This paper focuses on designing multi-objective biomass supply chain planning models that aim to simultaneously minimize the total cost and the carbon footprint from the transportation. Stochastic and fuzzy models were developed for making strategic (optimal plant locations) and tactical decisions (material flows, truck types, etc.), while capturing the uncertainty of the demand. An epsilon-constraint method was applied to generate optimal solutions from these models. Managerial insights are provided based on a practical case study at a biomass plant in the Lower Northern region of Thailand; nine biomass plant candidates, nine rice husks suppliers and eight trucks were considered in the case study. A sensitivity analysis has been conducted to compare the results from the two models. The stochastic model can take into account all the scenarios of demand, while the fuzzy model can handle only a certain level of demand defined by a centroid value. The stochastic model needs to take into account a large number of variables and constraints, and therefore, requires more runtime to define an optimal solution, as compared to the fuzzy model. The trade-off between the operating cost and carbon emissions from both the models are provided with managerial insights.