A BAYESIAN SEQUENTIAL SINGLE-MACHINE SCHEDULING PROBLEM TO MINIMIZE THE EXPECTED WEIGHTED SUM OF FLOWTIMES OF JOBS WITH EXPONENTIAL PROCESSING TIMES

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