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This paper deals with a specially structured n-job and 2-machine flow shop scheduling problem with jobs in a string of disjoint job blocks including weightage of jobs and processing times associated with probabilities. The jobs are attached with weights to indicate their relative importance. Also the processing times are not random but bear well defined relationship to one another. In flow shop scheduling the emphasis is on minimization of idle time/ elapsed time but minimization of elapsed time may not always lead to minimization of utilization time. The objective is to find an algorithm to minimize the utilization time of machines. The proposed algorithm is validated with the help of a numerical example.