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Silva Fennica 1926-1997
Acta Forestalia Fennica

Articles containing the keyword 'linear programming'

Category: Article

article id 5617, category Article
Teijo Palander. (1997). A local DLP-GIS-LP system for geographically decentralized wood procurement planning and decision making. Silva Fennica vol. 31 no. 2 article id 5617.
Keywords: Finland; GIS; linear programming; dynamic linear programming; DLP; geographical decentralization; local wood procurement; participatory planning; wood procurement
Abstract | View details | Full text in PDF | Author Info

Linear programming (LP) is an important method for allocation of wood inventory stock. It is, for instance, used alone in tactical planning systems, which currently are in wide use at the higher hierarchical level in the functionally decentralized planning of the Finnish forest industry. Unfortunately, LP as a solution method has not been capable of handling spatial data that seem to characterize planning systems in geographical decentralization. In the present study, GIS was used to assimilate data from different wood procurement functions, to calculate transportation distances and cost figures, and to write the data in ASCII files, which were then used as input for the LP model. Using the experiments and methods of GIS on a planning system developed according to participatory planning, the results of this study suggest that the participatory method was faster than the conventional LP method, when solved using actual data. The participatory method was also capable of providing the same global optimum for a wood allocation problem. The implications of these results for improving operational and tactical planning of wood procurement in Finland are discussed.

  • Palander, E-mail: tp@mm.unknown (email)
article id 5509, category Article
Markku Siitonen. (1993). Experiences in the use of forest management planning models. Silva Fennica vol. 27 no. 2 article id 5509.
Keywords: forest policy; forest inventories; stand management; linear programming; forest resources
Abstract | View details | Full text in PDF | Author Info

Model-based information systems have proved valuable planning tools for analysing the production possibilities of forests as well as for understanding forest resources dynamics, stand management practices and forest economics. Computerized forest models implemented in the users’ information systems facilitate the transfer and application of research results in practical forestry.

Conclusions and visions concerning modelling are drawn from experiences in developing the MELA system and its application in solving timber production problems on both the national and forest holding level in Finland. The precondition for predicting forest resource dynamics and for planning the utilization of forests is to accept conditions, uncertainties and a restricted period of time.

The interactive process of forest resource, growth and drain monitoring, and forest management planning supported by forest research and modelling, are the means to enable an operational information base for a dynamic regulation and adaptation strategy for forest resource management under changing conditions and uncertainty.

The PDF includes an abstract in Finnish.

  • Siitonen, E-mail: ms@mm.unknown (email)
article id 5244, category Article
Juha Lappi, Markku Siitonen. (1985). A utility model for timber production based on different interest rates for loans and savings. Silva Fennica vol. 19 no. 3 article id 5244.
Keywords: linear programming; timber production; forest economics; income from fellings; utility model; income flow; present discounted value
Abstract | View details | Full text in PDF | Author Info

The paper discusses the evaluation of timber production policies with different income (timber drain) schedules. Special attention is given to the temporal smoothness of the income flow. A utility model is formulated in which the objective is to maximize a fixed consumption pattern, and money can be saved and borrowed at different interest rates. We thus have smoothness requirements only for consumption, the capital market then determines the smoothness of the optimal income flow. Present discounted value and maximization of even income flow criteria are special cases of the utility model. Consumption can be maximized by linear programming. A sample problem is presented.

The PDF includes a summary in Finnish.

  • Lappi, E-mail: jl@mm.unknown (email)
  • Siitonen, E-mail: ms@mm.unknown
article id 4918, category Article
Pekka Kilkki, Raimo Pökälä, Markku Siitonen. (1975). Metsätalousyksikön puuntuotannon suunnittelu lineaarista ohjelmointia käyttäen. Silva Fennica vol. 9 no. 2 article id 4918.
English title: Linear programming in the planning of timber production in a forestry unit.
Original keywords: metsäsuunnittelu; puuntuotanto; lineaariset mallit
English keywords: forest planning; linear programming; timber production; methods
Abstract | View details | Full text in PDF | Author Info

The planning of timber production in a forestry unit is divisible into two phases. In the first phase, planning provides the decision-maker with a number of possible timber production policies; these policies define the production possibility boundary. After the decision-maker has chosen one of these policies, planning moves to the second phase, in which a detailed programme is prepared with a view to meeting the requirements of the timber production policy accepted. The paper indicates one possibility of solving these two tasks simultaneously. In the first phase, the solution of the primal linear programming problem is employed and in the second phase the respective dual or shadow price solution.

The PDF includes a summary in English.

  • Kilkki, E-mail: pk@mm.unknown (email)
  • Pökälä, E-mail: rp@mm.unknown
  • Siitonen, E-mail: ms@mm.unknown

Category: Article

article id 7630, category Article
Esko Mikkonen. (1983). Eräiden matemaattisen ohjelmoinnin menetelmien käyttö puun korjuun ja kuljetuksen sekä tehdaskäsittelyn menetelmävalinnan apuvälineenä. Silva Fennica vol. 0 no. 183 article id 7630.
English title: The usefulness of some techniques of the mathematical programming as a tool for the choice of timber harvesting system.
Original keywords: matemaattinen ohjelmointi; standardi lineaarinen optimointi; parametrinen optimointi; tavoiteoptimointi; sekalukuoptimointi; kokonaislukuoptimointi; puunhankinnan suunnittelu
English keywords: mixed integer programming; integer programming; goal programming; wood procurement; mathematical programming; standard linear programming; parametric programming
Abstract | View details | Full text in PDF | Author Info

The applicability of five mathematical programming methods, namely standard linear programming, parametric programming, goal programming, mixed integer programming and integer programming is discussed as a planning tool for the choice of wood procurement method.

