This paper shows a multi-objectives mixed-integer non-linear programming (MINLP) model for a petrochemical supply chain under uncertainty environments, namely disruption risks and less knowledge of parameters. In this model, two efficient queuing systems are applied in nylon plastic manufacturing and recycling centers, in which a Jackson network is also used. The aims are to minimize the average tardiness to deliver products, total cost and transportation cost. In addition the developed model specifies the optimal locations for a new distribution center (DC), collection center and disposal center as well as the optimal allocation of customer zones to each DC. This model is solved in three stages: (1) a Jackson network determines the queuing parameters, (2) an Lp-metric approach makes the multi-objectives into a single objective, and (3) an efficient Lagrangian relaxation based on a sub-gradient approach solves the presented model. Additionally, a real case study is shown in details to depict the application of the presented model. At the end, the sensitivity analyses are carried out to check the optimal objectives by changing the important parameters. (C) 2016 Elsevier Ltd. All rights reserved.