In the present scenario the recent engineering and industrial built-up units are facing hodgepodge of problems in a lot of aspects such as machining time, electricity, man power, raw material and customers constraints. The job-shop scheduling is one of the most significant industrial behaviours, particularly in manufacturing planning. This paper proposes the permutation flow shop sequencing problem with the objective of makespan minimization using the new modified proposed method of johnsons algorithm as well as the guptas heuristic algorithm. This paper involves the determination of the order of processing of n jobs in m machines. Although since the problem is known to be np-hard for three or more machines, that produces near optimal solution of the given problem. The proposed method is very simple and easy to understand followed by a numerical illustration is given.