Model tightening for integrated timber harvest and transportation planning

Abstract

Integrated timber harvest and transportation planning problems can be modeled as 0-1 mixed integer programming problems, but initial computations led to large integrality gaps which cannot be overcome easily. In this paper we show how this situation can be substantially improved by a combination of techniques, such as: addition of logical inequalities, lifting of inequalities and careful selection of Branch-and-Bound branching priorities based on a consideration of double-contraction. We compare various combinations of tightening techniques in terms of number of (integer) variables and constraints, LP bound, number of nodes in the Branch-and-Bound tree and CPU time.