Nonlinear Programming Approaches to Multistand Timber Harvest Scheduling

Abstract

Abstract This paper describes several nonlinear programming formulations of multistand (analysis area) timber harvest scheduling problems and compares these formulations with more traditional approaches. The strengths of the nonlinear programming approaches include the abilities to represent explicit nonlinear timber yield functions and to define continuous harvest timing variables. Optimal control theory has these capabilities but, to date, the technique has not proven applicable to multistand problems or to problems with common exogenous constraints. Linear programming works well with multistand problems but utilizes piecewise approximations of yield functions and discrete time periods. Both nonlinear and linear programming can accommodate common programming constraints such as output targets and limits on inputs. The nonlinear programming formulations were solved using a version of the generalized reduced gradient algorithm. It was discovered that a local optimum exists for each number of harvests on each analysis area. Because nonlinear programming finds local optima, the global optimum was determined with multiple advanced starts. A nonlinear programming formulation that can handle time-period-based constraints is provided, but could not be solved. For. Sci. 36(4):894-907.