Scheduling Jobs with Stochastic Holding Costs

TL;DR

This paper develops learning-based scheduling algorithms for jobs with unknown stochastic holding costs, achieving near-optimal performance by balancing exploration and exploitation in a complex multi-class setting.

Contribution

It introduces a novel $c$ rule scheduling approach that learns job costs and switches from preemptive to nonpreemptive scheduling, with theoretical regret guarantees.

Findings

Algorithms achieve near-optimal regret bounds.

Numerical results confirm the effectiveness of the proposed methods.

Regret lower bounds match the upper bounds closely.

Abstract

We study a single-server scheduling problem for the objective of minimizing the expected cumulative holding cost incurred by jobs, where parameters defining stochastic job holding costs are unknown to the scheduler. We consider a general setting allowing for different job classes, where jobs of the same class have statistically identical holding costs and service times, with an arbitrary number of jobs across classes. In each time step, the server can process a job and observes random holding costs of the jobs that are yet to be completed. We consider a learning-based $c\mu$ rule scheduling which starts with a preemption period of fixed duration, serving as a learning phase, and having gathered data about jobs, it switches to nonpreemptive scheduling. Our algorithms are designed to handle instances with large and small gaps in mean job holding costs and achieve near-optimal performance guarantees. The performance of algorithms is evaluated by regret, where the benchmark is the minimum possible total holding cost attained by the $c\mu$ rule scheduling policy when the parameters of jobs are known. We show regret lower bounds and algorithms that achieve nearly matching regret upper bounds. Our numerical results demonstrate the efficacy of our algorithms and show that our regret analysis is nearly tight.