Two stage bilevel programming approach for representation of biorefinery investment decision making in a pre-established timberlands supply chain

Abstract

This work studies the supply allocation problem, using a Stackelberg game, for an established timberlands supply chain with an additional decision of a new biorefinery investment. 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 make its decisions first on the quantity harvested, and the manufacturers make their decisions on how much to utilize. This game is represented in a bilevel mathematical programming model. 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 is a bilevel timberlands model with parameter uncertainty. Studying this problem formulation revealed interesting insight concerning solving multiperiod problems with bilevel stages as well as decision maker behavior for the timberlands model.