Machine allocation problems in manufacturing networks

In this paper we discuss two server (machine) allocation problems that occur in manufacturing networks. The manufacturing network is modelled as an open network of queues. The server allocation problems are solved by means of a marginal analysis scheme. We show that for the first problem our algorithm generates undominated allocations. Furthermore, the algorithm provides us with bounds to check how close the allocation generated is to the optimal allocation. In the second problem the algorithm presented generates optimal allocations within time bounded by a polynomial function in the size of the network.

[1]  Yves Dallery,et al.  An efficient method to determine the optimal configuration of a flexible manufacturing system , 1988 .

[2]  Gabriel R. Bitran,et al.  Tradeoff Curves, Targeting and Balancing in Manufacturing Queueing Networks , 1989, Oper. Res..

[3]  Richard Weber.  Note-On the Marginal Benefit of Adding Servers to G/GI/m Queues , 1980 .

[4]  Mario Gerla,et al.  On the Topological Design of Distributed Computer Networks , 1977, IEEE Trans. Commun..

[5]  J. George Shanthikumar,et al.  Optimal server allocation in a system of multi-server stations , 1987 .

[6]  J. A. Buzacott,et al.  Flexible manufacturing systems: a review of analytical models , 1986 .

[7]  Robert B. Cooper,et al.  Queueing systems, volume II: computer applications : By Leonard Kleinrock. Wiley-Interscience, New York, 1976, xx + 549 pp. , 1977 .

[8]  J. Little.  A Proof for the Queuing Formula: L = λW , 1961 .

[9]  W. Whitt,et al.  The Queueing Network Analyzer , 1983, The Bell System Technical Journal.

[10]  Peter W. Jones,et al.  Stochastic Modelling and Analysis , 1988 .

[11]  M. E. Dyer,et al.  Note---On the Validity of Marginal Analysis for Allocating Servers in M/M/c Queues , 1977 .

[12]  Iram J. Weinstein,et al.  Technical Note - Comment on an Integer Maximization Problem , 1973, Oper. Res..

[13]  Bennett Fox,et al.  Discrete Optimization Via Marginal Analysis , 1966 .

[14]  Frank Kelly,et al.  Reversibility and Stochastic Networks , 1979 .

[15]  Alan J. Rolfe.  A Note on Marginal Allocation in Multiple-Server Service Systems , 1971 .