A problem of scheduling $n$ unit-time jobs with a small number of distinct release dates and deadlines, on identical parallel machines, to minimize the number of active machines is studied. The feature that makes this problem challenging is that no machine can stand idle between its start and completion times. A number of properties of this problem is established, and heuristic and optimal algorithms based on these properties are designed. They include optimal algorithms with running times $O\left(k{n}^k\right)$ and $O\left(k{n}^2{3}^n\right)$ for the general case, where $k$ is the number of distinct release dates and deadlines, optimal $O(nlogn)$ algorithms for the cases of a common release date or a common deadline, and an optimal $O\left(k{n}^2\right)$ algorithm for the case of agreeable release dates and deadlines. Algorithms to find lower and upper bounds on the optimal (minimal) number of active machines are developed, and an integer linear programming (ILP) formulation with $O\left(k\right)$ variables and $O\left(k^2\right)$ constraints is provided. Computer experiments demonstrated that the ILP problem is solved by CPLEX to optimality within a few hours for $n\le 400$ and $k\le 50$, and that the quality of the lower and upper bounds is sufficiently good.

调度问题 $ñ$研究了在相同的并行计算机上具有少量不同发布日期和截止日期的单位时间工作，以最大程度地减少活动计算机的数量。使该问题具有挑战性的功能是，没有任何机器可以在其启动和完成时间之间处于空闲状态。建立了此问题的许多属性，并设计了基于这些属性的启发式和最佳算法。它们包括具有运行时间的最佳算法$Ø（ķ{ñ}^{ķ}）$ 和 $Ø（ķ{ñ}^{\mathrm{2个}}{3}^{ñ}）$ 对于一般情况， $ķ$ 最佳发布日期和截止日期的数量 $Ø（ñ日志ñ）$ 共同发布日期或共同截止日期以及最佳情况的算法 $Ø（ķ{ñ}^{\mathrm{2个}}）$合理的发布日期和截止日期的算法。开发了用于找到最佳（最小）运行机器数上限和下限的算法，并给出了具有以下特征的整数线性规划（ILP）公式：$Ø（ķ）$ 变量和 $Ø（{ķ}^{\mathrm{2个}}）$提供了约束。计算机实验表明，CPLEX可以在几小时内将ILP问题解决到最佳状态。$ñ\le 400$ 和 $ķ\le 50$，并且上下限的质量足够好。