The Waste-to-Biomethane Logistic Problem: A Mathematical Optimization Approach

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.