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Chemical recycling of plastics is a promising technology to reduce carbon footprint and ease the pressure of waste treatment. Specifically, highly efficient conversion technologies for polyolefins will be the most effective solution to address the plastic waste crisis, given that polyolefins are the primary contributors to global plastic production. Significant challenges encountered by plastic waste valorization facilities include the uncertainty in the composition of the waste feedstock, process yield, and product price. These variabilities can lead to compromised performance or even render operations infeasible. To address these challenges, this work applied the robust optimization-based framework to design an integrated polyolefin chemical recycling plant. Data-driven surrogate model was built to capture the separation units behavior and reduce the computational complexity of the optimization problem. It was found that when process yield and price uncertainties were considered, wax products became more favorable, and pyrolysis became the preferred reaction technology.