摘要
This paper presents a novel multi-time-stage input–output-based modeling framework for simulating the dynamics of bioenergy supply chains. One of the key assumptions used in the model is that the production level at the next time-stage of each segment of the energy supply chain adjusts to the output surplus or deficit relative to targets at the current time period. Furthermore, unlike conventional input–output models, the technology matrix in this approach need not be square, and thus can include coefficients denoting flows of environmental goods, such as natural resources or pollutants. Introducing a feedback control term enables the system to regulate the dynamics, thus extending the model further. This is an important feature since the uncontrolled dynamic model exhibits oscillatory or unstable behavior under some conditions; in principle, the control term allows such undesirable characteristics to be suppressed. Numerical simulations of a simple, two-sector case study are given to illustrate dynamic behavior under different scenarios. Although the case study uses only a hypothetical system, preliminary comparisons are made between the simulation results and some broad trends seen in real bioenergy systems. Finally, some of the main policy implications of the model are discussed based on the general dynamic characteristics seen in the case study. In particular, insights from control theory can be used to develop policy interventions to impart desirable dynamic characteristics to nascent or emerging biofuel supply chains. These interventions can be used to guide the growth of bioenergy supplies along final demand trajectories with minimal fluctuation and no instability.