at Oregon State University to support these decisions. It picks information from a GIS, has a graphic interactive interphase and a heuristic algorithm. The system is being used by several companies in Chile and one in Colombia with significant improvements. We discuss alternative exact algorithmic approach solutions, based on different forms of decomposing and strengthening the original formulation. The short term harvesting problem basically needs to match concrete orders for the next 3 to 8 weeks for wood products in length, diameter and quality with standing timber. Decisions made include stands to be harvested in each period (week), bucking patterns to be used in the field, transportation of products to destinations such as sawmills and pulp plants to satisfy demands and need for harvesting machinery and trucks. An LP model with column generation (to handle the large number of possible bucking patterns) was implemented and is being used successfully by most Chilean forest firms. The significant gains obtained are due to a much better use of the timber. Another operational model was developed for eucalyptus plantations in Brasil. In the transportation system, trucks must carry daily products from origins in the forest to destinations. A typical problem will have 8 to 25 origins, 4 to 10 destinations, 60 to 250 trucks depending on the size of the firm. Traditional manual scheduling led to high queuing and low use of trucks. A system was developed to support these decisions. The system, run daily through a control center is based on a simulation model with heuristics. It has led to cost reductions between 15% to 25%. The system is being used by most Chilean forest firms, as well as in Brasil and South Africa. A next step is to incorporate communication technology to make decisions in real time. We discuss a proposed exact algorithmic formulation of the problem. Finally, we analyze the harvesting problem from a supply chain perspective, including downstream operations such as sawmills, and discuss how integration of decisions along the chain may improve the overall performance.


“The hybrid simulation approach to modeling stand level forest ecosystem management; applications of FORECAST in

Canada and elsewhere”

J. P. Kimmins, Brad Seely, Clive Welham, Robin Duchesneau and Eliot McIntire

Dept of Forest Sciences, UBC, Vancouver, B.C. ,Canada,V6T 1Z4

604-822-3549 or 8549 e-mail: [email protected], [email protected]

Hybrid simulation modeling as represented in the stand-level, ecosystem management model FORECAST involves the combination of empirical data on the past growth of a forest (historical bioassay data), data on rates of certain ecological processes, and estimates of the rates of other processes calculated from knowledge of those processes and simple field measures of their results (a back-casting approach to calibration of process simulation). These data are combined in a series of setup programs in which simulation rules are developed. These rules are then used in the ecosystem simulation program together with a file that describes the initial state of all the variables that are to be represented in the simulation, and a file that describes the stand management system and scenario that are to be simulated. This multi-value model can represent all the major silvicultural treatments, and their effect on a wide variety of values and ecosystem structures and conditions. Most uniform silvicultural systems can be simulated in this aspatial model, including multi cohort systems and mixtures. It is not suitable for truly all aged forests. FORECAST is currently being used in several commercial forestry applications in British Columbia and Saskatchewan, and by forest researchers in the UK and Norway. These applications range from investigations of alternative management scenarios and silvicultural systems, to carbon storage and sequestration, to the driver of a large forest estate timber supply model and a stand/landscape wildlife habitat suitability model. FORECAST is also being applied in the analysis of multiple rotation yield decline in Chinese fir in eastern China. The model is currently being linked to wind, insect and disease models, and a climate change capability is being developed. FORECAST is used to drive two educational and extension software packages – FORTOON and POSSIBLE FOREST FUTURES. It has been linked to the stand level visualization software SVS and to World Construction Set visualizations. An example of its use in a meta-model consisting of the timber supply model ATLAS, the wildlife habitat suitability model SIMFOR and to visualization systems for application in a complex land use/forest management conflict in BC will be given. The performance of FORECAST has been compared with the stand level growth and yield model TASS in an analysis of the question: How much detail do we need in a stand model? The results of this comparison will be presented. Finally, FORECAST has the capability to be used as a model of ecological succession. An example of this application will be given.


