Stochastic scheduling problem with varying weight for each job

Abstract

This paper studies the preemptive stochastic online scheduling problem, which is a simple combination of online and stochastic scheduling. The processing times of jobs are assumed to be subject to independent probability distributions, and we assume that jobs arrive overtime, which means there is no knowledge about the jobs that arrive in the future. We particularly consider the preemptive setting where a job is allowed to be interrupted during its processing. The weight (holding cost ratio) associated with each job may change during its processing, and the objective is to minimize the expected value of total holding cost for all jobs. For the single and m identical machine problems, we propose scheduling policies, SPGS [semi-preemptive Gittins Index Priority Policy (GIPP) on single machine] and SPGI (semi-preemptive GIPP on identical machines), respectively, both of which are proved to be constant-factor approximation. 

Scheduling of crude oil refinery operation with desalting as a separate task

“…Good planning and scheduling of crude oil operation is a crucial optimization tool to enhance the performance of a plant to sustain in the current dynamic and competitive era. [9][10][11][12] Such process scheduling operations are formulated mainly using discrete-time and continuous-time representations. [13][14][15][16][17][18] In the case of discrete-time representation, the scheduling time is divided into several time intervals with a known duration and allows events to occur only at the boundaries.…”

“…Good planning and scheduling of crude oil operation is a crucial optimization tool to enhance the performance of a plant to sustain in the current dynamic and competitive era 9–12 . Such process scheduling operations are formulated mainly using discrete‐time and continuous‐time representations 13–18 .…”