PurposeThis paper aims to propose an integrated supplier selection, order allocation, transportation planning model, along with investment planning for corporate social responsibility (CSR), over a given multi-period horizon under uncertainty. Furthermore, a customer’s behavior to pay more money for items with CSR attributes is considered in the total market demand.Design/methodology/approachThe objective functions, i.e. social value of purchasing, total profit (TP), total delivery lead-time, total air pollution, total water pollution and total energy consumption with regard to a number of constraints are jointly considered in a multi-product system. It is worth noting that operational- and sustainable-related parameters are usually vague and imprecise in this area. Therefore, this paper develops a new fuzzy multi-objective optimization model to capture this inherent fuzziness in critical data.FindingsThrough the numerical examples in the textile industry, the application of the model and usefulness of solution procedures are carried out. The numerical results obtained from the proposed approach indicate the efficiency of the solution algorithm in different instances. Moreover, the authors observe that social investment of the buyer, to stimulate market demand, can affect the TP and also involve the total contribution of suppliers in social responsibility.Originality/valueThis research work concentrates on providing a procurement and inventory model through the lens of sustainability to enable textile supply chain managers and related industries to apply the approach to their inventory control and supply management. Totally, the proposed methodology could be applied by many fabric buyers of textile industry tackling purchasing issues and attempting to perfect understanding of social supply chains.