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

Chihoon Lee, Xin Liu, Yunan Liu, Ling Zhang

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

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.

Original languageEnglish
Pages (from-to)140-173
Number of pages34
JournalStochastic Systems
Volume11
Issue number2
DOIs
StatePublished - Jun 2021

Keywords

  • abandonment
  • asymptotic optimality
  • double-ended queue
  • optimal control
  • time-varying demand

Fingerprint

Dive into the research topics of 'Optimal Control of a Time-Varying Double-Ended Production Queueing Model'. Together they form a unique fingerprint.

Cite this