Purpose The purpose of this article is to develop a bi-directional relaxed flexible bay structure (BRFBS) in the layout for the unequal area facility layout problems (UA-FLPs) and test the suitability of the proposed approach using literature data. Design/methodology/approach This research adopts a two-stage solution approach for UA-FLPs to form BRFBS in the layout. The solution to UA-FLPs is carried out in discrete space. The proposed heuristic method optimises the layout plan for minimising the material handling cost (MHC), and also, it indirectly optimises the space utilisation by reducing the empty space in the layout. The first stage of layout design assumes that all facilities are equal in size and uses quadratic assignment problem (QAP) model. QAP is solved with a simulated annealing heuristic method. In the second stage, a heuristic method is proposed to find the optimum width for each bay and the dimension for facilities. The proposed heuristic method is tested with numerical data available in the literature. Results are compared with the results obtained by layout planning software, and with the simulated annealing algorithm for flexible bay structure (SA-FBS) heuristic procedure for continuous space UA-FLPs. Findings The proposed two-stage solution approach gives the BRFBS for the UA-FLPs. BRFBS helps to create proper aisle structure in the layout plan. The layout configuration and solution of the proposed method is better than the layout planning software solution and SA-FBS solution. The application of the proposed heuristic method to case data gave lesser MHC, better space utilisation and better aisle formation than the existing layout. Research limitations/implications The proposed approach has the limitation that it can be applied only to UA-FLPs solved in discrete space. When the UA-FLPs are solved in continuous space, then it is not possible to make application of this approach to form bi-directional relaxed flexible bays in the layout plan. Practical implications Most of the modern industries are automated, and they use material handling equipment (MHE) like automated guided vehicles (AGVs). Design of layout plans that help to create proper aisle structure for AGV’s in the layout plan is a challenging to the researchers. The BRFBS configuration is more suitable in the flexible manufacturing system where AGVs are used for material transportation. Originality/value This paper proposes a novel two-stage heuristic method for solving the UA-FLPs in discrete space. The proposed approach generates a BRFBS in the layout plan. The BRFBS helps to create a proper aisle structure suitable for better material handling operations. Hence, this type of layout helps in easy interaction of the MHE (e.g. AGVs) with the boundaries of the facilities touching the aisle.