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 θ_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.