Two stage stochastic bilevel programming model of a pre-established timberlands supply chain with biorefinery investment interests

• Economic analysis of new biorefineries for an established timber supply chain.
• Stackelberg game representation for interactions in timber and harvest sectors.
• Analysis of solution methods for two-stage multiperiod stochastic bilevel problems.
• System robustness studies utilizing serial deletion of system components.
• Sensitivity analysis on uncertain scenario parameters.

This work studies the supply allocation problem, using a Stackelberg game, for an established timberlands supply chain with an additional decision of new biorefinery investments. In a timberlands system, harvester and manufacturer decision makers have separate objectives to maximize their respective profits. This interaction is represented with a turn based Stackelberg game. The harvesters decide first on the quantity harvested, and the manufacturers decide on how much to utilize. This game is modeled with a bilevel mathematical program. The novel feature of this paper's bilevel formulation is the inclusion of parametric uncertainty in a two stage model. The first stage problem involves logistical decisions around biorefinery investments, such as location and capacity, while the second stage problem involves a bilevel timberlands model with parameter uncertainty. Studying this problem formulation revealed interesting insights for solving multiperiod problems with bilevel stages as well as the decision maker's behavior for the timberlands model.