Optimal Control of a Time-Varying Double-Ended Production Queueing Model

Motivated by production systems with nonstationary stochastic demand, we study a double-ended queueing model having backorders and customer abandonment. One side of our model stores backorders, and the other side represents inventory. We assume first-come- first-serve instantaneous ful fillment discipline. Our goal is to determine the optimal (nonstationary) production rate over a finite time horizon to minimize the costs incurred by the system. In addition to the inventory-related (holding, perishment) and demand-related (waiting, abandonment) costs, we consider a cost that penalizes rapid fluctuations of production rates. We develop a deterministic fluid control problem (FCP) that serves as a performance lower bound for the original queueing control problem (QCP). We further consider a high-volume system and construct an asymptotically optimal production rate for the QCP, under which the FCP lower bound is achieved asymptotically. Demonstrated by numerical examples, the proposed asymptotically optimal production rate successfully captures the time variability of the nonstationary demand.