Equitable Scheduling on a Single Machine

TL;DR

This paper studies an equitable scheduling problem on a single machine, where multiple clients' jobs must meet deadlines over several days, analyzing complexity and providing algorithms for different variants.

Contribution

It introduces a novel multi-instance scheduling problem emphasizing fairness, and analyzes its computational complexity, offering efficient algorithms and intractability results.

Findings

Identified polynomial algorithms for certain problem variants.

Proved NP-hardness for other variants.

Provided complexity classifications for equitable scheduling.

Abstract

We introduce a natural but seemingly yet unstudied generalization of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. Our generalization lies in simultaneously considering several instances of the problem at once. In particular, we have $n$ clients over a period of $m$ days, where each client has a single job with its own processing time and deadline per day. Our goal is to provide a schedule for each of the $m$ days, so that each client is guaranteed to have their job meet its deadline in at least $k \le m$ days. This corresponds to an equitable schedule where each client is guaranteed a minimal level of service throughout the period of $m$ days. We provide a thorough analysis of the computational complexity of three main variants of this problem, identifying both efficient algorithms and worst-case intractability results.