发表机构
The University of British Columbia; Lyft, Inc.; Amazon.com, Inc.（不列颠哥伦比亚大学; Lyft公司; 亚马逊公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究带电池充电约束的作业调度问题，提出部分与完全充电模型下的多项式算法及近似算法，覆盖32种变体，并通过实验验证性能。
AI 中文摘要
电池供电设备（例如从仓库出发工作的投递无人机）必须在作业之间停下来充电，而充电所花费的时间会延迟其后所有作业。固定充电时长的调度模型无法描述这种设备：当它获取更多能量时，充电时间会更长。我们研究一台执行一批已知执行时间、能量需求和可选截止期限的不可抢占作业的设备。在“部分充电”下，设备可在作业之间获取任意数量的能量；在“完全充电”下，每次充电都将电池充满。四种目标函数和四种执行时间与能量需求之间的关系产生32种变体。当获取q单位能量需要q时间单位时，我们证明16种部分充电变体中有14种是多项式可解的，并针对平均完成时间（两个NP难变体之一）给出紧的2近似算法。在完全充电下，能量需求相等的四种变体是多项式可解的，其余12种是NP难的；针对制造跨度，我们给出5/4近似算法。当每次充电还产生固定的“设置时间”h时，能量相等的变体仍为多项式可解，而若h是输入的一部分，其余24种变体为强NP难。针对这些变体，我们给出仅在作业数量上呈指数级的精确算法，以及针对制造跨度和（当电池初始为空时）加权平均完成时间的近似算法。在合成和基于轨迹的作业集上的实验将算法与精确最优解进行比较。该模型是离线和确定性的，我们未在硬件上验证调度方案。
英文摘要
A battery-powered device, such as a delivery drone that works from a depot, must stop to recharge between jobs, and the time spent recharging delays every job that follows. Scheduling models that fix the duration of a recharge do not describe a device whose recharge takes longer when it acquires more energy. We study a single device that executes a batch of non-preemptive jobs with known execution times, energy demands, and optional deadlines. Under \emph{partial recharging} the device may acquire any amount of energy between jobs; under \emph{complete recharging} every recharge fills the battery. Four objectives and four relationships between execution time and energy demand give 32 variants. When acquiring $q$ units of energy takes $q$ time units, we show that 14 of the 16 partial-recharging variants are polynomial, and we give a tight 2-approximation for the average completion time, one of the two NP-hard variants. Under complete recharging, the four variants with equal energy demands are polynomial and the other 12 are NP-hard; for makespan we give a $5/4$-approximation. When each recharge also incurs a fixed \emph{setup time} $h$, the equal-energy variants remain polynomial and the other 24 are strongly NP-hard if $h$ is part of the input. For these we give exact algorithms that are exponential only in the number of jobs, and approximation algorithms for makespan and, when the battery starts empty, for the weighted average completion time. Experiments on synthetic and trace-derived job sets compare the algorithms with exact optima. The model is offline and deterministic, and we have not validated the schedules on hardware.
