Supply chain network design considering carbon footprint, water footprint, supplier’s social risk, solid waste, and service level under the uncertain condition

Abstract Supply chain network design (SCND) plays a crucial role in transforming a supply chain sustainable. Recently, various SCND models have been developed especially focusing on carbon footprint reduction. The current study argues that emphasizing only on carbon footprint cannot entirely transform a supply chain sustainable. There are other dimensions (water footprint, solid waste, and social factor), which need to be taken care of for implementing sustainability. Till now, most of the sustainable SCND models have been developed in deterministic conditions, and very few models have been reported in a stochastic environment. To fill the gaps of existing literature, the current study proposes a multi-product and multi-echelon SCND model by addressing carbon footprint, water footprint, solid waste, social sustainability, service level, different transportation modes and inventories in stochastic condition. The study intends to minimize the total cost and estimate the flow of materials across the various echelons of the supply chain. The model considers the demand and capacity as stochastic variables. Further, chance-constrained programming has been used to model the uncertainty of parameters. In the current research, an individual-level chance constraint with right-hand side uncertainty has been adopted. The applicability of the proposed model has been demonstrated with a numerical example and sensitivity analyses have been conducted by changing model parameters, like probability, carbon footprint, water footprint, solid waste, service level, and social factor. The suggested model facilitates decision-maker to estimate the optimum flow of material across the supply chain for delivering materials of predetermined carbon footprint, water footprint, solid waste, social sustainability, and service level. The model helps the manager to implement the sustainability holistically across the supply chain. Graphic abstract