Skip to main content
Springer Nature Link
Log in

Spatial uncertainty in harvest scheduling

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Forest harvest scheduling is a complicated management exercise because of the diverse and competing uses of forest resources, such as economic productivity, recreation and flora and fauna sustainability. In an effort to ensure the long-term viability of forest resources, restrictions are typically placed on the size of harvest areas, green-up intervals and proximity between disturbed areas in the United States. In order to satisfy consumer demands and maintain spatial and temporal restrictions, forest planners rely widely on optimization models to develop harvest schedules. A problematic element of work to date, however, is that spatial information relied upon in such analysis is typically uncertain in many ways, particularly spatial location and harvest unit boundaries. This paper develops new optimization models that explicitly account for spatial uncertainty in harvest scheduling. Application results demonstrate the effectiveness of this new perspective, enabling potential spatial uncertainty impacts to be better understood in management planning.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Aerts, J. C. J. H., Goodchild, M. F., & Heuvelink, G. (2003). Accounting for spatial uncertainty in optimization with spatial decision support systems. Transactions in GIS, 7(2), 211–230.

    Article  Google Scholar 

  • Altinel, I. K., Durmaz, E., Aras, N., & ÖzkIsacIk, K. C. (2009). A location-allocation heuristic for the capacitated multi-facility Weber problem with probabilistic customer locations. European Journal of Operational Research, 198(3), 790–799.

    Article  Google Scholar 

  • Bohle, C., Maturana, S., & Vera, J. (2010). A robust optimization approach to wine grape harvesting scheduling. European Journal of Operational Research, 200(1), 245–252.

    Article  Google Scholar 

  • Boychuk, D., & Martell, D. L. (1996). A multistage stochastic programming model for sustainable forest-level timber supply under risk of fire. Forest Science, 42(1), 10–26.

    Google Scholar 

  • Boyland, M., Nelson, J., & Bunnell, F. L. (2005). A test for robustness in harvest scheduling models. Forest Ecology and Management, 207(1–2), 121–132.

    Article  Google Scholar 

  • Brown, D. G. (1998). Classification and boundary vagueness in mapping presettlement forest types. International Journal of Geographical Information Science, 12(2), 105–129.

    Article  Google Scholar 

  • Church, R. L. (1999). Location modelling and GIS. In M. F. G. P. Longley, D. Maguire & D. Rhind (Eds.), Geographical information systems (2nd ed., pp. 293–303). New York: Wiley.

    Google Scholar 

  • Cohen, J. L. (1978). Multiobjective programming and planning. New York: Academic Press.

    Google Scholar 

  • Constantino, M., Martins, I., & Borges, J. G. (2008). A new mixed-integer programming model for harvest scheduling subject to maximum area restrictions. Operations Research, 56(3), 542–551.

    Article  Google Scholar 

  • Cooper, L. (1974). A random locational equilibrium problem. Journal of Regional Science, 14(1), 47–54.

    Article  Google Scholar 

  • De Groeve, T., & Lowell, K. (2001). Boundary uncertainty assessment from a single forest-type map. Photogrammetric Engineering and Remote Sensing, 67(6), 717–726.

    Google Scholar 

  • Drezner, T., & Drezner, Z. (1997). Replacing continuous demand with discrete demand in a competitive location model. Naval Research Logistics, 44(1), 81–95.

    Article  Google Scholar 

  • Edwards, G., & Lowell, K. (1996). Modeling uncertainty in photointerpreted boundaries. Photogrammetric Engineering and Remote Sensing, 62(4), 377–391.

    Google Scholar 

  • Eid, T. (2000). Use of uncertain inventory data in forestry scenario models and consequential incorrect harvest decisions. Silva Fennica, 34(2), 89–100.

    Article  Google Scholar 

  • Eriksson, L. O. (2006). Planning under uncertainty at the forest level: a systems approach. Scandinavian Journal of Forest Research, 21, 111–117.

    Article  Google Scholar 

  • Forsell, N., Wikström, P., Garcia, F., Sabbadin, R., Blennow, K., & Eriksson, L. (2011). Management of the risk of wind damage in forestry: a graph-based Markov decision process approach. Annals of Operations Research, 190(1), 57–74.

    Article  Google Scholar 

  • Goycoolea, M., Murray, A. T., Barahona, F., Epstein, R., & Weintraub, A. (2005). Harvest scheduling subject to maximum area restrictions: exploring exact approaches. Operations Research, 53, 490–500.

    Article  Google Scholar 

  • Hochbaum, D. S., & Pathria, A. (1997). Forest harvesting and minimum cuts: a new approach to handling spatial constraints. Forest Science, 43(4), 544–554.

    Google Scholar 

  • Hof, J. G., & Pickens, J. B. (1991). Chance-constrained and chance-maximizing mathematical programs in renewable resource management. Forest Science, 37(1), 308–325.

    Google Scholar 

  • Hof, J. G., Bevers, M., & Pickens, J. B. (1996). Chance-constrained optimization with spatially autocorrelated forest yields. Forest Science, 42(1), 118–123.

    Google Scholar 

  • Hoganson, H. M., & Rose, D. W. (1987). A model for recognizing forestwide risk in timber management scheduling. Forest Science, 33(2), 268–282.

    Google Scholar 

  • Klenner, W., Kurz, W., & Beukema, S. (2000). Habitat patterns in forested landscapes: management practices and the uncertainty associated with natural disturbances. Computers and Electronics in Agriculture, 27(1–3), 243–262.