“Solving a harvest machine location problem”

Andrés Pereira Department of Industrial Engineering

Universidad de Chile

Jorge Vera Department of Systems Engineering

P. Universidad Católica de Chile e-mail: [email protected]

Andrés Weintraub

Department Of Industrial Engineering Universidad de Chile

e-mail: [email protected] The use of harvesting machinery usually involves use of skidders for flat terrain, tower or cable logging for steeper areas (or areas where fragile soils need to be protected), as well as a corresponding secondary road network. Roads are needed to access the tower location and to be near skidder operations. The latter is important so that skidders, which are slow machines need not haul logs over distances over 300 or so to reach a road. Systems to schedule harvesting machinery and road building for a single area in the near future have so far relied on heuristics. Efforts have been made to solve this problem using exact formulations, based on different forms of decomposition, but these approaches have been able to solve reasonably well only small or medium sized problems. We analyze an approximate solution approach to a more general, multiperiod form of this problem. Consider a large number of independent areas that will be harvested in the next 10-15 periods (periods are considered as a season). Several decisions need to be made. a) Which areas will be harvested each period? b)How will each area be harvested. That is, where will the harvesting machines be located to insure that all timber is harvested efficintly. The problem can be characterized as follows. Given a specific basic location for a machine (tower a skidder), it is know through GIS information the reach of the machine for harvesting . We assume road building and transportation costs implicit in the machine locations, which reduces the computational complexity. This problem still has many 0-1 variables, as each area and period will have a large set of possible machine locations. If we consider for example 10 periods and 40 areas, and a typical area has 100 possible machine locations , the number of integer variables is 40.000, quite large if we attempt to solve the problem as a whole. We propose a decomposition approach, where two types of decisions are viewed in a hierarchical way. At a higher level. an approximate model decides on the sequencing of areas to harvest each period. At a lower level of decision , the machine location decisions are defined. We prove that given the monotonic and slow growth of timber, using the optimal solution of the machine locations only for the first period, we can obtain a solution for the higher level problem which has a small error bound in relation to using the optimal


machine allocation for each period. Naturally, once it is decided for each area the period of harvesting with this approximate higher level model, at lower level optimal decisions are taken for each area in the corrsponding period. Computational results show that solutions with this relatively small error can be obtained at significant computational savings. We note a similarity of this problem and a classical plant location problem, where the number of customers grows slowly, induced just by slow population growth .


“Packing: useful tool for planted forest management”

Robert A. Merriam 616 Pamaele St., Kailua, HI 96734, USA

Victor D. Phillips

College of Natural Resources University of Wisconsin-Stevens Point,

Stevens Point, WI 54481, USA After species and provenance selection, the most important decision for a new plantation is how many trees to plant on the chosen site. A planted-forest manager’s decisions on how much growing space to provide to trees initially at planting, which is later increased through mortality and thinning, are of paramount importance. At a given site and for a specified market objective(s), desirable stand density and rotation age are well known through practical experience for many tree species grown in commercial plantations. The scientific basis of stand-density and rotation age recommendations for a given species at a given site can be explained and quantified satisfactorily, however, if the growth of a free-growing tree and the growing space that it needs to remain free of competition are known. ‘Packing’, which integrates this information, is a simple, powerful descriptor of tree growth in young, even-aged, monoculture stands, and is a useful quantitative tool to help practicing foresters make critical management decisions successfully. In this paper, we present some terminology background, and then a quantification of Langsaeter’s general relation of increment versus stand density in graphic form where neither axis of the graph was quantified. We have found a relation between stand density and increment in early monoculture plantation stands that permits quantification of Langsaeter’s relation. The increment axis is in terms of the ratio of stand increment to that of a stand full of free-growing trees, while the stand density axis is the ratio of the number of trees in the stand to the number of free-growing trees in the full stand, or “packing.” Thus, unit stand density results in unit stand increment. Optimal stand density, i.e. a packing value of about 10, results in an increment of about 4 times the unit increment. Unit stand densities were derived from the work of O’Connor in South Africa in the early 1900’s. Keywords: Planted forests, tree plantations, growing space, competition, relative density, rotation age.


“Experimenting with industrial dynamics in the forest sector – a Beer Game application”

Erlend Ystrøm Haartveit Norwegian Forest Research Institute

Høgskoleveien 12, N-1432 Ås, Norway tel: 47 64 94 90 95


Dag E. Fjeld Swedish University of Agricultural Sciences

Faculty of Forestry, SLU, 901 83 Umeå, Sweden

tel: 46 90 786 58 56 e-mail: [email protected]

