Modeling and Exact Analysis of a Production Line with Two Unreliable Batch Machines and a Finite Buffer: Part I - Full Batches

This paper considers a production line with two unreliable batch machines and a finite buffer. Batch machines process a set of parts simultaneously; the maximum number in the set is the size of the machine. The purpose of this paper is twofold: (i) to present a model of this system and its exact analysis; (ii) to present new qualitative insights and interpretations of system behavior. We demonstrate new generalized conservation of flow and flow rate-idle time relationships. We also present various performance measures of interest such as production rate, machine efficiencies, probabilities of blocking and starvation, and expected in-process inventory. We demonstrate an equivalence property and describe deadlock behavior. The effect of the sizes of machines on the performance measures is examined, new phenomena and insights are established, and possible interpretations are presented.

[1]  Stanley B. Gershwin,et al.  A decomposition method for analyzing inhomogeneous assembly/disassembly systems , 2000, Ann. Oper. Res..

[2]  Stefan Helber,et al.  A New Decomposition Approach for Non-Cyclic Continuous Material Flow Lines with a Merging Flow of Material , 2004, Ann. Oper. Res..

[3]  John A. Buzacott,et al.  Operations and Shipment Scheduling of a Batch on a Felxible Machine , 2003, Oper. Res..

[4]  Lawrence M. Wein,et al.  A Product Design Problem in Semiconductor Manufacturing , 1992, Oper. Res..

[5]  Stanley B. Gershwin,et al.  Modeling and Analysis of Three-Stage Transfer Lines with Unreliable Machines and Finite Buffers , 1983, Oper. Res..

[6]  Andrea Matta,et al.  Performance evaluation of continuous production lines with machines having different processing times and multiple failure modes , 2003, Perform. Evaluation.

[7]  E. Muth.  The Reversibility Property of Production Lines , 1979 .

[8]  Reza H. Ahmadi,et al.  Batching and Scheduling Jobs on Batch and Discrete Processors , 1992, Oper. Res..

[9]  Jewgeni H. Dshalalow,et al.  Queueing systems with state dependent parameters , 1998 .

[10]  Tayfur Altiok,et al.  Performance analysis of manufacturing systems , 1996 .

[11]  Andrea Matta,et al.  Analysis of two-machine lines with multiple failure modes , 2002 .

[12]  Hong Chen,et al.  Empirical Evaluation of a Queueing Network Model for Semiconductor Wafer Fabrication , 1988, Oper. Res..

[13]  Stanley B. Gershwin,et al.  An Efficient Decomposition Method for the Approximate Evaluation of Tandem Queues with Finite Storage Space and Blocking , 1987, Oper. Res..

[14]  G. Strang.  Introduction to Linear Algebra , 1993 .

[15]  Stanley B. Gershwin,et al.  Hewlett-Packard Uses Operations Research to Improve the Design of a Printer Production Line , 1998, Interfaces.

[16]  Gabriel R. Bitran,et al.  Approximations for Product Departures from a Single-Server Station with Batch Processing in Multi-Product Queues , 1989 .

[17]  Lawrence M. Wein,et al.  Optimal Control of a Two-Station Tandem Production/Inventory System , 1994, Oper. Res..

[18]  Ben Atkinson,et al.  Queueing theory in manufacturing systems analysis and design , 1993 .

[19]  Warren B. Powell,et al.  The Bulk Service Queue with a General Control Strategy: Theoretical Analysis and a New Computational Procedure , 1986, Oper. Res..

[20]  Stanley B. Gershwin,et al.  Modeling and analysis of production lines with and without preventative maintenance , 1983 .

[21]  Yves Dallery,et al.  On modeling failure and repair times in stochastic models of manufacturing systems using generalized exponential distributions , 1994, Queueing Syst. Theory Appl..

[22]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[23]  Yves Dallery,et al.  An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers , 1988 .

[24]  Chris N. Potts,et al.  Supply chain scheduling: Batching and delivery , 2003, Oper. Res..

[25]  P. J. Egbelu.  Unit load design and its impact on manufacturing systems performance , 1994 .

[26]  Tetsuya Takine,et al.  Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations , 2005, Queueing Syst. Theory Appl..

[27]  J. Diebold.  Automation , 1955, Industry, Innovation and Infrastructure.

[28]  G. F. Newell.  Approximate Behavior of Tandem Queues , 1979 .

[29]  Oded Berman,et al.  Efficiency and production rate of a transfer line with two machines and a finite storage buffer , 1982 .

[30]  George D. Mostow.  Fundamental structures of Algebra , 1963 .

[31]  Yves Dallery,et al.  Manufacturing flow line systems: a review of models and analytical results , 1992, Queueing Syst. Theory Appl..

[32]  Gérard P. Cachon.  Exact Evaluation of Batch-Ordering Inventory Policies in Two-Echelon Supply Chains with Periodic Review , 2001, Oper. Res..

[33]  Vassilis S. Kouikoglou.  Sensitivity analysis and decomposition of unreliable production lines with blocking , 2000, Ann. Oper. Res..

[34]  C. R. Glassey,et al.  Dynamic batching heuristic for simultaneous processing , 1991 .

[35]  R. Serfozo,et al.  Optimal control of batch service queues , 1973, Advances in Applied Probability.

[36]  Vincent Hodgson,et al.  The Single Server Queue. , 1972 .

[37]  Stanley B. Gershwin,et al.  Assembly/Disassembly Systems: An Efficient Decomposition Algorithm for Tree-Structured Networks , 1991 .

[38]  Xiaolan Xie,et al.  Approximate analysis of transfer lines with unreliable machines and finite buffers , 1989 .

[39]  Stanley B. Gershwin.  Design and operation of manufacturing systems: the control-point policy , 2000 .

[40]  Peter J. Kolesar,et al.  Operating Characteristics of a Simple Shuttle under Local Dispatching Rules , 1972, Oper. Res..

[41]  D. Simchi-Levi,et al.  Uniform distribution of inventory positions in two-echelon periodic review systems with batch-ordering policies and interdependent demands , 2002, Eur. J. Oper. Res..

[42]  David D. Yao,et al.  A queueing network model for semiconductor manufacturing , 1996 .

[43]  Alain Patchong,et al.  Special Issue: 2002 Franz Edelman Award for Achievement in Operations Research and the Management Sciences: Improving Car Body Production at PSA Peugeot Citroën , 2003, Interfaces.

[44]  Shang Zhi,et al.  A proof of the queueing formula: L=λW , 2001 .