Abstract
We consider a decentralized, pull-type manufacturing system with each stage having its own input and output stock keeping activities. Material handling between stages is carried out according to a fixed quantity, non-constant withdrawal cycle. We approximate the system behavior using a two-node decomposition approach, which decomposes the system into smaller subsystems. The analysis of two-node subsystems is achieved using a matrix-recursive approach due to phase-type modeling of certain random variables. Our solution algorithm resolved a major difficulty (due to batch transfers) in the analytical approach to study multi-stage manufacturing systems. We also discuss system behavior and suggest several rules-of-thumb to improve system performance.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abdou, G. and S.P. Dutta. (1993). “A Systematic Simulation Approach for the Design of JIT Manufacturing Systems.” Journal of Operations Management 11, 225–238.
Albino, V., M. Dassisti, and G. Okogbaa. (1995). “Approximation Approach for the Performance Analysis of Production Lines under a Kanban Discipline.” International Journal of Production Research 40, 197–207.
Altiok, T. (1985). “On the Phase-Type Approximations of General Distributions.” IIE Transactions 17, 110–116.
Altiok, T. and R. Ranjan. (1995). “Multi-Stage, Pull-Type Production/Inventory Systems.” IIE Transactions 27, 190–200.
Altiok, T. (1997). Performance Analysis of Manufacturing Systems. New York: Springer.
Berkley, B.J. (1991). “Tandem Queues and Kanban-Controlled Lines.” International Journal of Production Research 29, 2057–2081.
Berkley, B.J. (1992). “A Review of the Kanban Production Control Research Literature.” Production and Operations Management 1, 393–411.
Berkley, B.J. (1993). “Setting Minimum Performance Levels for Two-Card Kanban-Controlled Lines.” International Journal of Production Research 31, 1003–1021.
Berkley, B.J. (1996). “A Simulation Study of Container Size in Two-Card Kanban Systems.” International Journal of Production Research 34, 3417–3445.
Bonvik, A.M., C.E. Couch, and S.B. Gershwin. (1997). “A Comparison of Production-Line Control Mechanisms.” International Journal of Production Research 5, 183–200.
Buzacott, J.A. and D. Kostelski. (1987). “Matrix-Geometric and Recursive Algorithm Solution of a Two-Stage Unreliable Flow Line.” IIE Transactions 19, 429–438.
Dallery, Y. and G. Liberopoulos. (2000). “Extended Kanban Control System: Combining Kanban and Base Stock.” IIE Transactions 32, 369–386.
Di Mascolo, Y. Frein, and Y. Dallery. (1996). “An Analytical Method for Performance Evaluation of Kanban Controlled Production Systems.” Operations Research 44, 50–64.
Gurgur, C.Z. and T. Altiok. (2002a). “An Analytical Method for Performance Evaluation of Decentralized, Multi-Stage, Multi-Product Production/Inventory Systems.” Working Paper, Department of Industrial and Systems Engineering, Rutgers University.
Gurgur, C.Z. and T. Altiok. (2002b). “Optimal Configuration of Production and Procurement Policies in Decentralized, Multi-Stage, Multi-Product, Pull-Type Production/Inventory Systems.” Working Paper, Department of Industrial and Systems Engineering, Rutgers University.
Herzog, U., L. Woo, and K.M. Chandy. (1975). “Solution of Queuing Problems by Recursive Technique.” IBM J. Res. Dev. 19, 295–300.
Karaesmen, F. and Y. Dallery. (2000). “A Performance Comparison for Pull-Type Control Mechanisms for Multi-Stage Manufacturing.” International Journal of Production Economics 68, 59–71.
Karmakar, U.S. and S. Kekre. (1989). “Batching Policy in Kanban Systems.” Journal of Manufacturing Systems 8, 317–328.
Mitra, D. and I. Mitrani. (1990). “Analysis of a Kanban Discipline for Cell Coordination in Production Lines I.” Management Science 36, 1548–1566.
Monden,Y. (1983). Toyota Production System. Atlanta, GA: Industrial Engineering and Management Press.
Neuts, M.F. (1981). Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Baltimore, MD: John Hopkins University Press.
Onvural, R.O., H.G. Perros, and T. Altiok. (1987). “On the Complexity of the Matrix-Geometric Solution of Exponential Open Queuing Networks with Blocking.” In G. Pujolle, S. Fdida, and A. Horlait (eds.), Proc. Intl. Workshop on Modeling Techniques and Performance Evaluation, pp. 3-12.
Savsar, M. (1996). “Effects of Kanban Withdrawal Policies and other Factors on the Performance of JIT Systems-A Simulation Study.” International Journal of Production Research 34, 2879–2899.
So, K.C. and S.C. Pinault. (1988). “Allocating Buffer Storage in a Pull System.” International Journal of Production Research 26, 1959–1980.
Stewart,W.J. (1978). “Comparison of Numerical Techniques in Markov Modeling.” Communications of the ACM 21, 144–152.
White, R.E., J.N. Pearson, and J.R. Wilson. (1999). “JIT Manufacturing: A Survey of Implementations in Small and Large U.S. Manufacturers.” Management Science 45, 1–15.
Womack, J.P., D.T. Jones, and D. Roos. (1991). The Machine that Changed the World: The Story of Lean Production. New York: Harper Perennial.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gurgur, C.Z., Altiok, T. Approximate Analysis of Decentralized, Multi-Stage, Pull-Type Production/Inventory Systems. Annals of Operations Research 125, 95–116 (2004). https://doi.org/10.1023/B:ANOR.0000011187.52502.37
Issue Date:
DOI: https://doi.org/10.1023/B:ANOR.0000011187.52502.37