Joint Multi-item Multi-supplier Sustainable Lot-Sizing Model Applying Combined BWM, TOPSIS, Possibilistic Programming, and ϵ-constraint Method

Procurement decisions are critical in sustainable supply chain (SC) transformation. Until now, mainly deterministic supplier selection and lot-sizing models have been suggested. Moreover, it is not easy to make a SC sustainable solely by focusing on carbon footprint. Other sustainability factors, such as social, water, and waste management need to be considered. Therefore, the present study proposed a three-stage multiobjective, multisupplier, multiperiod joint supplier selection, and lot-sizing model, considering carbon footprint, water footprint, solid and liquid waste, and use of recycled materials in a stochastic environment. The model optimizes three objectives (cost, carbon emission, and social sustainability). The model considers different model parameters uncertain, such as costs, emission, solid waste, liquid waste, recycled material, quality rejection, and capacity. The present study suggests quantifying social sustainability and further using it in the lot-sizing model. The study has applied three stages. First, best–worst method and TOPSIS are used to assess suppliers' social scores. Second, the proposed possibilistic lot-sizing model uses the suppliers' social scores. In the third stage, the ϵ-constraint approach is used to generate tradeoff curves. The model generates optimal solutions for various levels of uncertainty, which are utilized to develop cost, emission, and social tradeoff curves.