Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-05T23:29:12.324Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  27 July 2009

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

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
Copyright
Copyright © Cambridge University Press 1997

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Avi-Itzhak, B. (1965). A sequence of service stations with arbitrary input and regular service times. Management Science 11: 565571.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: 223236.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: 449461.CrossRefGoogle Scholar
4.Friedman, H.D. (1965). Reduction methods for tandem queuing systems. Operations Research 13: 121131.CrossRefGoogle Scholar
5.Greenberg, B.S. & Wolff, R.W. (1988). Optimal order of servers for tandem queues in light traffic. Management Science 34: 500508.CrossRefGoogle Scholar
6.Huang, C.C. & Weiss, G. (1990). On the optimal order of M machines in tandem. Operations Research Letters 9: 299303.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. 307325.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: 405414.Google Scholar
9.Suresh, S. & Whitt, W. (1990). Arranging queues in series: A simulation experiment. Management Science 36: 10801091.CrossRefGoogle Scholar
10.Tembe, S.V. & Wolff, R.W. (1972). The optimal order of service in tandem queues. Operations Research 22: 824832.CrossRefGoogle Scholar
11.Weber, R.R. (1979). The interchangeability of tandeom −/M/l queues in series. Journal of Applied Probability 16: 690695.CrossRefGoogle Scholar
12.Weber, R.R. (1992). The interchangeability of tandem queues with heterogeneous customers and dependent service times. Advances in Applied Probability 23: 727737.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: 895912.CrossRefGoogle Scholar
14.Whitt, W. (1985). The best order for queues in series. Management Science 31: 475487.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: 457473.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: 137153.CrossRefGoogle Scholar