Stochastic production planning for a biofuel supply chain under demand and price uncertainties

In this paper, we propose a stochastic production planning model for a biofuel supply chain under demand and price uncertainties. The supply chain consists of biomass suppliers, biofuel refinery plants and distribution centers. A stochastic linear programming model is proposed within a single-period planning framework to maximize the expected profit. Decisions such as the amount of raw materials purchased, the amount of raw materials consumed and the amount of products produced are considered. Demands of end products are uncertain with known probability distributions. The prices of end products follow Geometric Brownian Motion (GBM). Benders decomposition (BD) with Monte Carlo simulation technique is applied to solve the proposed model. To demonstrate the effectiveness of the proposed stochastic model and the decomposition algorithm, a representative supply chain for an ethanol plant in North Dakota is considered. To investigate the results of the proposed model, a simulation framework is developed to compare the performances of deterministic model and proposed stochastic model. The results from the simulation indicate the proposed model obtain higher expected profit than the deterministic model under different uncertainty settings. Sensitivity analyses are performed to gain management insight on how profit changes due to the uncertainties affect the model developed.