Introduction The ”Beer Distribution Game” (Beer Game) is used in many logistics courses to give students an entertaining experience of participating in a commodity distribution chain. The game provides empirical evidence of industrial dynamics in a four-stage supply chain where production demand at each stage are controlled by market ”pull” principles. Because of the structure of the game, most players experience demand amplification and find themselves unable to secure a stable operation of the system. The results of the game are judged in terms of supply chain costs (sum of inventory and stock-out penalties), while the chain dynamics is described using statistical measures of weekly demand and supply oscillations. A primary characteristic of wood procurement process is the sorting of the raw material into a number of quality classes for further processing into products or product components. In terms of logistics or supply chain theory, this represents an unusual case, having a divergent material flow. For this reason two divergent-flow versions of the Beer Game have been developed for use in forestry education. In this paper they are referred to as Wood Supply Games. The original Beer Game consists of four stages: the brewery, which produces the beer, and ships it through a distributor and a wholesaler, before the retailer sells the beer according to consumer demand. The Wood Supply Games also have four stages: wood supply group, paper mill/sawmill, wholesalers and retailers. When comparing the Beer Game with the Wood Supply Games the stages are numbered from first to fourth, starting with the brewery and the wood supply group, respectively. The first divergent version is based on a chain with a common source for raw materials (the forest) that diverges at the first position (wood supply group) into two chains. One chain is for sawlogs, with a sawmill (second position), followed by a wholesaler and a retailer of lumber (third and fourth positions). The other chain is for pulpwood, with a paper mill followed by two stages for distribution of paper products. In this paper, this game is referred to as the divergent version of the Wood Supply Game.


The second divergent version has the same basic structure as the first, but includes the flow of chips from the sawmill to the paper mill position (second positions for each chain). The by-products from the sawmill create an additional point of divergence for the lumber chain, but a point of convergence for the paper chain. In this paper this game is referred to as the integrated version of the Wood Supply Game. Different restrictions for material flow may be applied to the different structures. In the divergent version, the mix of sawlogs or pulpwood ordered by wood supply group (first position) is subjected to limitations of range (e.g. minimum and maximum percentage of pulpwood). In the integrated version, the mix of chips and pulpwood used to produce paper may also be subjected to varying limitations of range (e.g. minimum and maximum percentage of chips). The integrated version also divides lumber and paper production into main products (lumber, paper) and by-products. Supply chains in reality have a network structure, rather than being a linear sequence of actors with vendor/customer relationships. While most models of supply chains are unable to take into account effects of dependencies not following the main flow of materials, the two versions of the Wood Supply Game, may be used to study such effects. The results of the games are highly variable and dependent on the decision-making behaviour of the actors involved. In order to conduct valid statistical analyses of differences between supply chain structures, a great number of replications are required. Goal The goal of this paper is to generate hypotheses comparing supply chain costs and demand amplification between different supply chain structures. Empirical results from pilot studies of the divergent (three replications) and integrated (one replication) versions of the Wood Supply Game are compared with results from earlier studies of the Beer Game. In both versions of the Wood Supply Game, the same cost assumptions are used as in the original Beer Game. Results are, however, adjusted for different levels of demand required by the different structures. Results - Inventory Costs The total supply chain costs from earlier studies of the Beer Game are on average USD 2028 for the 35-week playing period. Results indicate that the total costs are somewhat higher for the divergent version (USD 2260/35 wks) and highest for the integrated version (USD 8508/35 wks). The differences between the structures are largest for the first position and smallest for the fourth position. Results - Peak Order Rates When studying how demand is amplified, two measures of the weekly order rates are used: the peak order and the sample variance of the 35 orders placed by each position. For all the cases, the peak demand for the final sales is 8 units per week. In the Beer Game, the largest peak demand is found for the first position (peak order = 32), and the smallest is found for the fourth position (peak order = 15). For the first position of the divergent Wood Supply Game, the peak order was 90 % higher than the first position of the Beer Game. For the second, third and fourth positions the differences were smaller, with peak orders for the divergent version 15-35 % higher than for the corresponding positions in the Beer Game. Peak order rates were highest for the Integrated Wood Supply game; 85-120% higher than the Beer Game for all positions.


