The decision makers and investors often exhibit their concern regarding with the interaction between the biomass allocation and the design of the SC infrastructure, therefore, exist a great interest in identifying the optimal facility locations (whether or not in combination with the capacity and technology) simultaneously with the determination of the optimal flow of biomass (and eventually bioenergy) among the various nodes of the network (Melo et al., 2009).
Recently Yue et al. (2014) have presented a literature survey that covers the challenges biofuel production is currently facing. The work gives an overview of biofuel technologies and different approaches to their implementation. It also reviews many papers regarding current
1.6 Mathematical Programming studies in the biofuels area. Consequently, there is a large compendium of works tackling strategic decisions in the field of biomass SC optimization describe the upstream biomass SC as a network structure in which nodes correspond with source locations, collection sites, transhipment sites, pre-treatment sites and/or conversion sites while arcs correspond with the product flow and transport operations (Bowling et al., 2011). Indeed, both Bowling et al. (2011) and Mol et al. (1997) use a MILP model in order to optimize the network structure together with the biomass flows according to a specified economic, energetic and/or environmental objective with the mass balances, capacities and demands as constraints. Into the models exists a set binary variables which determine whether or not a facility is built at a certain location, while continuous variables are related to the flows of biomass and energy from one node to another in the network structure. Zamboni et al. (2009b) presents a spatially-explicit MILP model for the integrated management of the key issues affecting corn-based ethanol SCs such as biomass suppliers and production facilities allocation as well as transport logistics. This formulation is based on cost minimization. Akgul et al. (2011) presents an optimization framework to determine the locations and sizes of bioethanol production facilities and the biomass as well as bioethanol flows between regions. Since is a problem of large scale, the authors adopted a neighbourhood flow representation into the mathematical formulation in order to solve the SC network problem.
Even though economic, energetic, environmental and social concerns simultaneously affect the decisions to be made in SCM, most optimization models concentrate on the optimization of economic issues. Marvin et al. (2012) addresses an optimization study focusing on the economic feasibility (net present value) of biomass-to-bioethanol SC in the U.S.A. taking into consideration several types of lignocellulosic biomass the biofuel production. A MILP optimization approach is presented by Leduc et al. (2010) in order to find the cost optimal facility location for lignocellulosic ethanol refineries in Sweden, which is also taken as base formulation by Natarajan et al. (2012) for the methanol and CHP production in Finland. On the other hand, Leão et al. (2011) has developed a model using MP techniques to optimize the structure for supplying oil (considering production, transportation and crushing of oil seeds and transportation of oil) to biodiesel plant. Similarly, Leduc et al. (2009) has used a MILP model to conduct an optimization for the optimal location for Jatropha biodiesel plant analysing various feedstock. Besides that,
Akgul et al. (2012b) considered the economic impact in a MILP framework for bioethanol SC network to determine locations and scales of biofuel production facilities, biomass cultivation and biofuel production rates, flow of biomass and biofuel between the components of supply chain, transportation modes of delivery for biomass and biofuel.
It is noteworthy that the influence of the temporal variation is very clear in tactical/operational decision making as well as in the long–term decisions, which are influenced by the temporal variability in the supply of biomass and growing energy demand. Therefore this temporal characteristic arises as multi-period and/or multi-stage MILP in order to optimize the overall system cost along the planning horizon which may be divided in multiple time periods. The consequence is that the decisions regarding to optimal location of the plants and biomass flows are performed in each time period together with the growth in demand, therefore the decision variables (binaries) come to determine whether or not to build a production plant while variables continuous determine the amounts of biomass and biofuel produced. An et al. (2011b) formulates a model dealing with a time-staged, multi-commodity, production/distribution system, prescribing facility locations and capacities, technologies, material flows and the demand profile of fuel by dividing a one-year planning horizon into four quarters in order to maximize the economic performance of a lignocellulosic biofuel SC. Huang et al. (2010) formulated a multi-period optimization model with yearly decisions to determine the location and capacity of the facilities with the possibility of adding capacity expansions onto existing refineries. Another multi-period SC design MILP model (Sharma et al. (2011)) formulated to maximize stakeholder value in the design of a biorefinery and the SC configuration, where the binary variables being used to technology and feedstock selection and decision to expand the capacity of the facilities. Besides that, Dunnett et al. (2008) present a MILP modelling framework with production and logistics features to provide the cost-optimal configurations of the lignocellulosic bioethanol SC considering several technologies, system scale, ethanol demand distribution scenarios and biomass supply. A case of study in Argentina with land usage consideration and crop competition was studied in Andersen et al. (2012) through a MILP multiperiod formulation for a 7-year planning period with monthly decisions for the optimal design and planning of the biodiesel SC. Furthermore, Wang et al. (2012b) presented an energy crop supply chain model to identify the optimal location and capacities
1.6 Mathematical Programming for a cogeneration facility, subject to the minimum cost of the overall system.