Extending the classic wood supply model to anticipate industrial fibre consumption

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 often a species-unbalanced subset of total fibre allocation. Failure to anticipate this bias in volume and species mix of industrial wood fibre consumption has been linked to increased risk of wood supply failure. In particular, we examine the distributed wood supply planning problem, which is a variant of the general wood supply planning problem where the roles of forest owner and fibre consumer are played by independent agents (e.g. wood supply planning on public forest land in Canada, where government stewards control wood supply and forest products industry firms consume the fibre). We use agency theory to describe the source of antagonism between public forest land owners (the principal) and industrial fibre consumers (the agent). We show that the distributed wood supply planning problem can be modelled more accurately using a bilevel formulation, and present an extension of the classic wood supply optimisation model which explicitly anticipates industrial fibre consumption behaviour. The general case of the bilevel wood supply optimisation problem is NP-hard, non-linear, and non-convex-it is difficult to solve to global optimality. By imposing certain restrictions on agent network topology, we show that the general case can be decomposed into convex sub-problems. We present a solution methodology that can solve this special case to global optimality, and compare output and solution times of classic and bilevel model formulations using a computational experiment on a realistic dataset. Experimental results show that solution time for the bilevel problem is comparable to solution time for the classic single-level problem, and that the bilevel formulation can mitigate risk of wood supply failure