A mathematical model of a flexible manufacturing system with limited in-process inventory

Abstract This paper describes a computationally simple, asymptotic model of a flexible job shop, especially designed for estimating the influence of limited in-process inventory level on the production rate. Its main features make it very similar to the one by Solberg. While Solberg's model consists of a closed queuing network, we propose an open queuing network with a limited amount of inprocess customers; a single customer class is assumed, the various actual processing routes being accounted for by routing probabilities. For such a queuing network, the product form of state probabilities is valid, and the normalization constant can be very simply obtained by a convolution algorithm, close to the one used by Solberg. Various performance indices are calculated, regarding the job shop behaviour over a long period of time. Comparison of analytical results of the model and simulation results are provided in order to estimate the amount of error introduced by assuming exponentially distributed processing times and Poisson inputs in the mathematical representation. Simulations were carried out in FORTRAN-based SLAM language.

[1]  Alan J. Mayne,et al.  Introduction to Simulation and SLAM , 1979 .

[2]  M. Reiser,et al.  A Queueing Network Analysis of Computer Communication Networks with Window Flow Control , 1979, IEEE Trans. Commun..

[3]  J. A. Buzacott,et al.  Open queueing network models of dynamic job shops , 1981 .

[4]  James J. Solberg,et al.  Analysis of Flow Control in Alternative Manufacturing Configurations , 1980 .

[5]  G. K. Hutchinson.  The Control of Flexible Manufacturing Systems: Required Information and Algorithm Structures , 1977 .

[6]  J. A. Buzacott,et al.  Models for Understanding Flexible Manufacturing Systems , 1980 .

[7]  Jeffrey P. Buzen,et al.  Computational algorithms for closed queueing networks with exponential servers , 1973, Commun. ACM.

[8]  Gianfranco Balbo,et al.  Computational algorithms for closed queueing networks , 1980 .

[9]  James J. Solberg,et al.  Capacity Planning with a Stochastic Workflow Model , 1981 .

[10]  Ernest Koenigsberg,et al.  Invariance Properties Of Queueing Networks And Their Application To Computer/Communications Systems , 1981 .

[11]  Peter J. Denning,et al.  The Operational Analysis of Queueing Network Models , 1978, CSUR.

[12]  W. J. Gordon,et al.  Closed Queuing Systems with Exponential Servers , 1967, Oper. Res..

[13]  J. A. Buzacott.  The production capacity of job shops with limited storage space , 1976 .

[14]  William L. Maxwell,et al.  Theory of scheduling , 1967 .

[15]  Paul J. Schweitzer,et al.  Maximum Throughput in Finite-Capacity Open Queueing Networks with Product-Form Solutions , 1977 .