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**Multi-objective routing within large scale facilities using open finite queueing networks.**
*(English)*
Zbl 0971.90014

Summary: The major objective of this paper is to examine the optimal routing in layout and location problems from a network optimization perspective where manufacturing facilities are modelled as open finite queueing networks with a multiobjective set of performance measures. The overall material handling system is broken down into a set of layout topologies. For each one of these topologies the optimal routing is determined so that the product throughput is maximized while minimizing the average sojourn time and holding costs. An approximate analytical decomposition technique for modelling open finite queueing networks, called the Generalized Expansion Method (GEM), developed by the authors, is utilized to calculate the desired outputs. A mathematical optimization procedure which is described in this paper is then used to determine the optimal routes. As will be demonstrated, the design methodology of combining the optimization and analytical queueing network models provides a very effective procedure for evaluating alternative topologies while simultaneously determining the average sojourn times and the maximum throughputs of the best routes.

### MSC:

90B22 | Queues and service in operations research |

90C35 | Programming involving graphs or networks |

90C29 | Multi-objective and goal programming |

### Keywords:

queueing networks; logistics; material handling systems; optimal routing; multi-criteria decision analysis; decomposition methods; mathematical programming
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\textit{L. Kerbache} and \textit{J. M. Smith}, Eur. J. Oper. Res. 121, No. 1, 105--123 (2000; Zbl 0971.90014)

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