TY - JOUR
T1 - Optimal Control of a Time-Varying Double-Ended Production Queueing Model
AU - Lee, Chihoon
AU - Liu, Xin
AU - Liu, Yunan
AU - Zhang, Ling
N1 - Publisher Copyright:
© 2021 The Author(s).
PY - 2021/6
Y1 - 2021/6
N2 - Motivated by production systems with nonstationary stochastic demand, we study a double-ended queueing model having back orders and customer abandonment. One side of our model stores back orders, and the other side represents inventory. We assume first-come-first-served instantaneous fulfillment 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 and perishment) and demand-related (waiting and 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 for which an upper bound of the gap between the optimal values of the QCP and FCP is characterized 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 non-stationary demand.
AB - Motivated by production systems with nonstationary stochastic demand, we study a double-ended queueing model having back orders and customer abandonment. One side of our model stores back orders, and the other side represents inventory. We assume first-come-first-served instantaneous fulfillment 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 and perishment) and demand-related (waiting and 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 for which an upper bound of the gap between the optimal values of the QCP and FCP is characterized 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 non-stationary demand.
KW - abandonment
KW - asymptotic optimality
KW - double-ended queue
KW - optimal control
KW - time-varying demand
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U2 - 10.1287/stsy.2019.0066
DO - 10.1287/stsy.2019.0066
M3 - Article
AN - SCOPUS:85128499255
VL - 11
SP - 140
EP - 173
JO - Stochastic Systems
JF - Stochastic Systems
IS - 2
ER -