A Bayesian Sequential Single Machine Scheduling Problem to Minimize the Expected Weighted Sum of Flowtimes of Jobs with Exponential Processing Times

Operations Research · 1993 · Volume 41 · Issue 5

Abstract

In this paper, we consider a scheduling problem in which m classes, J 1 , J 2 , …, 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.

Keywords

dynamic programming/optimal control: Bayesian, dynamic allocation index, production/scheduling: sequencing, stochastic, single machine

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