State‐of‐the‐art Survey: Open Queueing Networks: Optimization and Performance Evaluation Models for Discrete Manufacturing Systems

Abstract

In this survey we review methods to analyze open queueing network models for discrete manufacturing systems. We focus on design and planning models for job shops. The survey is divided in two parts: in the first we review exact and approximate decomposition methods for performance evaluation models for single and multiple product class networks. The second part reviews optimization models of three categories of problems: the first minimizes capital investment subject to attaining a performance measure (WIP or lead time), the second seeks to optimize the performance measure subject to resource constraints, and the third explores recent research developments in complexity reduction through shop redesign and products partitioning.

Performance evaluation and capacity planning in a metallurgical job-shop system using open queueing network models

“…Due to these characteristics, the network WIP (in-process inventory) and the production leadtimes (cycle times) tend to be high. More detailed descriptions of job-shop systems represented as queueing networks are found in, e.g., Askin and Standridge (1993), Buzacott and Shanthikumar (1993), Karmarkar (1993), Suri et al (1993), Gershwin (1994), Bitran and Morabito (1996), Chase et al (2005) and Ritzman and Krajewski (2006).…”

Interacting hospital departments and uncertain patient flows : theoretical models and applications

“…We only include formulations specific for the model of Subsection 5.3.1. See [17] for more details on the method.…”

“…From [17], it follows that the aggregate mean arrival rate can be determined from the following system of linear equations,…”

“…Jackson networks [83] and BCMP networks [12]) which require assumptions that are too limiting for our purposes. Approximate decomposition methods are reviewed in [17] and applied in a clinical setting by [211]. For this approximation, it is assumed that arrivals are independent and identically distributed (IID) and that the first and second moments of the arrival rate and service time distributions are known.…”

“…To analyze the queueing network we use the approximate decomposition [17] method for multi-class open queueing networks. Exact methods are only possible in a few situations (e.g.…”