Open AccessOptimal Control of a Time-Varying Double-Ended Production Queueing Model
Author(s) -
Chihoon Lee,
Xin Liu,
Yunan Liu,
Ling Zhang
Publication year - 2021
Publication title -
stochastic systems
Language(s) - English
Resource type - Journals
ISSN - 1946-5238
DOI - 10.1287/stsy.2019.0066
Subject(s) - queueing theory , asymptotically optimal algorithm , production (economics) , upper and lower bounds , abandonment (legal) , mathematical optimization , mathematics , optimal control , time horizon , computer science , economics , statistics , microeconomics , mathematical analysis , political science , law
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 nonstationary demand.