摘要:

A long‐standing problem in forestry management is the optimal harvesting of a growing population of trees to maximize the resulting discounted aggregate net revenue. For anongoing forest, the trees are harvested and replanted repeatedly; for aonce‐and‐for‐allforest, there is no replanting after a single harvest. In this paper, we outline a new formulation for the optimal‐harvest problem which avoids difficulties associated with functional‐differential equations or partial differential equations of state in the relevant optimal‐control problem encountered in recent studies of the ongoing‐forest problem. Our new formulation is based on the observation that tree logging is necessarily ordered by practical and/or regulatory considerations (e.g., it is illegal to cut the younger trees first in some jurisdictions); random access to tree sites does not occur in practice. The new formulation is described here for the simpler problem of a once‐and‐for‐all forest. New results for nonuniform initial age distributions and variable unit harvest costs for this simpler problem are reported herein; results for an ongoing forest will be reported in [10]. The new model is also of interest from a control‐theoretic viewpoint, as it exhibits the unique feature of having time as astate variable, in contrast to its usual role as an independent variable in conven

ISSN:0022-2526    

DOI:10.1002/sapm1983683189

年代:1983

数据来源: WILEY

摘要:

A study is made of several nonlinear boundary‐value problems of singular perturbation type for which a straightforward application of boundary‐layer theory leads to spurious solutions. It is shown that these problems can be treated successfully by a slight modification of the method of matched asymptotic expansions. The analysis leads to several novel features which are not present in routine singular perturbation probl

ISSN:0022-2526    

DOI:10.1002/sapm1983683227

年代:1983

数据来源: WILEY