A note on the regularity of a new metric for measuring even-flow in forest planning

In this work we deal with the mathematical analysis of a new metric for measuring even-flow in even-aged forest management planning. We begin writing the most used way of measuring even-flow, and showing the main disadvantages of this classical procedure. Next, we introduce the new metric and study the regularity of the corresponding function, which results to be continuous and to have continuous derivatives in almost all points. We give an explicit expression for these derivatives and analyze its usefulness by comparing a gradient-type method with a derivative-free algorithm (widely used in forestry) to maximize even-flow in a forest of 51 Eucalyptus globulus Labill. stands in Galicia (NW Spain). We observe that gradient-type methods work well with the new even-flow metric, which enables this type of methods for solving the multi-objective problems that can be formulated in forest planning. (C) 2019 Elsevier B.V. All rights reserved.