A Bayesian sequential single machine scheduling problem to minimize the expected weighted sum of flowtimes of jobs with exponential processing times

In this paper, the authors consider a scheduling problem in which m classes, J1,J2,...,Jm, of independent jobs with ready time 0 are to be processed by a single machine. The number of jobs of class Ji is ni and the processing times of these ni jobs are independent and identically distributed exponentially distributed with unknown parameter θi, which has a conjugate gamma prior. The objective is to minimize the expected (weighted) sum of flowtimes of all the jobs, where Ri is the weight for a job of class Ji. The problem is formulated as a dynamic program and optimal strategies are derived.