A mathematical model for a hybrid first/second generation of biodiesel supply chain design with limited and reliable multimodal transport

Designing a biofuel supply chain plays an important role in the reduction of biomass transportation costs. This study aims to present a comprehensive decision support tool (DST) for designing of the integrated biodiesel supply chain (BSC). In addition, so far no research has been found that examined hybrid first/second generation of biodiesel with considering all economic, environmental and social costs. In achieving this goal, we developed a new optimization model using mixed integer linear programming with the objective of maximizing the total profits of BSC incorporating environmental and social costs.  To do so, practical constraints including the limit of biomass, the capacity of technologies, the land availability, and especially limited capacity of each transportation vehicles are applied to this mathematical model. The main purpose of this study is to develop a DST to evaluate the commercial feasibility of BSC with focusing on multimodal and reliable transport.  To illustrate the capability of the proposed model, Iran is considered as a real application. The findings of this study indicate that some factors such as biomass availability, transportation reliability, and biofuel price can play as a pivotal role in this supply chain design and optimization. All in all, 31% increase in amount of produced biodiesel leads a marginal increase in environmental-related costs.