Asymptotically Optimal Energy Consumption and Inventory Control in a Make-to-Stock Manufacturing System

We study energy consumption and inventory control in a make-to-stock manufacturing system. We consider a Markovian system with a single server. The server consumes energy, and the associated energy cost depends on the server state: a busy server consumes more power than an idle server does, and an idle server consumes more power than a turned-off server does. However, when a turned-off server is turned on, it must complete a set-up process which is costly and lasts for a while. The objective of the system controller 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. We consider the asymptotic regime in which the server is in the conventional heavy-traffic regime. We formulate a Brownian control problem (BCP) which is a mixed impulse-singular control problem. Depending on the system parameters, the optimal BCP solution is of either control-band or barrier type. From the optimal BCP solution, we propose a simple heuristic control policy and prove its asymptotic optimality. Finally, we demonstrate the close-to-optimal performance of the heuristic control policy by numerical experiments