The current paper investigates a two-stage flow shop scheduling model with no idle restriction, in which the time taken by machines to set-up is separately considered from the processing time. Owing to inherent usefulness as well as relevance in real-world situations, jobs' weight has additionally included. To eliminate machine idle time and cutting machine cost of rental, the reason for the conduct of the study is to provide a heuristic algorithm which, once put into practice, processes jobs in an optimal way, guarantees in smallest conceivable make span. Multiple computational examples generated in MATLAB 2019a serve as testament to the efficacy of the proposed strategy. The outcomes are contrasted with the current methods that Johnson, Palmer and NEH have demonstrated.