An efficient method to determine the optimal configuration of a flexible manufacturing system. (English) Zbl 0708.90037

Summary: A frequently encountered design issue for a flexible manufacturing system (FMS) is to find the lowest cost configuration, i.e. the number of resources of each type (machines, pallets,...), which achieves a given production rate. In this paper, an efficient method to determine this optimal configuration is presented. The FMS is modelled as a closed queueing network. The proposed procedure first derives a heuristic solution and then the optimal solution. The computational complexity for finding the optimal solution is very reasonable even for large systems, except in some extreme cases. Moreover, the heuristic solution can always be determined and is very close (and often equal) to the optimal solution. A comparison with a previous method of B. Vinod and J. Solberg [Int. J. Prod. Res. 23, 1141-1151 (1985; Zbl 0591.90046)] shows that our method performs very well.


90B30 Production models
90C90 Applications of mathematical programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
90B10 Deterministic network models in operations research
90C60 Abstract computational complexity for mathematical programming problems
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)


Zbl 0591.90046
Full Text: DOI


[1] J.A. Buzacott and D.D. Yao, Flexible manufacturing systems: A review of analytical models, Manage. Sci. 32(1986). · Zbl 0649.90061
[2] Y. Dallery, On queueing network models of flexible manufacturing systems, Large-Scale Systems 11(1986)109.
[3] J.J. Solberg, A mathematical model of computerized manufacturing systems,Proc. 4th Int. Conf. on Production Research, Tokyo, Japan (1977).
[4] W.J. Gordon and G.F. Newell, Closed queueing networks with exponential servers, Oper. Res. 15(1967)252. · Zbl 0168.16603
[5] J.P. Buzen, Computational algorithms for closed queueing networks with exponential servers, Commun. ACM 16, 9(1973)527. · Zbl 0261.68031
[6] M. Reiser and S.S. Lavenberg, Mean value analysis of closed multichain queueing networks, J. ACM 27, 2(1980)313. · Zbl 0441.68036
[7] R. Suri, Robustness of queueing network formulae, J. ACM 30, 3(1983)564. · Zbl 0628.68036
[8] P.J. Denning and J.P. Buzen, The operational analysis of queueing network models, Computing Surveys 10 3(1978)225. · Zbl 0385.68038
[9] Y. Dallery and R. David, Some new results on operational analysis, Performance ’84, Paris (1984).
[10] J.G. Shanthikumar and D.D. Yao, Optimal server allocation in a system of multi-server stations, Manage. Sci. 33, 9(1987)1173. · Zbl 0636.90034
[11] B. Vinod and J.J. Solberg, The optimal design of flexible manufacturing systems, Int. J. Prod. Res. 23, 6(1985)1141. · Zbl 0591.90046
[12] R.R. Muntz and D. Wong, Asymptotic properties of closed queueing network models,Proc. 8th Annual Princeton Conf. on Info. Sc. and Systems, Princeton University (1974). · Zbl 0318.60074
[13] L. Kleinrock,Queueing Systems, Vol. 2 (Wiley, New York, 1976). · Zbl 0361.60082
[14] Y. Dallery and R. Suri, Approximate disaggregation and performance bounds for queueing networks with multiple-server station, Performance Evaluation Review 14, 1(1986)111.
[15] J. Zahorjan, K.C. Sevcik, D.L. Eager and B. Galler, Balanced job bound analysis of queueing networks, Commun. ACM 25, 2(1982)134.
[16] Y. Dallery, An improved balanced job bound analysis of closed queueing networks, Oper. Res. Lett. 6, 2(1987)77. · Zbl 0624.60111
[17] R. Suri and R.R. Hildebrant, Modelling flexible manufacturing systems using mean value analysis, J. Manufacturing Systems 3, 1(1984)27.
[18] F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios, Open, closed and mixed networks of queues with different classes of customers, J. ACM 22, 2(1975)248. · Zbl 0313.68055
[19] Y. Dallery and R. David, Operational analysis of multiclass queueing networks,IEEE Conf. on Decision and Control, Athens, Greece (1986).
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