zbMATH — the first resource for mathematics

Analysis of multistation production systems with limited buffer capacity. I: The subsystem model. (English) Zbl 0893.90080
Summary: We seek efficient techniques to evaluate the performance of multistation production systems with limited interstation buffers and station breakdown. Our ultimate objective is to develop a practical computer implementation that can be used for analysis and design. Practically implies two design considerations: flexibility and computational efficiency. The approach must be flexible enough to be applicable to production systems with various topologies and station characteristics. These include series arrangements of production systems, as well as network topologies and rework (feedback) systems. Similarly, the technique must be computationally expedient. Our approach is based on a framework to model single-buffer subsystems to be used within a decomposition technique to evaluate the performance of the entire system. The first part presents a quasi-birth-death process model for the subsystems. Exploiting the spectral characteristics of the associated matrix polynomial, we develop a novel solution procedure for the steady-state probabilities where the computational effort is independent of the buffer size. The solution procedure is applicable to quasi birth-death processes. The efficient solution procedure developed in this part is used as a building block in decomposing and analyzing multistation production systems with various topologies in the second part of the study.

90B30 Production models
90B22 Queues and service in operations research
Full Text: DOI
[1] Papadapoulos, H.T.; Heavy, C.; Browne, J., Queueing theory in manufacturing analysis and design, (1993), Chapman & Hall Cambridge
[2] Koenigsberg, E., Production lines and internal storage—A review, Management science, 5, 410-433, (1959)
[3] Gershwin, S.B.; Herman, O., Analysis of transfer lines consisting of two unreliable machines with random processing times and limited storage buffers, AIIE transactions, 13, 1, 2-11, (1981)
[4] Berman, O., Efficiency and production rate of a transfer line with two machines and finite storage buffer, European journal of operational reserach, 9, 295-308, (1982) · Zbl 0475.90035
[5] Okamura, K.; Yamashina, H., Analysis of effect of buffer storage capacity in transfer line systems, AIIE transactions, 9, 2, 127-135, (1977)
[6] Jafari, M.A.; Shanthikumar, J.G., Exact and approximate solutions to two-stage transfer lines with general uptime and downtime distributions, IIE transactions, 19, 4, 412-420, (1987)
[7] Rao, N.P., Two-stage production systems with intermediate storage, AIIE transactions, 7, 4, 414-421, (1975)
[8] Wijngaard, J., The effect of interstage buffer storage on the output of two unrealible production units in series with different production rates, AIIE transactions, 11, 1, 42-47, (1979)
[9] Yeralan, S.; Franck, W.E.; Quasem, M.A., A continuous materials flow production line model with station breakdown, European journal of operational research, 27, 289-300, (1986) · Zbl 0603.90063
[10] Shanthikumar, J.G.; Tien, C.C., An algorithmic solution to two-stage transfer lines with possible scrapping of units, Management science, 29, 9, 1069-1086, (1983) · Zbl 0522.90043
[11] Hajek, B., Birth and death process on the integers with phases and general boundaries, Journal of applied probability, 19, 3, 488-499, (1982) · Zbl 0502.60053
[12] Neuts, M.F., Matrix-geometric solutions in stochastic models: an algorithmic approach, (1981), Johns Hopkins Press Baltimore, MD · Zbl 0469.60002
[13] Buzacott, J.A.; Kostelski, D., Matrix-geometric and recursive algorithm solution of a two-stage unreliable flow line, IIE transactions, 19, 4, 429-438, (1987)
[14] Yeralan, S.; Muth, E.J., A general model of a production line with intermediate buffer and station breakdown, IIE transactions, 19, 2, 130-139, (1987)
[15] Hatcher, J.M., The effect of internal storage on the production rate of a series of stages having exponential service times, AIIE transactions, 1, 2, 150-156, (1969)
[16] Gershwin, S.B.; Schick, I.C., Modeling and analysis of three-stage transfer lines with unreliable machines and finite buffers, Operations reserach, 31, 2, 354-380, (1983) · Zbl 0507.90042
[17] Altiok, T.; Stidham, S., The allocation of interstate buffer capacities in production lines, IIE transactions, 15, 4, 292-299, (1983)
[18] Dallery, Y.; David, R.; Xie, X.L., An efficient algorithm for analysis of transfer lines with unreliable machines and finite buffers, IIE transactions, 20, 3, 280-283, (1988)
[19] Gershwin, S.B., An efficient decomposition method for the approximate evaluation of production lines with finite storage space and blocking, analysis and optimization of systems, (), Part 2
[20] Gershwin, S.B., An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking, Operations research, 35, 2, 291-305, (1987) · Zbl 0626.90027
[21] Jafari, M.A.; Shanthikumar, J.G., An approximate model of multistage automatic transfer lines with possible scrapping of work pieces, IIE transactions, 19, 3, 252-265, (1987)
[22] B. Tan and S. Yeralan, Analysis of multistation production systems with limited buffer capacity, Part 2—The decomposition method, Mathl. Comput. Modelling (to appear). · Zbl 0893.90081
[23] Lancaster, P.; Gohberg, I.; Rodman, L., Matrix polynomials, (1982), Academic Press New York
[24] Muller, D.E., A method for solving algebraic equations using an automatic computer, Mathematical tables and other aids to computation, 10, 208-215, (1956) · Zbl 0072.34002
[25] Tan, B., A decomposition method for multistation production systems, ()
[26] Buzacott, J.A.; Hanifin, L.E., Models of automic transfer lines with inventory banks, A review and comparison, AIIE transactions, 10, 2, 197-207, (1978)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.