    Article  Google Scholar 

  • Meilby, H., Strange, N., & Thorsen, B. J. (2001). Optimal spatial harvest planning under risk of windthrow. Forest Ecology and Management, 149(1–3), 15–31.

    Article  Google Scholar 

  • Murray, A. T. (1999). Spatial restrictions in harvest scheduling. Forest Science, 45(1), 45–52.

    Google Scholar 

  • Murray, A. T. (2003). Site placement uncertainty in location analysis. Computers, Environment and Urban Systems, 27(2), 205–221.

    Article  Google Scholar 

  • Murray, A. T., & Church, R. L. (1995). Heuristic solution approaches to operational forest planning problems. OR Spectrum, 17(2), 193–203.

    Article  Google Scholar 

  • Murray, A. T., & Church, R. L. (1996). Analyzing cliques for imposing adjacency restrictions in forest models. Forest Science, 42(2), 166–175.

    Google Scholar 

  • Murray, A. T., & Weintraub, A. (2002). Scale and unit specification influences in harvest scheduling with maximum area restrictions. Forest Science, 48(4), 779–789.

    Google Scholar 

  • Murray, A. T., & Grubesic, T. H. (2011). Spatial optimization and geographic uncertainty: implications for sex offender management strategies. In M. Johnson (Ed.), Community-based operations research: decision modeling for local impact and diverse populations (pp. 121–142). Berlin: Springer.

    Google Scholar 

  • Murray, A. T., Goycoolea, M., & Weintraub, A. (2004). Incorporating average and maximum area restrictions in harvest scheduling models. Canadian Journal of Forest Research, 34(2), 456–464.

    Article  Google Scholar 

  • Naesset, E. (1998). Positional accuracy of boundaries between clearcuts and mature forest stands delineated by means of aerial photointerpretation. Canadian Journal of Forest Research, 28(3), 368–374.

    Article  Google Scholar 

  • Orzanco, M., Lowell, K., & Fortin, M. (2004). Assessing the spatial uncertainty of boundaries on forest maps using an ecological similarity index. In R. McRoberts (Ed.), Proceedings of the joint meeting of the 6th international symposium on spatial accuracy assessment in natural resources and environmental sciences and the 15th annual conference of the international environmetrics society, Portland, Maine.

  • Palma, C. D., & Nelson, J. D. (2009). A robust optimization approach protected harvest scheduling decisions against uncertainty. Canadian Journal of Forest Research, 39(2), 342–355.

    Article  Google Scholar 

  • Peter, B., & Nelson, J. (2005). Estimating harvest schedules and profitability under the risk of fire disturbance. Canadian Journal of Forest Research, 35(6), 1378–1388.

    Article  Google Scholar 

  • Pickens, J. B., & Dress, P. E. (1988). Use of stochastic production coefficients in linear programming models: objective function distribution, feasibility, and dual activities. Forest Science, 34(3), 574–591.

    Google Scholar 

  • Pkukkala, T. (1998). Multiple risks in multi-objective forest planning: integration and importance. Forest Ecology and Management, 111(2–3), 265–284.

    Article  Google Scholar 

  • Radoux, J., & Defourny, P. (2007). A quantitative assessment of boundaries in automated forest stand delineation using very high resolution imagery. Remote Sensing of Environment, 110(4), 468–475.

    Article  Google Scholar 

  • Reeves, L. H., & Haight, R. G. (2000). Timber harvest scheduling with price uncertainty using Markovitz portfolio optimization. Annals of Operations Research, 95(1), 229–250.

    Article  Google Scholar 

  • Snyder, L. V. (2006). Facility location under uncertainty: a review. IIE Transactions, 38(7), 547–564.

    Article  Google Scholar 

  • Snyder, S., & ReVelle, C. (1997). Dynamic selection of harvests with adjacency restrictions: the share model. Forest Science, 43(2), 213–222.

    Google Scholar 

  • Thompson, E. F., Halterman, B. G., Lyon, T. J., & Miller, R. L. (1973). Integrating timber and wildlife management planning. The Forestry Chronicle, 49(6), 247–250.

    Article  Google Scholar 

  • Von Gadow, K. (2000). Evaluating risk in forest planning models. Silva Fennica, 34(2), 181–191.

    Article  Google Scholar 

  • Weintraub, A., & Vera, J. (1991). A cutting plane approach for chance constrained linear programs. Operations Research, 39, 776–785.

    Article  Google Scholar 

  • Weintraub, A., & Abramovich, A. (1995). Analysis of uncertainty of future timber yields in forest management. Forest Science, 41(2), 217–234.

    Google Scholar 

  • Weintraub, A., Church, R. L., Murray, A. T., & Guignard, M. (2000). Forest management models and combinatorial algorithms: analysis of state of the art. Annals of Operations Research, 96(1), 271–285.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. GeoDa Center for Geospatial Analysis and Computation, School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ, 85287-5302, USA

    Ran Wei & Alan T. Murray

Authors
  1. Ran Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alan T. Murray
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alan T. Murray.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wei, R., Murray, A.T. Spatial uncertainty in harvest scheduling. Ann Oper Res 232, 275–289 (2015). https://doi.org/10.1007/s10479-012-1178-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10479-012-1178-2

Keywords

Search

Navigation