Optimal Forest Stand Aggregation and Harvest Scheduling Using Compactly Formulated Integer Programming

Abstract

Abstract:We propose an alternative approach for optimal forest stand aggregation for implementing harvest scheduling, which allows for multiple harvests using a compact formulated integer programming that seeks an optimal aggregated pattern among candidates for forest management units over the planning horizon. We deal with aggregation of small forest stands by introducing the concept of a "hyper unit" as a possible aggregated management unit, which is predefined with the use of adjacency relationship among the set of forest stands. Our proposed approach is based on an optimization framework of a traditional spatially constrained harvest scheduling problem which is used to choose the best set of treatments for the aggregated management units, as well as the original un-aggregated forest stands, while allowing for multiple harvests. We also apply adjacency constraints to create aggregated management units, which are separated from other units, as well as un-aggregated forest stands such that, no adjacent units are harvested in the same period.

Optimal Aggregation of Forest Units to Clusters as “Danchi” under Lower and Upper Size Bounds for Forest Management in Japan

“…It is of interest to investigate if the objective value becomes 0, by which we know that no individual forest unit remains unaggregated. In Yoshimoto et al (2010) and Yoshimoto et al (2017), because of a priori enumeration, there are always some individual forest units that may not be aggregated for "Danchi". Note that the objective can be arranged in many ways on forest managers' preference.…”

“…Yoshimoto et al (2010) proposed an alternative approach to seek a set of clusters for "Danchi" based on the "hyper unit" approach, where one hyper unit is generated a priori as a candidate cluster for "Danchi" from each forest unit by a predefined rule to meet lower and upper size requirements. Yoshimoto et al (2017) incorporated this approach into a Model I type spatially constrained harvest scheduling with multiple harvests over static treatments. Because of the predefined rule or a priori enumeration to generate a set of feasible clusters for "Danchi", their approach is still not exact to solve lower and upper size-bounded clusters for "Danchi".…”