We study a make-to-stock manufacturing system in which a single server makes the production. The server consumes energy, and its power consumption depends on the server state: a busy server consumes more power than an idle server, and an idle server consumes more power than a turned-off server. When a server is turned on, it completes a costly set-up process that lasts a while. We jointly control the finished goods inventory and the server’s energy consumption. The objective is to minimize the long-run average inventory holding, backorder, and energy consumption costs by deciding when to produce, when to idle or turn off the server, and when to turn on a turned-off server. Because the exact analysis of the problem is challenging, we consider the asymptotic regime in which the server is in the conventional heavy-traffic regime. We formulate a Brownian control problem (BCP) with impulse and singular controls. In the BCP, the impulse control appears due to server shutdowns, and the singular control appears due to server idling. Depending on the system parameters, the optimal BCP solution is either a control-band or barrier policy. We propose a simple heuristic control policy from the optimal BCP solution that can easily be implemented in the original (non-asymptotic) system. Furthermore, we prove the asymptotic optimality of the proposed control policy in a Markovian setting. Finally, we show that our proposed policy performs close to optimal in numerical experiments.

中文翻译：

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按库存制造系统中的渐近最优能耗和库存控制


我们研究了一种按库存生产的制造系统，其中单个服务器进行生产。服务器消耗能源，其功耗取决于服务器状态：繁忙的服务器比空闲的服务器消耗更多的电量，空闲的服务器比关闭的服务器消耗更多的电量。当服务器打开时，它会完成一个持续一段时间、成本高昂的设置过程。我们共同控制成品库存和服务器的能耗。目标是通过决定何时生产、何时闲置或关闭服务器以及何时打开已关闭的服务器，最大限度地减少长期平均库存持有、缺货和能源消耗成本。由于对问题的精确分析具有挑战性，因此我们考虑服务器处于传统大流量状态的渐近状态。我们制定了具有脉冲和奇异控制的布朗控制问题（BCP）。在BCP中，由于服务器关闭而出现脉冲控制，由于服务器空闲而出现奇异控制。根据系统参数，最佳 BCP 解决方案是控制带策略或屏障策略。我们从最优 BCP 解决方案中提出了一种简单的启发式控制策略，可以在原始（非渐近）系统中轻松实现。此外，我们证明了所提出的控制策略在马尔可夫环境中的渐近最优性。最后，我们表明我们提出的策略在数值实验中表现接近最优。