Production control and combined discrete/continuous simulation modeling in failure-prone transfer lines

In this paper, we consider a production system consisting of multiple tandem machines subject to random failures. The objective of the study is to find the production rates of the machines in order to minimize the total inventory and backlog costs. By combining analytical formalism and simulation-based statistical tools such as design of experiments (DOE) and response surface methodology (RSM), an approximation of the optimal control policy is obtained. The combined discrete/continuous simulation modeling is used to obtain an estimate of the cost in a fraction of the time necessary for discrete event simulation by reducing the number of events related to parts production. This is achieved by replacing the discrete dynamics of part production by a set of differential equations that describe this process. This technique makes it possible to tackle optimization problems that would otherwise be too time consuming. We provide some numerical examples of optimization and compare computational times between discrete event and discrete/continuous simulation modeling. The proposed combination of DOE, RSM and combined discrete/continuous simulation modeling allows us to obtain the optimization results in a fairly short time period on widely available computer resources.

[1]  R. Akella,et al.  Optimal control of production rate in a failure prone manufacturing system , 1985, 1985 24th IEEE Conference on Decision and Control.

[2]  A. Alan B. Pritsker,et al.  Simulation with Visual SLAM and AweSim , 1997 .

[3]  Asbjoern M. Bonvik.  Performance analysis of manufacturing systems under hybrid control policies , 1996 .

[4]  Jack P. C. Kleijnen,et al.  Short-term robustness of production management systems: A case study , 2003, Eur. J. Oper. Res..

[5]  Stanley B. Gershwin,et al.  Scheduling manufacturing systems with work-in-process inventory control: multiple-part-type systems , 1994 .

[6]  Ram Akella,et al.  Optimal control of production rate in a failure prone manufacturing system , 1985 .

[7]  J. Quadrat.  Numerical methods for stochastic control problems in continuous time , 1994 .

[8]  S. Gershwin,et al.  Analytic methods for calculating performance measures of production lines with buffer storages , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[9]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[10]  H. Kushner.  Numerical Methods for Stochastic Control Problems in Continuous Time , 2000 .

[11]  P. Venkataraman,et al.  Applied Optimization with MATLAB Programming , 2001 .

[12]  Roland P. Malhamé,et al.  Decomposition/aggregation-based dynamic programming optimization of partially homogeneous unreliable transfer lines , 2004, IEEE Transactions on Automatic Control.

[13]  El-Kébir Boukas,et al.  Production and corrective maintenance planning problem of a failure prone manufacturing system , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[14]  Suresh P. Sethi,et al.  Optimal feedback production planning in a stochastic N-machine flowshop , 1995, Autom..

[15]  Jerry Banks,et al.  Handbook of simulation - principles, methodology, advances, applications, and practice , 1998, A Wiley-Interscience publication.

[16]  Yves Dallery,et al.  An improved decomposition method for the analysis of production lines with unreliable machines and finite buffers , 1999 .

[17]  Mitchell H. Burman,et al.  New results in flow line analysis , 1995 .

[18]  Suresh P. Sethi,et al.  Optimal feedback production planning in a stochastic two-machine flowshop , 1994 .

[19]  Ali Gharbi,et al.  Experimental design in production and maintenance control problem of a single machine, single product manufacturing system , 1999 .

[20]  Stanley B. Gershwin,et al.  Efficient algorithms for buffer space allocation , 2000, Ann. Oper. Res..

[21]  James E. Schor.  Efficient algorithms for buffer allocation , 1995 .

[22]  Yves Dallery,et al.  Approximate analysis of production systems operated by a CONWIP/finite buffer hybrid control policy , 2000 .

[23]  Ali Gharbi,et al.  Optimal production control problem in stochastic multiple-product multiple-machine manufacturing systems , 2003 .

[24]  Semyon M. Meerkov,et al.  c-bottlenecks in serial production lines: identification and application , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[25]  Xiaolan Xie,et al.  Approximate analysis of transfer lines with unreliable machines and finite buffers , 1989 .