Abstract
In this paper we show some structural results of a kanban system by using results about the underlying GSMP. The main results from this connection are: dominance of allocations, optimal partition, upper and lower bounds on throughput, consistency of the IPA derivative, convexity of throughput as a function of service time parameters and concavity of throughput with respect to number of kanbans. Although the dominance and the partition results were obtained previously by sample path arguments, the proofs here are less cumbersome and generalize the earlier results. The second-order properties for kanban lines are new. These results form a basis for results in multi-product lines where proofs by sample paths require extensive notation.
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References
V. Ananthram and P. Tsoucas, Concavity of throughput in tandem queues, Working Paper, University of Maryland (1989).
D.W. Cheng and D.D. Yao, Tandem queues with general blocking: A unified model and comparison results, Working Paper (January 1991).
J.-L. Deleersnyder, Th.J. Hodgson, H. Muller and P. O'Grady, Pull systems: An analytic approach, Manag. Sci. 35 (1989) 1079–1091.
P. Glasserman, Structural conditions for perturbation analysis derivation estimation: Finite time performance indices, Oper. Res. 39 (1991) 724–738.
P. Glasserman, J. Hu and S.G. Strickland, Strongly consistent steady-state derivative estimates, Prob. Eng. Inf. Sci. 5 (1991) 391–413.
P. Glasserman and D.D. Yao, Monotonicity in generalized semi-Markov processes, Working Paper, Columbia University (October 1989).
P. Glasserman and D.D. Yao, GSMP: Antimatroidal structure and second order properties, Working Paper, Columbia University (January 1990).
P. Glasserman and D.D. Yao, Structured buffer-allocation problems in production lines, Working Paper, Columbia University (May 1991).
W.J. Gordon and G.F. Newell, Closed queueing networks with exponential servers, Oper. Res. 15 (1967) 252–267.
U.S. Karmarkar and S. Kekre, Batching policies in kanban systems, J. Manuf. Sys. 8 (1990) 317–328.
L.E. Meester and J.G. Shanthikumar, Concavity of the throughput of tandem queueing systems with finite buffer storage space, Adv. Appl. Prob. 22 (1990) 764–767.
D. Mitra and I. Mitrani, Analysis of a kanban discipline for cell coordination in production lines, Manag. Sci. 36 (199) 1548–1566.
J.A. Muckstadt and S. Tayur, A comparison of alternative kanban control mechanisms, Technical Report No. 962, Cornell University (April 1991).
D. Stoyan,Comparison Methods for Queues and Other Stochastic Models (Wiley, 1983).
S. Tayur, Analysis of a kanban controlled serial manufacturing system, Ph.D Thesis, Cornell University (August 1990).
S. Tayur, Structural properties and a heuristic for kanban controlled serial lines, SORIE Technical Report no. 934, Cornell University (August 1991).
S. Tayur, Controlling serial production lines with yield losses using kanbans, Technical Report No. 947, Cornell University (December 1990).
S. Tayur, Analysis of a multi-product kanban controlled system, Working Paper, Carnegie Mellon University (December 1991).
D.L. Woodruff, M.L. Spearman and W.J. Hopp, CONWIP: A pull alternative to kanban, Int. J. Prod. Res. 28 (1990) 879–894.
P. Zipkin, A kanban-like production controlled system: Analysis of simple models, Working paper 89-1, Columbia University (1989).
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Tayur, S.R. Properties of serial kanban systems. Queueing Syst 12, 297–318 (1992). https://doi.org/10.1007/BF01158805
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DOI: https://doi.org/10.1007/BF01158805