Abstract Maximizing the value of resources and producing less waste are strategic decisions affecting sustainability and competitive advantage. Sustainable closed-loop supply chains (CLSCs) are designed to minimize waste by circling back (repairing, reselling, or dismantling for parts) previously discarded products into the value chain. This study presents a novel two-stage fuzzy supplier selection and order allocation model in a CLSC. In Stage 1, we use the fuzzy best-worst method (BWM) to select the most suitable suppliers according to economic, environmental, social, and circular criteria. In Stage 2, we use a multi-objective mixed-integer linear programming (MOMILP) model to design a multi-product, multi-period, CLSC network, and inventory-location-routing, vehicle scheduling, and quantity discounts considerations. In the proposed MOMILP, the total network costs, the undesired environmental effects, and the lost sales are minimized while job opportunities and sustainable supplier purchases are maximized. A fuzzy goal programming approach is proposed to transform the MOMILP into a single objective model. We present a case study to demonstrate the applicability of the proposed method in the garment manufacturing and distribution industry.