Modeling and optimization of a supply chain of renewable biomass and biogas: Processing plant location

Because of its sustainability, less environmental pollution and high profitability, rapidly growing number of the bio-methane gas (BMG) production systems implies successful commercialization in the new economic venture for renewable bioenergy. Covering from the collection and storage of feedstock (crops, grass, wood residue, and livestock waste) to the distribution of end product, this paper concerns with the optimization of supply chain cost for a BMG production system. The BMG production process is divided into four stages (collecting feedstock to the hubs, transporting feedstock from hubs to reactor(s), then transporting BMG from reactor(s) to condenser(s) and finally shipping the liquefied BMG from condensers to demand points. A mixed-integer mathematical model is proposed to optimally locate the hubs (to collect feedstock) and the BMG plants (reactors and condensers) so as to minimize the total cost of operating this supply chain system for renewable energy. The optimal solutions for the model cannot be readily obtained through convex optimization due to the complexity of the constrained objective function involving with mixed-integer variables. A genetic algorithm is devised to find the optimal solution and several numerical experiments are conducted to verify its performances. Large instances of the representative problems are solved with better quality solutions efficiently and the solution quality overpowers the existing solutions obtained by traditional Lingo and other comparable software. The impact of the model and solution approaches have both technological advancement in solving such problems and economic value to the biogas energy generation.