Paying attention to cost reduction, increasing delivery speed and continuously improving the quality of products and services in a competitive environment has become a requirement for industries. Complexities at different levels and relationships along with uncertainty throughout the chain have challenged the decision-making of the supply chain. The general purpose of this research is to model and develop a multi-level, multi-product, multi-period supply chain network model with conflicting goals such as cost minimization, delivery time minimization, and system reliability maximization. This research is practical in terms of purpose and results and based on operational research approach, it is cross-sectional in terms of time and quantitative in terms of variables. In this research, a multi-objective mathematical model has been presented assuming that the demand is random and follows the probability distribution function. In order to validate the presented model, the supply chain data of the steel industry and Lingo software were used, and by applying the design of experiments, the mathematical relationship related to the cost objective function was estimated, and the multi-objective model was solved with the epsilon constraint approach. At the end, validation and sensitivity analysis of some parameters was done. The results showed that the presented model is able to optimize 4-level supply chains providing several non-perishable products that have random demand and their distribution is probable and improve the reliability of the supply chain.