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

39 Pages Posted: 6 May 2019

See all articles by Chihoon Lee

Chihoon Lee

Stevens Institute of Technology

Xin Liu

Clemson University

Yunan Liu

North Carolina State University - Department of Industrial Engineering

Ling Zhang

North Carolina State University - Department of Industrial Engineering

Date Written: April 6, 2019

Abstract

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.

Suggested Citation

Lee, Chihoon and Liu, Xin and Liu, Yunan and Zhang, Ling, Optimal Control of a Time-Varying Double-Ended Production Queueing Model (April 6, 2019). Available at SSRN: https://ssrn.com/abstract=3367263 or http://dx.doi.org/10.2139/ssrn.3367263

Chihoon Lee

Stevens Institute of Technology ( email )

Hoboken, NJ 07030
United States

Xin Liu

Clemson University ( email )

101 Sikes Ave
Clemson, SC 29634
United States

Yunan Liu

North Carolina State University - Department of Industrial Engineering ( email )

Raleigh, NC 26695-7906
United States

Ling Zhang (Contact Author)

North Carolina State University - Department of Industrial Engineering ( email )

Raleigh, NC 26695-7906
United States

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