Dynamic Optimization Model for a Lignocellulosic Biorefinery Supply Chain

Abstract

Lignocellulosic biorefining system studies have not adequately addressed the integrated nature of the supply chain from feedstock source (farms) to product demand points. The literature typically focuses on systems of single processing facilities with a tendency to study the agricultural side of the supply chain and dismiss the product distribution considerations, such as proximity to demand centers, other processing facilities, or the nature of product market demand. This study offers a more holistic approach by modeling the supply chain from multiple agricultural production sources (farms) to multiple biorefineries, as well as the product distribution to multiple demand locations. The objectives are to establish a dynamic modeling framework for a biorefinery supply chain and to illustrate the use of that framework. The model is designed with the following considerations in mind. 1) Which feedstocks should be purchased? 2) When and from where should they be purchased? 3) Where, how much, and how long should feedstocks be stored? 4) Where, when, how many, and how large should the biorefineries be built? 5) How much and when should the products be produced? 6) How much and where should the products be distributed? 7) How should processing capacity expand over time? The modeling methodology employs a dynamic mathematical program. The supply chain is defined by a system of constraint expressions and optimized by maximizing total system profit. The profit function is defined to include product revenue and system costs, such as feedstock costs, transportation costs, and operating costs. The factors influencing the parameterization of the model are discussed and example parameter values are given. The model is validated and executed to obtain an example solution. The results are presented and discussed to illustrate how the modeling framework can be used to help support biorefinery system planning decisions. This original contribution shows that biorefinery supply chains modeled to incorporate the interactions between multiple farms, biorefineries, and demand locations can provide insights that would not be possible with single system studies or ?supply side only? models. It is shown that mathematical programming offers useful tools for biorefinery supply chain studies. Topics for further research are discussed.