In this paper, we
propose a new mathematical optimization
approach
to make decisions on the optimal design of the complex logistic system
required to produce biogas from waste. We provide a novel and flexible
decision-aid tool that allows decision makers to optimally determine
the locations of different types of plants (pretreatment, anaerobic
digestion, and biomethane liquefaction plants) and pipelines involved
in the logistic process, according to a given budget, as well as the
most efficient distribution of the products (from waste to biomethane)
along the supply chain. The method is based on a mathematical optimization
model that we further analyze and that, after reducing the number
of variables and constraints without affecting the solutions, is able
to solve real-size instances in reasonable CPU times. The proposed
methodology is designed to be versatile and adaptable to different
situations that arise in the transformation of waste to biogas. The
results of our computational experiments, both in synthetic and in
a case study instance, prove the validity of our proposal in practical
applications. Synthetic instances with up to 200 farms and potential
locations for pretreatment plants and 100 potential locations for
anaerobic digestion and biomethane liquefaction plants were solved,
exactly, within <20 min, whereas the larger instances with 500
farms were solved within <2 h. The CPU times required to solve
the real-world instance range from 2 min to 6 h, being highly affected
by the given budget to install the plants and the percent of biomethane
that is required to be injected in the existing gas network.