Abstract

ABSTRACT In industrial forest plantations, the spatial distribution of management units for harvest scheduling influences the timber production cost and the non-renewable resources consumption, due to issues related to transport logistic. In this context, this research aimed to formulate Integer Linear Programming (ILP) by means of the application of Floyd-Warshall network optimization algorithm to generate timber production routes, minimizing the production costs resulting from harvest activities and forest road maintenance. Then, scenarios were simulated considering different minimal harvest ages for Pinus spp. and Eucalyptus spp. stands. The planning horizon was five years with annual periodicity. The study area was 23,330 hectares of forests, located in Paraná state (southern Brazil). We compared the simulated scenarios according to the following parameter indicators: harvest income, building road network and the production unit cost. The decreasing of the minimal harvest age reduces the mean production of management units scheduled to be harvested, in other hand, it requires fewer roads to be built, and consequently increases the production unit cost. The solutions obtained by using ILP models presented an optimality gap lower than 0.1%.

Highlights

  • Average productivity of stands and its spatial distribution, considering the displacement of harvest operation team and the transport of logs, represent two of the main factors that contribute to the forest harvest performance

  • Kirby et al (1986) were one the first authors to describe an integer formulation called Integrated Resource Planning Models (IRPM) of forest management, the class of operational research models that simultaneously integrates the problem of harvest and the configuration of the forest road network

  • The optimization problems of forest planning developed in this study are considered complex due to the large number of constraints and decision variables involved in the formulation of Integer Linear Programming (ILP) models, becoming in many cases impossible to obtain the optimal integer solution within the processing limit time defined

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Summary

Introduction

Average productivity of stands and its spatial distribution, considering the displacement of harvest operation team and the transport of logs, represent two of the main factors that contribute to the forest harvest performance. The road network should be an integrated part of the forest harvest planning, what makes it a very complex task. The computational procedures of harvest optimization integrated to the road network can reduce the budget and the environmental impact caused by such activity. These mathematical tools allow the production of scenarios that represents the problem at hand, providing important information to support the decisionmakings (MCDILL, 2014). Kirby et al (1986) were one the first authors to describe an integer formulation called Integrated Resource Planning Models (IRPM) of forest management, the class of operational research models that simultaneously integrates the problem of harvest and the configuration of the forest road network. Guignard et al (1998) and Andalaft et al (2002) described scientific approaches of IRPM formulation by the exact method through the Mixed Integer Linear Problems (MILP), using the Branchand-Bound algorithm

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