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Branch and Bound Algorithm for Ordering of Tandem Constant-Service Stations

Published online by Cambridge University Press:  27 July 2009

Janice Kim Winch
Janice Kim Winch
Affiliation:
Pace University, Lubin School of Business, One Pace Plaza, New York, New York 10038
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Abstract

We study tandem ordering of constant-service stations with unlimited buffers and arbitrary arrival process where service at each station adds a certain value to the job. The goal is to order the stations such that the total expected value of the jobs in the system or, equivalently, the work-in-process inventory cost is minimized. Assuming that the added value–service length ratio increases with the service length, we provide a branch and bound method that finds an optimal order.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 11 , Issue 4 , October 1997 , pp. 413 - 439
Copyright
Copyright © Cambridge University Press 1997

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References

1.Avi-Itzhak, B. (1965). A sequence of service stations with arbitrary input and regular service times. Management Science 11: 565–571.CrossRefGoogle Scholar
2.Chao, X., Pinedo, M., & Sigman, K. (1989). On the interchangeability and stochastic ordering of exponential queues in tandem with blocking. Probability in the Engineering and Informational Sciences 3: 223–236.CrossRefGoogle Scholar
3.Ding, J. & Greenberg, B.S. (1991). Optimal order for servers in series with no queue capacity. Probability in the Engineering and Informational Sciences 5: 449–461.CrossRefGoogle Scholar
4.Friedman, H.D. (1965). Reduction methods for tandem queuing systems. Operations Research 13: 121–131.CrossRefGoogle Scholar
5.Greenberg, B.S. & Wolff, R.W. (1988). Optimal order of servers for tandem queues in light traffic. Management Science 34: 500–508.CrossRefGoogle Scholar
6.Huang, C.C. & Weiss, G. (1990). On the optimal order of M machines in tandem. Operations Research Letters 9: 299–303.CrossRefGoogle Scholar
7.Pinedo, M. (1982). On the optimal order of stations in tandem queues. In Disney, R.L. & Ott, T.J. (eds.), Applied probability–Computer science: The interface, Vol. II. Boston: Birkhauser, pp. 307–325.CrossRefGoogle Scholar
8.Rosenblatt, M.J. & Lee, H.L. (1996). The effects of work-in-process inventory costs on the design and scheduling of assembly lines with low throughput and high component costs. HE Transactions 28: 405–414.Google Scholar
9.Suresh, S. & Whitt, W. (1990). Arranging queues in series: A simulation experiment. Management Science 36: 1080–1091.CrossRefGoogle Scholar
10.Tembe, S.V. & Wolff, R.W. (1972). The optimal order of service in tandem queues. Operations Research 22: 824–832.CrossRefGoogle Scholar
11.Weber, R.R. (1979). The interchangeability of tandeom −/M/l queues in series. Journal of Applied Probability 16: 690–695.CrossRefGoogle Scholar
12.Weber, R.R. (1992). The interchangeability of tandem queues with heterogeneous customers and dependent service times. Advances in Applied Probability 23: 727–737.CrossRefGoogle Scholar
13.Weber, R.R. & Weiss, G. (1994). The cafeteria process—Tandem queues with 0–1 dependent service times and the bowl shape phenomenon. Operations Research 42: 895–912.CrossRefGoogle Scholar
14.Whitt, W. (1985). The best order for queues in series. Management Science 31: 475–487.CrossRefGoogle Scholar
15.Winch, J.K. & Avi-Itzhak, B. (1995). Ordering of tandem constant-service stations to minimize in-process stock cost. Probability in the Engineering and Informational Sciences 9: 457–473.CrossRefGoogle Scholar
16.Yamazaki, G., Sakasegawa, H., & Shanthikumar, J.G. (1992). On optimal arrangement of stations in a tandem queueing system with blocking. Management Science 38: 137–153.CrossRefGoogle Scholar