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Articles containing the keyword 'mixed integer programming'.

Category: Research article

article id 1347, category Research article
Paulo Borges, Even Bergseng, Tron Eid, Terje Gobakken. (2015). Impact of maximum opening area constraints on profitability and biomass availability in forestry – a large, real world case. Silva Fennica vol. 49 no. 5 article id 1347. https://doi.org/10.14214/sf.1347
Highlights: We solved a large and real world near city forestry problem; The inclusion of maximum open area constraints caused 7.0% loss in NPV; Solution value at maximum deviated 0.01% from the true optimum value; The annual energy supply of 20–30 GWh estimated from harvest residues could provide a small, but stable supply of energy to the municipality.

The nature areas surrounding the capital of Norway (Oslomarka), comprising 1 700 km2 of forest land, are the recreational home turf for a population of 1.2 mill. people. These areas are highly valuable, not only for recreational purposes and biodiversity, but also for commercial activities. To assess the impacts of the challenges that Oslo municipality forest face in their management, we developed four optimization problems with different levels of management constraints. The constraints consider control of harvest level, guarantee of minimum old-growth forest area and maximum open area after final harvest. For the latter, to date, no appropriate analyses quantifying the impact of such a constraint on economy and biomass production have been carried out in Norway. The problem solved is large due to both the number of stands and number of treatment schedules. However, the model applied demonstrated its relevance for solving large problems involving maximum opening areas. The inclusion of maximum open area constraints caused 7.0% loss in NPV compared to the business as usual case with controlled harvest volume and minimum old-growth area. The estimated supply of 20-30 GWh annual energy from harvest residues could provide a small, but stable supply of energy to the municipality.

  • Borges, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: paulo.borges@nmbu.no (email)
  • Bergseng, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: even.bergseng@nmbu.no
  • Eid, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: tron.eid@nmbu.no
  • Gobakken, Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, P.O. Box 5003, 1432 Aas, Norway ORCID ID:E-mail: terje.gobakken@nmbu.no
article id 457, category Research article
Karin Öhman, Ljusk Ola Eriksson. (2010). Aggregating harvest activities in long term forest planning by minimizing harvest area perimeters. Silva Fennica vol. 44 no. 1 article id 457. https://doi.org/10.14214/sf.457
The study presents a new approach for aggregating stands for harvest in strategic forest planning. In fragmented landscapes this could benefit nature conservation as well as reduce costs. The approach is built on the idea of minimizing the outside perimeter of contiguous harvest areas. The formulation allows for the use of exact solution methods such as mixed integer programming. The method was tested in a landscape consisting of 2821 stands. The application showed that large and compact harvest areas were created with limited sacrifice of financial value. The mixed integer programs were in most cases solved within a couple of hours. The method needs to be tested on different landscapes with different degrees of fragmentation. It is also necessary to evaluate the long term consequences of the large clear cuts that appear to be a consequence of this problem formulation.
  • Öhman, SLU, Department of Forest Resource Management, SE-901 83 Umeå, Sweden ORCID ID:E-mail: karin.ohman@srh.slu.se (email)
  • Eriksson, SLU, Department of Forest Resource Management, SE-901 83 Umeå, Sweden ORCID ID:E-mail:
article id 356, category Research article
Hamish D. Marshall, Glen Murphy, Kevin Boston. (2006). Three mathematical models for bucking-to-order. Silva Fennica vol. 40 no. 1 article id 356. https://doi.org/10.14214/sf.356
The aim of this paper is to investigate different mathematical approaches to buck-to-order log merchandizing. A new bucking-to-order planning model using mixed integer programming was developed to determine the optimal production from a stand given different market constraints and forest inventory data. Three different approaches: market prices, target cutting patterns and adjusted price list were tested for generating cutting instructions to fulfill the plan created by the new planning model. The three approaches were evaluated in four test stands. The market prices approach simply applied the market prices to each stand. The target cutting patterns approach applied the sample cutting patterns generated from the planning model to the stand. The adjusted price list used a dynamic programming algorithm embedded in a search heuristic to adjust both the prices and small end diameters of log products to achieve the production goals of the planning models. The results showed that developing a buck-to-order plan is important in obtaining good order fulfillment. The target cutting patterns and adjusted price list approaches certainly out performed the market prices approach. This paper shows that these two approaches are capable of achieving excellent order fulfillment. Further development and testing is needed to determine which method is the best at generating cutting instructions for buck-to-order merchandizing.
  • Marshall, Ensis Forests, Private Bag 3020, Rotorua, New Zealand ORCID ID:E-mail: hamish.marshall@ensisjv.com (email)
  • Murphy, Forest Engineering Department, Oregon State University, Corvallis, Oregon 97331, USA ORCID ID:E-mail:
  • Boston, Forest Engineering Department, Oregon State University, Corvallis, Oregon 97331, USA ORCID ID:E-mail:
article id 429, category Research article
Juho Rantala. (2004). Optimizing the supply chain strategy of a multi-unit Finnish nursery company. Silva Fennica vol. 38 no. 2 article id 429. https://doi.org/10.14214/sf.429
This paper introduces a capacitated mixed integer programming (CMIP) model for solving an integrated production-distribution system design problem (PDSDP) in the seedling supply chain management (SCM) of a multi-unit Finnish nursery company. The model was originally developed from a strategic perspective in which a company desires to evaluate the expansion or closure of its facilities. Nevertheless, the model is also used for solving operational and tactical level problems by applying applicable constraints. The data were collected from the company studied. The results proved that economies of scale could be exploited in seedling production more than the company does today; Compared to the company’s current supply chain strategy with 5 nursery units producing seedlings, when other supply chain strategies were applied the number of nursery units decreased by 2–4 units, and cost savings in the supply chain varied from 11.3% to 21.3%.
  • Rantala, Finnish Forest Research Institute, Suonenjoki Research Station, Juntintie 154, FI-77600 Suonenjoki, Finland ORCID ID:E-mail: juho.rantala@metla.fi (email)

Category: Article

article id 7630, category Article
Esko Mikkonen. (1983). Eräiden matemaattisen ohjelmoinnin menetelmien käyttö puun korjuun ja kuljetuksen sekä tehdaskäsittelyn menetelmävalinnan apuvälineenä. Acta Forestalia Fennica no. 183 article id 7630. https://doi.org/10.14214/aff.7630
English title: The usefulness of some techniques of the mathematical programming as a tool for the choice of timber harvesting system.

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, ORCID ID:E-mail:

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