Within supply chains activities, selecting appropriate suppliers based on the sustainability criteria (economic, environmental and social) can help companies move toward sustainable development. Although several studies have recently been accomplished to incorporate sustainability criteria into supplier selection problem, much less attention has been devoted to developing a comprehensive mathematical model that allocates the optimal quantities of orders to suppliers considering lot-sizing problems. In this research, we propose an integrated approach of rule-based weighted fuzzy method, fuzzy analytical hierarchy process and multi-objective mathematical programming for sustainable supplier selection and order allocation combined with multi-period multi-product lot-sizing problem. The mathematical programming model consists of four objective functions which are minimising total cost, maximising total social score, maximising total environmental score and maximising total economic qualitative score. The proposed model is developed based on the parameters achieved through the preprocessing of suppliers’ social, environmental and economic data by a rule-based weighted fuzzy approach and fuzzy analytical hierarchy process. The proficiency and applicability of the proposed approach is illustrated by a case study of packaging films in food industry. Considering sustainability criteria in the proposed model reveals that a higher value of sustainable purchasing is achievable in comparison with a single-objective cost-based model.