Development of a threat index to manage timber production on flammable forest landscapes subject to spatial harvest constraints

ABSTRACT We develop a stand-level fire threat index and incorporate it in a mixed integer programming model that can be used to help specify strategies that will maximize the expected volume harvested from a flammable forest over a finite planning horizon, subject to adjacency constraints. The inclusion of a threat index in our objective function implicitly identifies high volume harvest blocks that are most likely to burn over the planning horizon and accelerates the harvesting of those high risk stands to reduce the likelihood that they will burn before they are harvested. We illustrate the use of our model and evaluate its performance by simulating its application to two hypothetical flammable forest landscapes that are 16,000 hectares in size. Our results indicate that our inclusion of a threat index in our objective function produces timber harvest schedules that are better than those produced using an objective function that does not include potential fire loss measures, while satisfying harvest adjacency constraints.

[1]  C. Lockwood,et al.  Harvest scheduling with spatial constraints: a simulated annealing approach , 1993 .

[2]  G. Armstrong Sustainability of timber supply considering the risk of wildfire , 2004 .

[3]  Miguel Constantino,et al.  Imposing Connectivity Constraints in Forest Planning Models , 2013, Oper. Res..

[4]  Pete Bettinger,et al.  A prototype method for integrating spatially-referenced wildfires into a tactical forest planning model. , 2009 .

[5]  Charles ReVelle,et al.  Temporal and spatial harvesting of irregular systems of parcels , 1996 .

[6]  Kevin A. Crowe,et al.  A simulation-optimization model for selecting the location of fuel-breaks to minimize expected losses from forest fires , 2010 .

[7]  C. E. Van Wagner,et al.  Simulating the effect of forest fire on long-term annual timber supply , 1983 .

[8]  Francisco Barahona,et al.  Harvest Scheduling Subject to Maximum Area Restrictions: Exploring Exact Approaches , 2005, Oper. Res..

[9]  D. Boychuk,et al.  A Multistage Stochastic Programming Model for Sustainable Forest-Level Timber Supply Under Risk of Fire , 1996, Forest Science.

[10]  Francisco Barahona,et al.  Habitat Dispersion in Forest Planning and the Stable Set Problem , 1992, Oper. Res..

[11]  Sheng-Roan Kai,et al.  Design and Implementation of an Interactive Optimization System for Telephone Network Planning , 1992, Oper. Res..

[12]  K. Hirsch,et al.  Fire-smart forest management: A pragmatic approach to sustainable forest management in fire-dominated ecosystems , 2001 .

[13]  Yu Wei,et al.  An optimization model for locating fuel treatments across a landscape to reduce expected fire losses , 2008 .

[14]  Woodam Chung,et al.  Optimizing Fuel Treatments to Reduce Wildland Fire Risk , 2015, Current Forestry Reports.

[15]  G. Armstrong A stochastic characterisation of the natural disturbance regime of the boreal mixedwood forest with implications for sustainable forest management , 1999 .

[16]  Róbert Marušák,et al.  Spatially Constrained Harvest Scheduling for Strip Allocation and Biodiversity Management , 2010 .

[17]  James P. Minas,et al.  A spatial optimisation model for multi-period landscape level fuel management to mitigate wildfire impacts , 2014, Eur. J. Oper. Res..

[18]  Alan T. Murray Spatial restrictions in harvest scheduling , 1999 .

[19]  W. J. Reed,et al.  Optimal harvest scheduling at the forest level in the presence of the risk of fire , 1986 .

[20]  Mauricio Acuna,et al.  Integrated spatial fire and forest management planning , 2010 .

[21]  Alan T. Murray,et al.  Review of combinatorial problems induced by spatial forest harvesting planning , 2006, Discret. Appl. Math..

[22]  Jeffrey L. Arthur,et al.  Optimal spatial patterns of fuel management and timber harvest with fire risk , 2010 .

[23]  David W. Savage,et al.  Evaluation of two risk mitigation strategies for dealing with fire-related uncertainty in timber supply modelling , 2010 .

[24]  Pete Bettinger,et al.  An overview of methods for incorporating wildfires into forest planning models , 2010, Math. Comput. For. Nat. Resour. Sci..

[25]  Miguel Constantino,et al.  Addressing Wildfire Risk in a Landscape-Level Scheduling Model: An Application in Portugal , 2015 .

[26]  Horand I. Gassmann,et al.  Optimal harvest of a forest in the presence of uncertainty , 1989 .

[27]  Young-Hwan Kim,et al.  Spatial optimization of the pattern of fuel management activities and subsequent effects on simulated wildfires , 2009, Eur. J. Oper. Res..

[28]  John von Neumann,et al.  IFORS' Operational Research Hall of Fame , 2006, Int. Trans. Oper. Res..