Theoretically, the goal programming approach seems to be the best routine for mathematical handling of problems related to wood procurement. The parametric approach must include enough large post-optimality analysis routine. If the effect of the variables expressed with different measures is to be studied, interpretation of the economic information given by the approach becomes a problem. The other drawback is that the approach does not allow determination of the hierarchy of the goals objectively as they depend on the subjective preferences of the decision maker.

From the practical point of view, standard linear programming is the best method if the objective function can be formulated in economic terms, for instance. If there are several goals to be attained or satisfied the best method is goal programming.

According to the sub-studies, every method under consideration can be used as a solution routine for the minimization of wood procurement costs. In cost minimization the best methods are goal programming and standard linear programming. The best method for harvesting system evaluation purposes is parametric because it allows varied cost calculations within a certain cost range. The best method for harvesting equipment investment planning is mixed integer programming with binary decision variables.

The more complicated and restricted the problem environment is, the better the mathematical programming approach will be, also in harvesting related problems.

The PDF includes a summary in English.

  • Mikkonen, E-mail: em@mm.unknown (email)

Category: Research article

article id 10074, category Research article
Sebastian Kühle, Alfred Teischinger, Manfred Gronalt. (2019). Optimal location of laminated beech production plants within the solid hardwood supply network in Austria. Silva Fennica vol. 53 no. 3 article id 10074.
Keywords: decision support system; facility location; laminated timber products; mixed integer linear programming; supply chain network design
Highlights: This paper provides data to the solid hardwood business and develops a mixed integer linear program model to design a laminated beech wood supply network; It covers the strategic decision where to locate a new production facility within the existing supply network with the lowest supply network cost; Sufficient sawn wood suppliers and potential facility locations are provided.
Abstract | Full text in HTML | Full text in PDF | Author Info

Due to changes in forest management in various European countries, hardwood forest areas and amounts will increase. Sustainable and individual utilization concepts have to be developed for the upcoming available resource. Studies conclude that there is low potential for hardwoods in the traditional appearance market thus the application areas have to be extended to new structural innovative products. This paper examines the extension to a future laminated beech wood supply network which would be a combination of already existing and new production facilities. For a better future use of hardwood raw materials it is necessary to consider the entire supply chain. This also better shows a total hardwood value chain. Therefore, this paper provides data to the solid hardwood business and develops a mixed integer linear programming to design a laminated beech wood supply network. The model is applied to Austria as the sample region. It covers the important strategic decisions where to locate a downstream facility within the existing production network with the lowest supply network cost. Fourteen scenarios are developed to examine various future network configurations. Results about optimal material flows and used sawmills as well as downstream production facilities are presented in form of material and financial performances. Two optimal laminated beech production locations are determined by the calculated scenarios results, and the impact of a new sawmill is analyzed which is focused on beech.

  • Kühle, BOKU - University of Natural Resources and Life Sciences, Vienna, Department of Material Science and Process Engineering, and Renewable Institute of Wood Technology Materials, Konrad-Lorenz-Straße 24, 3430 Tulln, Austria E-mail: (email)
  • Teischinger, BOKU - University of Natural Resources and Life Sciences, Vienna, Department of Material Science and Process Engineering, and Renewable Institute of Wood Technology Materials, Konrad-Lorenz-Straße 24, 3430 Tulln, Austria E-mail:
  • Gronalt, BOKU - University of Natural Resources and Life Sciences, Vienna, Department of Economics and Social Sciences, Institute of Production and Logistics, Feistmantelstraße 4, 1180 Vienna, Austria E-mail:
article id 578, category Research article
Kevin Boston, Pete Bettinger. (2001). Development of spatially feasible forest plans: a comparison of two modeling approaches. Silva Fennica vol. 35 no. 4 article id 578.
Keywords: forest planning; heuristics; linear programming; wildlife goals
Abstract | View details | Full text in PDF | Author Info
Spatial goals are becoming more frequent aspects of forest management plans as regulatory and organizational policies change in response to fisheries and wildlife concerns. The combination of green-up constraints (harvesting restrictions that prevent the cutting of adjacent units for a specified period of time) and habitat requirements for red-cockaded woodpeckers (RCW) in the southeastern U.S. suggests that spatially feasible forest plans be developed to guide management activities. We examined two modeling approaches aimed at developing management plans that had both harvest volume goals, RCW habitat, and green-up constraints. The first was a two-stage method that in one stage used linear programming to assign volume goals, and in a second stage used a tabu search – genetic algorithm heuristic technique to minimize the deviations from the volume goals while maximizing the present net revenue and addressing the RCW and green-up constraints. The second approach was a one-stage procedure where the entire management plan was developed with the tabu search – genetic algorithm heuristic technique, thus it did not use the guidance for timber volume levels provided by the LP solution. The goal was to test two modeling approaches to solving a realistic spatial harvest scheduling problem. One is where to volume goals are calculated prior to developing the spatially feasible forest plan, while the other approach simultaneously addresses the volume goals while developing the spatially feasible forest plan. The resulting forest plan from the two-stage approach was superior to that produced from the one-stage approach in terms of net present value. The main point from this analysis is that heuristic techniques may benefit from guidance provided by relaxed LP solutions in their effort to develop efficient forest management plans, particularly when both commodity production and complex spatial wildlife habitat goals are considered. Differences in the production of forest products were apparent between the two modeling approaches, which could have a significant effect on the selection of wood processing equipment and facilities.
  • Boston, Forest Fibre Solutions, Carter Holt Harvey, Tokoroa, New Zealand E-mail: (email)
  • Bettinger, Department of Forest Resources, Oregon State University, Corvallis, OR 97331 E-mail:

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