Results - Order Variance In the Beer Game, the variance of order rates decreases along the flow of materials, from 72 at first position (brewery) to 13 at the fourth position (retailer). For the first position of the divergent version the variance of order rates was approximately 400% greater than what was found for this position in the Beer game. For the second and third positions, the variance of order rates increased by 55-75% compared to the corresponding positions in the Beer Game. The fourth position produced only slightly higher variances (20%) than the fourth position in the Beer Game. The variance of order rates was greatest for the integrated version of the Wood Supply Game. Even for the smallest relative increase the observed variance was 450 % higher than found in the Beer Game. For the first position, which also is the point of divergence, the variance was more than 800 % higher than the first position in the Beer Game. All three measures of supply chain efficiency (where high costs, high order peak values and high order variance indicate low efficiency) show the same ranking of the supply chain structures. The highest efficiency was found for the original Beer Game. The divergent version of the Wood Supply Game produces results on an intermediate level, and the integrated version had the lowest supply chain efficiency. The effect of restrictions in the Wood Supply Game The divergent version of the Wood Supply Game has been run with strict constraints at the point of divergence (first position), and with relaxed constraints. Relaxing the constraints implies that the flexibility with respect to the proportions of sawlogs/pulpwood in the total mix delivered from the forest increases. Relaxing constraints at the point of divergence appears to reduce the impact of the diverging structure to the point that results are similar to the original Beer Game. On the background of pilot experiments with the divergent version, the following hypothesis is proposed: H1: In a simple diverging environment, increasing the rigidity of constraints applied to the point of divergence will negatively influence supply chain performance. In the integrated version the dependencies between the lumber and the paper chain are even greater. An interesting observation is that if one of the chains is not managed well, costs seem to increase for both chains, particularly for the upstream positions (the first and second positions). This is partly a result of the points of divergence at the wood supply group and at the sawmill, (first and second positions), and partly the effect of the convergence at the paper mill (second position). It is not possible, given the data, to estimate the two effects separately. The results obtained using the integrated version had moderate constraints for the linkage between the paper mill and the sawmill (second positions). That is, the paper mill had high degrees of freedom when selecting the mixture of chips and pulpwood to enter paper production, and the sawmill had small penalties for not being able to deliver chips. On the background of the pilot experiment with the integrated version, the following hypothesis is proposed: H2: Given the same rigidity of constraints, further increasing the complexity (degree of divergence/convergence) in a supply chain will negatively affect performance. This hypothesis is vague due to the limited experience with the Wood Supply Game. However, even the integrated version is suitable for further studies in an educational environment. Students may vary the constraints with the aim of increasing the knowledge of


effects of divergence and dependencies between linked supply chains operating in different markets.


“Strategic and Tactical Forest Planning Models in the Chilean Industry: a 10-year experience and challenges ahead”

Gonzalo Paredes Forest Management Institute

Mauricio Ruiz-Tagle and Aurelio Solis

Informatics Institute, Austral University of Chile Valdivia, Chile

Chilean forest companies have experienced notorious managerial developments over the last two decades in order to face the challenges raised by forest products exports, competition, globalization and, more recently, by forest sustainability certification requirements. With a forest patrimony compossed by only one or two species, the managerial requirements have multiplicated as improved genetic material is incorporated into the forest base, as well as different silvicultural techniques, management regimes and harvest techniques are adopted. The products of the industrial plantations are now demanded by competing mills, thus requiring very efficient and sustainable log allocations. The incorporation of mathematical programming tools, particularly linear and mixed integer programming models, into the strategic and tactical decission making processes of the companies, has been possible after successfully solving a number of issues related to the economics and modeling techniques. A hierarchical approach, strongly based upon the economics of resources allocation, has been developed at the Austral University. Started in 1990, the models are now used at the strategic and tactical level, over one million hectares, by the main Chilean companies. The main features of this modelling approach are presented as well as the challenges ahead.


“Forest to Product Modeling using Hierarchical Planning An Approach for Evaluation of Ecosystem Management

Scenarios”

Thomas C. Maness, Associate Professor John D. Nelson, Associate Professor

Faculty of Forestry, University of British Columbia

Vancouver BC V6T 1Z4 A major difficulty in public forest management planning is in dealing with the multiple objectives of the many stakeholders. Forest management in BC has reached an evolutionary stage where it is increasingly important to satisfy the diverse social needs of the public in addition to considerations such as sustained yield and environmental quality. The increasing focus on these important goals has had a large impact on the forest industry. Up to now this impact has been felt in a regulatory fashion. Forest products companies often confront these social-constraints without the ability to affect change through better long-term planning. The question that faces us now as we reevaluate the forest tenure system in British Columbia is whether our planning models can properly consider social needs in context -- so that planning can be conducted to provide guidance on the interrelationships in the entire ecosystem. In this paper we present a forest to product planning model under development that uses a hierarchical planning approach. The model considers environmental issues, socio-economic goals, log quality and value-added manufacturing. It will integrate long-term harvest scheduling functions, including environmental and forest practices issues, with tactical decisions such as log allocation, merchandising, manufacturing and marketing, and operational issues such as what product to make when. A diagram of the model is shown on the next page. The model is segregated into three planning levels, each with different time horizons and optimization strategies. The strategic level looks out over 100 years and considers the broad goals for sustainability and diversity, and determines the available cut blocks for harvesting in the next decade. The goal of the strategic level is to guide the evolution of a natural forest toward some targeted condition defined by sustainability in health, species diversity and provision of public and market values. Heuristic optimization techniques are used for the tactical level. The tactical level considers the socio-economic goals of the region including employment, community stability and development as well as the economic interests of the companies, and allocates cut blocks to companies to achieve the overall goals. The goal of the tactical level is to ensure fairness in timber allocation, encourage further manufacturing within the district and promote community stability. We are currently experimenting with different optimization methods for the tactical level, including data envelopment analysis (DEA) techniques.


