In this paper, we adopt an interactive approach for bi-level multi-objective supply chain model (BL-MOSCM). The essential target is to decide the ideal request designation of items where the client’s demands and supply for the items are vague demand. This study considers two decision-makers (DMs) operating at two separate groups of supply chain network (SCN), that is, a bi-level decision-making process. In the current BL-MOSCM, the leader locates quantities dispatched to retailers, and afterward, the follower chooses his amounts reasonably. The pioneer’s goal is to reduce the all-out conveyance expenses, also, the follower’s goal is to reduce the all-out conveyance time of the SCN and simultaneously adjusting the optimal request allotment from each source, plant, retailer, and distribution center, respectively. The BL-MOSCM is defuzzified and changed into a valent crisp structure based on the α-level methodology. Then the interactive methodology works on the α-(BL-MOSCM) by changing it into discrete multi-objective programming problems (MOPP). Also, each separate MOPP thinks through the ε-constraint methodology and the idea of satisfactoriness. The ε-constraint method aims at optimising one objective function, while considering all other objective functions as constraints. By obtaining the solution of the first level SCN utilizing the ε-constraint method, the second level SCN is also optimized considering the controlled variables of the first level. A novel test function is introduced to decide the compromise solution of the BL-MOSCM. Procedures for solving the uncertain BL-MOSCM via the interactive approach are introduced. A real-life case study was used to illustrate the proposed interactive methodology for the BL-MOSCM with fuzzy parameters. The obtained result shows the optimal quantities transported from the various sources to the various destinations that could enable managers to detect the optimum quantity of the product when hierarchical decision-making involving two levels. Finally, a comparison with the past studies is used to display the practicality and efficiency of the suggested methodology.