<p>The pharmaceutical supply chain is of great importance due to its close connection with human health and societal well-being. This paper develops an integrated multi-objective, multi-level, multi-period, mixed integer nonlinear programming (MINLP) model. The objectives of the model encompass all three aspects of sustainability (economic, environmental, and social). Transshipment is permitted between two separate levels. This model attempts to eliminate or reduce monopoly in the pharmaceutical industry by imposing restrictions. To handle demand uncertainty, robust possibilistic programming was employed. In addition to solving the model with GAMS, NSGA-II and the Memetic algorithm were applied to generate Pareto front solutions for this NP-hard problem. The Taguchi design method was utilized to tune and control the algorithm’s input parameters. Then, through the comparison criteria of multi-objective algorithms, such as diversity, spacing, number of Pareto solutions (NPS), mean ideal distance (MID), multi-objective coefficient of variation (MOCV), and diversification metric (DM), the applicability of metaheuristic algorithms was compared with each other. Also, ANOVA was employed to compare the mean of the criteria. The comparison results showed the superiority of the Memetic algorithm in the diversity criterion and the superiority of the NSGA-II algorithm in the spacing criterion. Finally, the feasibility and applicability of the model were examined with the help of a real case study in Arak city, and sensitivity analyses on demand were performed. This article offers managerial insights for sustainable pharmaceutical supply chain design under uncertainty using an integrated model and advanced solution methods.</p>