Supplier selection and order allocation are two of the most important stages in supply chain management. In recent years, these decisions have become major challenges since it has been increasingly important to consider the sustainability of the supply chain. This research presents an integrated methodology to solve a sustainable two-stage supplier selection and order allocation problem for a meat supply chain, considering economic, environmental and social criteria. The proposed integrated methodology includes four phases: (1) the fuzzy analytical hierarchy process (AHP) was used to assign the relative weights for sustainable criteria; (2) the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS) was used to rate suppliers vis-à-vis their sustainable performance; (3) a multi-objective programming model (MOPM) was formulated to obtain the optimal order allocations of quantity in order to minimise the costs of transportation, purchasing and administration, as well as environmental impact (particularly CO2 emissions) and the travel time of products, while maximising social impact and total purchasing value; and (4) TOPSIS was used to reveal the final solution in a set of Pareto solutions. In industry, many parameters are not known precisely. Therefore, the MOPM was reformulated into a fuzzy MOPM (FMOPM) to handle uncertainty. Afterward, the ε-constraint method and LP-metrics method were employed to optimise the developed FMOPM in terms of obtaining Pareto solutions. Finally, a case study was implemented to examine the applicability of the proposed methodology.