The operational level schedules harvests and assists with production decisions including which products to manufacture, inventory balancing, and technology investment. The goal of the operational level is to ensure that the right product is produced at the right time. The operational model uses mixed integer programming and is complete. The three levels are connected through shared data and communicating the marginal values of resources up through the various levels. The full model runs in an iterative fashion, each level passing information to and from the other levels until convergence. This procedure allows each level of the temporal hierarchy to focus on satisfying broadly different goals, yet the each level can also consider the impact on decisions on the other levels. The basic tenet is that the economic and operational functions of the forest industry must fit within the constraints

dictated by the strategic goals of the public landowner. The planning model will seek to find an optimal solution for forest development given that the long-term sustainability of the resource is paramount. However, the primary usefulness of the model may be in providing a tool to evaluate policy scenarios considering the many complex interrelationships in Forest Ecosystem Planning.

HARVESTING MODELATLAS:

Technical Landscape Analysis System

TIMBER ALLOCATIONMODEL

SAWMILL1(Large Diameters)

SPCM

SAWMILL2(Small Diameters)

SPCM

OTHERFACILITIES

(Future)

SecondaryManufacturing

FacilityVAFM

MARKET DATA

WOODSBUCKINGMODEL

DP

LOGPURCHASING

LOGSELLING

Strategic Level (100 Yr Outlook -- 10 Year plan)General Goal - Biodiversity & Economic Stability

CruiseData

EnvironmentalData

Socio-EconomicIndicators

Tactical Level (10 Yr Outlook -- 1 Year plan)General Goal - Resource Allocation

Operation Level (1 Yr Outlook -- Quarterly Plan)General Goal - Production Optimization


“Wood supply game - simulation”

Mr Kim Sjöström, Chief Technologist President of the worldwide WOOD LOGISTICS RESEARCH NETWORK

postal mailing address: Anjas 3 A 33, 02230 Espoo, Finland tel in Finland: 040 5500 780, internationally +358 405 500 780

fax +1 801 904 6757 homepage: http://members.surfeu.fi/sjostrom/

main email address: [email protected] The forest sector is an industry comprised of primary production and of raw-material-processing manufactures. Supply chains there, from consumption back to raw materials, are lengthy and filled with diverse stages. The sector in question is sensitive for example for economic fluctuations. When utilizing any raw material, the material flows diverge towards several different products (divergent logistics). If separate stages of the supply chain are independent decision-making units, parties of the chain are unable to work in synchron. Information is an important tool for management of logistics. Imperfect information -that always is present- causes problems to quantities, timing and location of the commodities. This game emulates supply chain(s) of the forest sector, attempting to make the flow of materials through the supply chains from raw material to consumption more lucid, to emphasize the importance of information sharing, industrial dynamics, as well as significance of constraints set by technical facts in the sector. We form at least two teams that compete against each other. Each team receives an own industrial alliance to play. A full team comprises of 8 persons. Each game round simulates one week. The length of the game may be e.g 50 weeks. The length of the supply chain is simulated by inserting at least four sequential stages (game positions) into each alliance. Their titles are not important, but we can call them as wood procurement, mill, wholesaler, retailer. The divergent nature of the sector is simulated by dividing the material into at least two sub-chains: from wood procurement to solid wood and to fiberwood branches. In this game, 50% to sawmill and 50% to pulp mill is regarded as the ideal division share. Deviation from this sharing ratio worsens the game result of the alliance: in this game, if you use good sawlogs to pulping, you will be penalized by a quality cost that is ten times the warehousing cost. In this game, warehousing costs are the gist of logistical performance. Each position owns a warehouse, where all inventory stored causes a cost. The inventory, in general, is a logistical “battlefield” where several interests, usually conflicting, meet. Chief interests tend to be the warehousing costs vs the service level. Availability of commodity is a factor of the service level: a needed quantity in the right spot at the right moment. If some quantity lacks when demand exists, it means minus to the company. In this game, bad service level is simulated by lack cost that is warehousing cost doubled. In each week, the players change only standardized information - only by placing an order, stating the quantity, to the closest upstream position. And, the wood procurement position decides each week the quantities it directs to sawmill and to pulping. No none sees the total situation of the entire alliance, not even the situation of one sub-chain. The game leader gives


