Recruitment of persons for various assignments with required talents in an organization is an important feature, since it plays a vital role in the growth of the organization. To achieve the required expertise in recruitment, in this paper Linear Stochastic Programming (LSP) is applied along with cluster analysis technique. The aim of this paper is to obtain an optimal allocation of persons to different jobs, so that the time taken to complete all the jobs is minimum. The time taken for a person to complete a job is assumed to follow Weibull distribution. The parameters of Weibull distribution is obtained through Maximum Likelihood Estimator (MLE) approach, along with Cohen's iterative process.