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A Reservation Value Approach to Harvest Scheduling with Stochastic Stumpage Prices

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This article presents a formulation of the multistand harvest scheduling problem with stochastic stumpage prices, where demand constraints on the periodic yield of some products exist over a long planning horizon. The model incorporates explicit information about future yields and the possibility of a future high stumpage price simultaneously for each analysis area and prescription. The underlying price uncertainty is modeled as a stationary process with normally distributed deviations. A test case, which involves two products, sawtimber and pulp, is introduced to illustrate the formulation. Sawtimber is assumed to be sold on the open market, while a certain periodic pulp harvest is required by contract to supply a mill at a set price. By maximizing the sum of current revenues and future reservation values subject to yield constraints, the model optimally decides when to harvest immature stands in response to low sawtimber prices, while retaining mature areas for future high prices. Results show significant present value improvements and a much greater probability of feasibility compared to traditional formulations. In addition, because of the possibility of a future high price, some stands are retained to and beyond the culmination of mean annual increment, thereby creating a residual forest with a greater diversity of age classes and more mature timber than is the case with traditional formulations. For. Sci. 42(4):465-473.

Keywords: Forest planning models; adaptive managerial responses; buy variables; rolling planning horizon

Document Type: Journal Article

Affiliations: Professor, School of Forestry and Wood Products, Michigan Technological University, Houghton, MI 49931

Publication date: 1996-11-01

More about this publication?
  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2015 Impact Factor: 1.702
    Ranking: 16 of 66 in forestry

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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