We introduce a natural but seemingly yet unstudied variant of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. The novelty of our new variant 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.

我们介绍了在单台机器上调度作业问题的一个自然但看似尚未研究的变体，以最大限度地减少迟到作业的数量。我们的新变体的新颖之处在于同时考虑问题的几个实例。特别是，我们在m天的时间内有n 个客户，每个客户每天都有自己的处理时间和截止日期。我们的目标是为m天中的每一天提供一个时间表，以保证每个客户的工作至少在\(k \le m\)天内完成。这对应于一个公平的时间表，其中每个客户在整个m期间都得到最低限度的服务水平保证。天。我们对该问题的三个主要变体的计算复杂性进行了全面分析，确定了有效算法和最坏情况下的难处理性结果。