A bi-level model formulation for the distributed wood supply planning problem

Abstract

The classic wood supply optimisation model maximises even-flow harvest levels and implicitly assumes infinite fibre demand. In many jurisdictions, this modelling assumption is a poor fit for actual fibre consumption, which is typically a subset of total fibre allocation. Failure of the model to anticipate this bias in industrial wood fibre consumption has been linked to increased risk of wood supply failure. In particular, we examine the distributed wood supply planning problem where the roles of forest owner and fibre consumer are played by independent agents. We use game theory to frame interactions between public forest land managers and industrial fibre consumers. We show that the distributed wood supply planning problem can be modelled more accurately using a bi-level formulation and present an extension of the classic wood supply optimisation model that explicitly anticipates industrial fibre consumption behaviour. We present a solution methodology that can solve a convex special case of the problem to global optimality and compare output and solution times of classic and bi-level model formulations using a computational experiment on a realistic dataset. Experimental results show that the bi-level formulation can mitigate risk of wood supply failure.