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

Gregory Paradis, Mathieu Bouchard, Luc LeBel, Sophie D'Amours
2018 Canadian Journal of Forest Research  
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
more » ... 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 bilevel formulation, and present an extension of the classic wood supply optimisation model which 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 bilevel model formulations using a computational experiment on a realistic dataset. Experimental results show that the bilevel formulation can mitigate risk of wood supply failure. (FMU) scale when government uses species-wise AAC volumes as contractual upper-bounds in TLs. 22 The classic model simulates a finite alternating sequence of harvesting and growth, and implicitly 23 assumes that all available fibre will be consumed in every planning period (regardless of operability, 24 quantity, quality, cost, or value creation potential). In practice this assumption is rarely respected. Fig-25 ure 1 shows the species-wise proportion of Canadian AAC consumed from 1990 to 2012. On average, 26 80% of softwood AAC and 45% of hardwood AAC were consumed, indicating a clear industrial pref-27 erence for softwood during this period. The classic model always simulates harvesting of the entire 28 AAC in every planning period, ignoring local constraints on processing capacity of certain types of 29 Published by NRC Research Press Page 4 of 36 https://mc06.manuscriptcentral.com/cjfr-pubs Canadian Journal of Forest Research fibre, fibre procurement cost, primary breakdown cost, and market price for primary harvested wood 30 products. Thus, the classic model implicitly assumes infinite fibre demand. This assumption is unre-31 alistic in many cases, which explains why historial harvest levels are systematically lower than AAC. 32 This bias is related to the infinite-demand assumption implicitly embedded in the classic wood supply 33 optimisation model and can, to a certain extent, be attributed to a poor alignment between industrial 34 fibre demand and wood supply planning. 35 Local industrial processing capacity may be insufficient to consume some parts of AAC. Other parts 36 of AAC may be economically unattractive (Mathey et al., 2009) or be operationally inaccessible. Thus, 37 the optimal solution of the classic model will likely never be executed, and the long-term state of the 38 forest will be systematically different from that predicted by the wood supply model. If this systematic 39 difference between predicted and actual outcomes is not entirely corrected by regular rolling-horizon 40 AAC re-planning, then the current policy may not be achieving the best possible compromise between 41 realizing short-term value-creation opportunities and maintaining long-term fibre supply stability and 42 forest productivity. 43 Paradis et al. (2013) simulate repeated wood supply planning cycles, modelling interaction be-44 tween government wood supply planners and industrial fibre consumers. They show that the classic 45 wood supply model may fail due to the aforementioned species-skewed negative fibre consumption 46 bias, and conclude that the wood supply planning process currently in place on public land in Canada 47 may be either overly constraining short-term value-creation opportunities, or not providing credible 48 assurance of the long-term sustainability of the wood supply. Given the pervasiveness of this bias in 49 practice, the classic wood supply optimisation model formulation does not constitute a rational basis 50 for the implementation of sustainable forest management. We endeavor to eliminate this bias from the 51 optimisation model used to determine AAC, thereby improving credibility of the wood supply planning 52 process. 53
doi:10.1139/cjfr-2017-0240 fatcat:t7vtxgq3enfcnkzz2clquuitiq