Equitable Scheduling on a Single Machine

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 ≤ 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. * Supported by DFG Research Training Group 2434 "Facets of Complexity". † Supported by the EPSRC grant EP/P020372/1. ‡ Supported by the DFG, project MATE (NI 369/17). 1 For instance, in 2018, ACM started its new conference series on "Fairness, Accountability, and Transparency (FAT)".