A column generation approach for solving a non-temporal forest harvest model with spatial structure constraints

Martins, Isabel Pavão; Constantino, Miguel; Borges, José G.

doi:10.1016/j.ejor.2003.07.021

Cited by 40 publications

(37 citation statements)

References 17 publications

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“…These may reduce fragmentation of old-growth forest areas and enhance biodiversity (e.g. Öhman and Eriksson 1998;Öhman 2000;Falcão and Borges 2002;Rebain and McDill 2003;Martins et al 2005;Tóth and McDill 2007;Hoganson 2006, 2008;Öhman and Wikström 2008). Other possible management goals could be to cluster harvest activities to reduce machine transportation (e.g.…”

Section: Discussionmentioning

confidence: 99%

Impact of maximum opening area constraints on profitability and biomass availability in forestry – a large, real world case

Borges¹,

Bergseng²,

Eid³

et al. 2015

Silva Fenn.

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• 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. AbstractThe nature areas surrounding the capital of Norway (Oslomarka), comprising 1 700 km 2 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.

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Section: Discussionmentioning

confidence: 99%

Impact of maximum opening area constraints on profitability and biomass availability in forestry – a large, real world case

Borges¹,

Bergseng²,

Eid³

et al. 2015

Silva Fenn.

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“…In this subsection, we propose a Dantzig-Wolfe decompositions of the bucket model by reformulating the set defined by constraints (4) and (8). A similar decomposition of the alternative model can also be presented by reformulating the set defined by these constraints and the connectivity constraints.…”

Section: Knapsack Decompositionsmentioning

confidence: 98%

Decompositions and a Matheuristic for a Forest Harvest Scheduling Problem

Martins¹,

Alvelos

Constantino

2015

Operational Research

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In this paper, we describe four decomposition models and a matheuristic based on column generation for the forest harvest scheduling problems subject to maximum area restrictions. Each of the four decomposition models can be seen as a Dantzig-Wolfe decomposition of the so-called bucket formulation (compact mixed integer program), in two cases with additional constraints on the connectivity of the buckets. The matheuristic is based on one of the decomposition models (the S -knapsack-and-clique decomposition) and relies on the interaction of column generation with a general purpose mixed integer programming solver. We compare the quality of the solutions obtained for benchmark instances with the bucket formulation and with applying column generation and solving the integer restricted master problem (MipHeur) for the same time limit. We concluded that the proposed matheuristic provides, in general, better solutions than both the other approaches for small and medium instances, while, for large instances, the MipHeur approach outperformed the other two. I. Martins ( )

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“…Três formulações ARM básicas são descritas na literatura: a formulação path (Martins et al 1999, McDill et al 2002, Murray e Weintraub 2002, Crowe et al 2003, com um número exponencial de restrições, a formulação cluster (Martins et al 1999e 2005, McDill et al 2002, Goycoolea et al 2005, Vielma et al 2007, com um número exponencial de variáveis, e a mais recente formulação bucket (Constantino et al 2008), com um número polinomial de variáveis e restrições. Provou-se teoricamente que a formulação cluster é mais forte do que a formulação path (Goycoolea et al 2009) e a formulação bucket (Martins et al2012), ou seja, a relaxação linear da formulação cluster dá melhores majorantes do que as relaxações lineares das restantes formulações.…”

Section: Modelos Com Restrições De Clareirasunclassified

Otimização de planos de exploração florestal em baldios do norte de Portugal

Cerveira¹,

Martins²,

Fonseca³

et al. 2014

Investigação Operacional Em Ação: Casos De Aplicação

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A column generation approach for solving a non-temporal forest harvest model with spatial structure constraints

Cited by 40 publications

References 17 publications

Impact of maximum opening area constraints on profitability and biomass availability in forestry – a large, real world case

Impact of maximum opening area constraints on profitability and biomass availability in forestry – a large, real world case

Decompositions and a Matheuristic for a Forest Harvest Scheduling Problem

Otimização de planos de exploração florestal em baldios do norte de Portugal

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