A scenario-adaptive optimization model for circular intertwined supply network design under uncertainty

• Developed a scenario-adaptive multi-objective MINLP model for sustainable circular Intertwined supply networks, under uncertainty. • Investigating the impact of integration of intertwining and circularity within supply chains on GHG emission and costs reduction. • Considerably reducing the amount of greenhouse emission and the amount of total cost through incorporating a recycling center and promoting interconnected flows. • Validating the mathematical model through presenting a case study with for an intertwined pharmaceutical–bioplastic supply network. • Applied fuzzy interactive programming with ME measure to handle uncertainty and used Grey Wolf Optimizer to solve large-sized instances efficiently. Intertwined supply networks are collaborative, cross-industry supply chains characterized by a high level of interconnectedness among their entities. This study demonstrates that integrating circular economy principles into such networks can cut greenhouse gas emissions by 4.97% and reduce total system costs by 11.03%, while strengthening economic efficiency and social responsibility under uncertainty. To realize these improvements, a novel multi-objective non-linear mixed-integer mathematical model is proposed with an embedded scenario differentiation mechanism that enables evaluation of configurations, from traditional decentralized supply chains to complex intertwined networks with varying levels of circularity, within a unified analytical model. The objective functions are to minimize system costs and greenhouse gas emissions and maximize social responsibility for optimal location decisions under uncertainty. The proposed model is first verified using the AUGMECON-2 method and validated via a case study of an intertwined pharmaceutical-bioplastic supply network, complemented by numerical experiments, sensitivity analyses, and a comparative study using the Grey Wolf Optimizer for large-scale instances