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This paper provides a simple heuristic algorithm to minimize utilization time for specially structured n-job and 2-machine flow shop scheduling problem with jobs in a string of disjoint job blocks having sequence independent setup times separated from processing times each associated with their respective probabilities including job weightage and transportation time where the optimization criteria is the utilization time of machines. In flow shop scheduling the emphasis is on minimization of elapsed time but minimization of elapsed time may not always lead to minimization of utilization time. Here, the objective is to find an algorithm to minimize the utilization time of machines. To minimize the utilization time an algorithm is proposed and a numerical example is given to validate the algorithm.