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A Problem of Forest Harvesting and Road Building Solved Through Model Strengthening and Lagrangean Relaxation

Author

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  • Nicolas Andalaft

    (Microsystems, Argentina)

  • Pablo Andalaft

    (Department of Industrial Engineering, University of Chile, Santiago, Chile)

  • Monique Guignard

    (Department of Operations and Information Management, The Wharton School, University of Pennsylvania, Philadelphia, Pennsylvania 19104)

  • Adrian Magendzo

    (Department of Industrial Engineering, University of Chile, Santiago, Chile)

  • Alexis Wainer

    (Forestal Terranova, Venezuela)

  • Andres Weintraub

    (Department of Industrial Engineering, University of Chile, Santiago, Chile)

Abstract

We consider a problem of forest planning on pine plantations over a two to five year horizon. Basic decisions concern the areas to harvest in each period, the amount of timber to produce to satisfy aggregate demands for log exports, sawmills and pulp plants, and the roads to build for access and storage of timber. A linear programming model with 0--1 variables describes the decision process. Solution strategies involve strengthening of the model, lifting some of the constraints, and applying Lagrangean relaxation. Results on real planning problems show that even as these problems become more complex, the proposed solution strategies lead to very good solutions, reducing the residual gap for the most difficult data set from 162% to 1.6%, and for all data sets to 2.6% or less.

Suggested Citation

  • Nicolas Andalaft & Pablo Andalaft & Monique Guignard & Adrian Magendzo & Alexis Wainer & Andres Weintraub, 2003. "A Problem of Forest Harvesting and Road Building Solved Through Model Strengthening and Lagrangean Relaxation," Operations Research, INFORMS, vol. 51(4), pages 613-628, August.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:4:p:613-628
    DOI: 10.1287/opre.51.4.613.16107
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    References listed on IDEAS

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    Cited by:

    1. Hauer, Grant & Cumming, Steve & Schmiegelow, Fiona & Adamowicz, Wiktor & Weber, Marian & Jagodzinski, Robert, 2010. "Tradeoffs between forestry resource and conservation values under alternate policy regimes: A spatial analysis of the western Canadian boreal plains," Ecological Modelling, Elsevier, vol. 221(21), pages 2590-2603.
    2. Monique Guignard, 2003. "Lagrangean relaxation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(2), pages 151-200, December.
    3. Quadrifoglio, Luca & Dessouky, Maged M. & Ordonez, Fernando, 2008. "Mobility allowance shuttle transit (MAST) services: MIP formulation and strengthening with logic constraints," European Journal of Operational Research, Elsevier, vol. 185(2), pages 481-494, March.
    4. Nader Naderializadeh & Kevin A. Crowe, 2020. "Formulating the integrated forest harvest-scheduling model to reduce the cost of the road-networks," Operational Research, Springer, vol. 20(4), pages 2283-2306, December.
    5. Fernando Veliz & Jean-Paul Watson & Andres Weintraub & Roger Wets & David Woodruff, 2015. "Stochastic optimization models in forest planning: a progressive hedging solution approach," Annals of Operations Research, Springer, vol. 232(1), pages 259-274, September.
    6. Alonso-Ayuso, Antonio & Escudero, Laureano F. & Guignard, Monique & Weintraub, Andres, 2018. "Risk management for forestry planning under uncertainty in demand and prices," European Journal of Operational Research, Elsevier, vol. 267(3), pages 1051-1074.
    7. Mikael Rönnqvist & Sophie D’Amours & Andres Weintraub & Alejandro Jofre & Eldon Gunn & Robert Haight & David Martell & Alan Murray & Carlos Romero, 2015. "Operations Research challenges in forestry: 33 open problems," Annals of Operations Research, Springer, vol. 232(1), pages 11-40, September.
    8. Sanei Bajgiran, Omid & Kazemi Zanjani, Masoumeh & Nourelfath, Mustapha, 2016. "The value of integrated tactical planning optimization in the lumber supply chain," International Journal of Production Economics, Elsevier, vol. 171(P1), pages 22-33.
    9. Bisera Andrić Gušavac & Selman Karagoz & Milena Popović & Dragan Pamućar & Muhammet Deveci, 2023. "Reconcilement of conflicting goals: a novel operations research-based methodology for environmental management," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(8), pages 7423-7460, August.
    10. Andres Weintraub P., 2007. "Integer programming in forestry," Annals of Operations Research, Springer, vol. 149(1), pages 209-216, February.
    11. Antonio Alonso-Ayuso & Laureano Escudero & Monique Guignard & Martín Quinteros & Andres Weintraub, 2011. "Forestry management under uncertainty," Annals of Operations Research, Springer, vol. 190(1), pages 17-39, October.
    12. Omid Sanei Bajgiran & Masoumeh Kazemi Zanjani & Mustapha Nourelfath, 2017. "Forest harvesting planning under uncertainty: a cardinality-constrained approach," International Journal of Production Research, Taylor & Francis Journals, vol. 55(7), pages 1914-1929, April.

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