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.