Discrete time model for two-machine one-buffer transfer lines with restart policy

The paper deals with analytical modeling of transfer lines consisting of two machines decoupled by one finite buffer. In particular, the case in which a control policy (referred as “restart policy”) aiming to reduce the blocking frequency of the first machine is addressed. Such a policy consists of forcing the first machine to remain idle (it cannot process parts) each time the buffer gets full until it empties again. This specific behavior can be found in a number of industrial production systems, especially when some machines are affected by outage costs when stops occur. The two-machine one-buffer line is here modeled as a discrete time Markov process and the two machines are characterized by the same operation time. The analytical solution of the model is obtained and mathematical expressions of the most important performance measures are provided. Some significant remarks about the effect of the proposed restart policy on the behavior of the system are also pointed out.

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

[2]  M.B.M. deKoster.  Estimation of Line Efficiency by Aggregation , 1987 .

[3]  H. T. Papadopoulos,et al.  The throughput rate of multistation reliable production lines , 1993 .

[4]  D Hemenway.  The decomposition method. , 1998, Epidemiology.

[5]  H. T. Papadopoulos,et al.  Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines , 1996 .

[6]  Tayfur Altiok,et al.  The Allocation of Interstage Buffer Capacities in Production Lines , 1983 .

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

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

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

[10]  Barış Tan,et al.  Analysis of multistation production systems with limited buffer capacity part 1: The subsystem model , 1997 .

[11]  C..  The throughput rate of multistation unreliable production lines , 2003 .

[12]  Stanley B. Gershwin,et al.  Integrated quality and quantity modeling of a production line , 2005, OR Spectr..

[13]  Stanley B. Gershwin,et al.  A decomposition method for the approximate evaluation of capacitated transfer lines with unreliable machines and random processing times , 1987 .

[14]  B. Atkinson.  Queuing Theory in Manufacturing Systems Analysis and Design , 1995 .

[15]  Semyon M. Meerkov,et al.  Lean buffering in serial production lines with non-exponential machines , 2005, OR Spectr..

[16]  J. A. Buzacott,et al.  AUTOMATIC TRANSFER LINES WITH BUFFER STOCKS , 1967 .

[17]  Barış Tan,et al.  Analysis of multistation production systems with limited buffer capacity part 2: The decomposition method , 1997 .

[18]  Semyon M. Meerkov,et al.  DT-bottlenecks in serial production lines: theory and application , 2000, IEEE Trans. Robotics Autom..

[19]  B. Zimmern,et al.  Études de la propagation des arrêts aléatoires dans les chaînes de production , 1956 .

[20]  Semyon M. Meerkov,et al.  c-Bottlenecks in serial production lines: Identification andapplication , 2001 .

[21]  Yushin Hong,et al.  The analysis of an unreliable two-machine production line with random processing times , 1993 .

[22]  H. T. Papadopoulos,et al.  Minimizing WIP inventory in reliable production lines , 2001 .

[23]  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..

[24]  Semyon M. Meerkov,et al.  Lean Buffering in Serial Production Lines With Nonidentical Exponential Machines , 2008, IEEE Transactions on Automation Science and Engineering.

[25]  Stanley B. Gershwin,et al.  An approximate analytical method for evaluating the performance of closed-loop flow systems with unreliable machines and finite buffers , 2007 .

[26]  H. T. Papadopoulos,et al.  A heuristic algorithm for the buffer allocation in unreliable unbalanced production lines , 2001 .

[27]  Michael Manitz,et al.  Queueing-model based analysis of assembly lines with finite buffers and general service times , 2008, Comput. Oper. Res..

[28]  Mitchell H. Burman,et al.  New results in flow line analysis , 1995 .

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

[30]  J. A. Buzacott,et al.  Models of automatic transfer lines with inventory banks a review and comparison , 1978 .

[31]  J. Buzacott,et al.  'Optimal' operating rules for automated manufacturing systems , 1982, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[32]  Diomidis Spinellis,et al.  A simulated annealing approach for buffer allocation in reliable production lines , 2000, Ann. Oper. Res..

[33]  Oded Berman,et al.  Analysis of transfer lines consisting of two unreliable machines with random processing times and finite storage buffers , 1981 .

[34]  Minghe Sun,et al.  Determining buffer location and size in production lines using tabu search , 1998, Eur. J. Oper. Res..

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

[36]  Stanley B. Gershwin,et al.  Efficient algorithms for buffer space allocation , 2000, Ann. Oper. Res..

[37]  Akif Asil Bulgak,et al.  Buffer size optimization in asynchronous assembly systems using genetic algorithms , 1995 .

[38]  John A. Buzacott,et al.  The Effect of Station Breakdowns and Random Processing Times on the Capacity of Flow Lines with In-Process Storage , 1972 .

[39]  H. T. Papadopoulos,et al.  Optimal buffer storage allocation in balanced reliable production lines , 1998 .

[40]  Stanley B. Gershwin,et al.  Manufacturing Systems Engineering , 1993 .

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

[42]  Semyon M. Meerkov,et al.  c-bottlenecks in serial production lines: identification and application , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[43]  George Adomian.  The Decomposition Method , 1989 .

[44]  H. T. Papadopoulos,et al.  Optimal buffer allocation in short m -balanced unreliable production lines , 1999 .

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