the consumption demand quantity each week to those positions closest to consumer stage. The game contains one or several variations in demand - we simulate economic fluctuations. I have used the simuation as a game for a couple of times in my teaching groups. Students seem to react positively to this sort of practical use og their logistics and professional knowledge. Some conclusions about applicability and application of the simulation:

1. This sort of setting is all too large to be lead as one enterprise. Positions of an alliance are not able to coordinate almost anything.

2. Practical chores of the game are a good way to simulate the daily business facing the

real-life mills, hindering them from focusing on the logistically important tasks. In that regard, perhaps computerization of the game is not highly desirable.

3. Divergent sub-chains tend to get rather unbalanced compared with each other. Of

two branches, one often is overfed and struggling with high warehousing costs, whereas the other is underfed and accumulating lack penalties.

4. Positions closest to demand tend to accumulate lower sums of costs than positions

further upstream. Oscillations amplify towards upstream. 5. Sometimes, despite of its high penalty, it however would be more advisable to use

sawlogs to pulping - in certain cases, the accumulated warehousing & penalty costs are higher than the waste cost.

6. Many students of our field (having used this), display yet tendency towards “safe”

thinking of producing high quantities, rather than making the suppply chain “lean”.


“Estimating the efficiency of a forest supply chain and the value of horizontal cooperation”

Mattias Forsberg (MSc. Forestry) SkogForsk

Uppsala Science Park S-751 83 UPPSALA +46 (18) 18 85 25

[email protected] Swedish forestry is considered being highly competitive on the global market. Due to the high cost structure the forest supply chains are focused on reducing the costs of the forest operation to stay competitive. More efficient planning on a tactical level have been proved to be a key process to unlock a greater efficiency in secondary transportation. Chapter 1 of this paper starts by giving an introduction to the structure of Swedish forest operations. The second chapter introduces the concept of strategic planning and its influence on the secondary transportation. The third chapter summarizes some of the previous work done in developing suitable methods for Operations Research in strategic- and tactical planning. In the fourth chapter the scope of the authors research is presented. Chapter 5 and 6 introduces two case studies where a model for tactical planning have been used to analyze the potential for increased efficiency of the round wood transportation in Swedish forestry.


“A dynamic linear programming approach to adaptive logistics: Application to optimal coordination under risk in the forest

sector”

Peter Lohmander http://www.lohmander.com/

Typical decision problems in companies in the forest sector and in several other sectors of the economy are sequential. A series of decisions are taken over time. Important information, which was not available (or perfectly predictable) when the first decisions in the chain were taken, becomes available before the final decisions have to be taken. In this situation, the optimal first (and later!) decisions in the chain can usually not be found via deterministic multi period optimizations methods. The standard approach to adaptive dynamic optimization is stochastic dynamic programming. That approach however makes it computationally impossible to handle a large state space, typical in logistics problems. This paper focuses on a linear programming approach to the true adaptive multi period problem with sequential information. It has been found that you really can handle such problems, typical to many companies in the forest sector and many other sectors, in case "dynamic information constraints" are introduced in the linear programming constraint set. An application to a sample forest company problem is included in the paper. The objective is to minimize the expected present value of the total cost (including costs of harvesting, transport and stocks) during one year. The developments of snow, rain and road problems are not known in advance. The information concerning these matters is sequentially revealed, exactly as in the real world. The forest harvesting volume constraints, the sequentially revealed road capacity constraints and the stock level constraints however have to be met, irrespective of what happens. The wood deliveries necessary for full industrial production in different periods have to reach the forest industry mills. In a more complete version of this model, one could maximize the expected present value of all activities in the firm, making it possible to stop industrial production in some cases. Of course, one could easily include harvester and forwarder capacity constraints. Other developments would be to introduce quadratic harvesting and transport cost functions with increasing marginal costs in each period. The model would then still converge to the global optimum in a finite number of iterations and the number of dimensions could be very large, thanks to the efficient quadratic programming algorithms.

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