Modelling different types of uncertainty in biofuel supply network design and planning: A robust optimization approach

This article proposes a mixed-integer programming (MILP) model to determine the strategic and tactical level decisions of lignocellulosic bioethanol supply chain subject to different sources and types of uncertainty. A comprehensive classification, including sources of uncertainty, corresponding parameters and possible reasons which may cause the uncertainty, as well as an up to date and systematic literature review of biofuel supply chain optimal design and planning studies which consider uncertain input data are presented. To handle different types of uncertainty, including randomness, epistemic and deep uncertainties, a hybrid robust optimization model is proposed. Uncertainty in technology is presented as imprecise conversion rates, which are expressed as probabilistic scenarios. Biomass yield is treated as fuzzy numbers while demand is assumed to vary in a known interval. Furthermore, fixed costs of the biorefineries are calculated according to the piecewise linear functions in which segments are capacity level intervals. In order to investigate the performance of the proposed models a case study is developed for bioethanol supply chain located in Iran. Computational results show that the proposed robust model outperforms deterministic model in terms of given performance measures.