Spatially constrained harvest scheduling for multiple harvests by exact formulation with common matrix algebra
Spatially constrained harvest scheduling for multiple harvests by exact formulation with common matrix algebra
复制标题
通过使用公共矩阵代数的精确公式来实现多次收获的空间约束收获调度
DOI：
10.1007/s10310-015-0507-0
复制
发表时间：
2016
影响因子：
1.5
通讯作者：
A. Konoshima,M.
中科院分区：
文献类型：
--
作者：
Yoshimoto;A. Konoshima,M.
目前开发的空间约束的收获调度问题的精确配方大多只考虑一个单一的收获随着时间的推移，为个别森林单位。我们提出了一种新的方法，制定调度问题，允许多个收获随着时间的推移，使用公共矩阵代数。我们结合联合收割机的概念模型I制定，它定义的治疗，以克服问题的多个收获，与相邻的治疗约束。通过引入两种邻接矩阵，解决了空间和时间上的捕获问题。一个是一个普通的空间邻接矩阵的森林单元的位置，另一个是一个新引入的活动邻接矩阵，以确定并发采伐活动在一组可能的治疗一个森林单元。这两个邻接矩阵的Kronecker积用于生成所有森林单元之间的处理的整个邻接约束，以避免相邻的收获。我们的方法的优点是，它依赖于模型I公式的概念，以满足空间限制，并使用公共矩阵代数系统地确定所有森林单元的处理的决策变量，以便转换和扩展现有的非空间森林规划模型（例如，FORCED）考虑多个收获和绿化的限制，可以很容易地实现在空间上明确的方式。
Exact formulations currently developed for spatially constrained harvest scheduling problems mostly consider only a single harvest over time for individual forest units. We propose a new method for formulating the scheduling problem of allowing multiple harvests over time by using common matrix algebra. We combine the concept of Model I formulation, which defines treatments to overcome issues of multiple harvests, with that of adjacency constraints for treatments. Conflicting harvests over space and time are resolved by introducing two kinds of adjacency matrices. One is an ordinary spatial adjacency matrix for the forest unit location, and the other is a newly introduced activity adjacency matrix to identify concurrent harvesting activities in a set of possible treatments for one forest unit. The Kronecker product of these two adjacency matrices is used to generate the entire adjacency constraint for treatments among all forest units to avoid adjacent harvests. The advantage of our approach is that it relies on the concept of the Model I formulation to satisfy spatial restrictions and identify decision variables for treatments of all forest units systematically using common matrix algebra, so that conversion and extension of existing non-spatial forest planning models (e.g., FORPLAN) to consider multiple harvests and green-up constraints can easily be achieved in a spatially explicit manner.