In this research article aims to develop a heuristic for minimizing the total material processing time and idle time of the critical machine in a flow shop. This heuristic is proposed through the Exponential Distribution (ED) factor which helps in developing a mathematical model with less computational instance. When the idle time of the critical machine is reduced then it is indirectly affects the total material processing time of the flow shop, which makes the objective of critical machine utilization as vital. And a set of constrain had been established to position the critical machines in the flow shop. For several instance, computational experiments had done using the benchmark problems, among other heuristics ED heuristic yields a better result.