(400g) Design and Optimization of Modular Biorefinery Supply Chain Under Uncertainty

Besides efficient catalysts and process design, supply chain logistics also played an essential role in achieving the full economic and environmental benefits of biomass-based chemical production.¹ Although biomass provides a cheap and accessible resource for sustainable feedstock, its supply is often affected by temporal and spatial distributions.² For example, crop residuals are an ideal source of biomass feedstock but are only available during fall when the crop is harvested.³ Biomass availability is also affected by the dominant crop or plant species in different regions, leading to large spatial variability of the feedstock supply. Proper placement of production facilities and strategies to reduce the transportation between supply, facility, and market would reduce the total production cost but also the emissions.⁴ Modular biorefinery supply chain has emerged as a flexible and scalable approach that provides more options to adjust the production according to the feedstock availability and product demands.^{5, 6} Bhosekar et al. demonstrated the economics of numbers and risk management in the modular supply chain.⁷ Modular production also enjoys other benefits, such as faster start-up, lower investment risk, and easier maintenance.^{8, 9}

Allman and Zhang developed the deterministic modular supply chain model with movable units to capture the effects of demand variability and illustrated the correlation between the value of module mobility and the “demand center of mass.”¹⁰ They further considered the supply side of the modular supply chain to show the “supply center of mass” in a stochastic programming model.³ In this work, we formulated a two-stage stochastic programming model for the biomass supply chain with modular units and warehouses to analyze the effects of both supply and demand driven forces through the entire supply chain. The first-stage integer decisions are related to the purchase and movement of modules. Next, the actual biomass supply (corn stover, poplar, and willow) in each region and the product demand at the market are observed.¹¹ Operational level decisions are then made on the warehouse inventory level and transportation of raw materials and products between supply regions, production facilities, warehouses, and end markets.^{2, 3, 7}

The supply chain optimization model for distributed biorefinery operation with mobile modules involves variables at each location, planning time period, and uncertain scenario, leading to a large-scale optimization problem with mixed-integer decisions.^{10, 12} Nonlinear relationships may also exist in the operational, inventory holding, or backorder costs, which increase the computational complexity. However, this model has a special block angular structure that could be exploited in a decomposition framework to reduce the computational time.¹³ Benders decomposition is widely applied in capacitated supply chain planning problems and two-stage stochastic programming by fixing complicating variables, solving the decoupled subproblems, and adding cuts.¹⁴ Moreover, Lagrangean decomposition creates copies of variables for different constraints and then adds penalties for the discrepancies (e.g., nonanticipitativity constraint).¹⁵ This method has been utilized to solve multi-period MINLP planning for oil infrastructure¹⁶ and multi-product batch scheduling.¹⁷ Those decomposition-based solution approaches have been utilized in the supply chain model to solve the proposed modular biomass supply chain model more efficiently. We also applied the proposed optimization approach to different scenarios to understand the performance of the modular biorefinery system under various module sizes, supply/demand distributions, and the trade-off between economic and environmental objectives.

Reference

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