Analytical results for the performance and the control of stochastic flow systems

Design and control problems of failure-prone production lines are explored by means of simple mathematical models. The fluctuations of the performances are introduced via random environments which are modelled by non-Markovian alternating renewal processes. The production output can either be discrete or continuous processes. For these modelling frameworks, we calculate explicitly the average and the variance of the following quantities: (1) the cumulate production output, (2) the random time needed to complete a given production batch and (3) the output of a buffered production dipole. Finally, the optimal control of a single failure prone machine which delivers a single part type is considered. The demand rate is taken to be constant. Deviations of the production output from the demand are penalized by a convex cost function. The operating states of the machine are again modelled by a non-Markovian alternating process. Under the assumption that a hedging point policy is optimal, we calculate explicitly the position of this hedging stock as a function of the coefficient of variation of the time to failure.

Published in:
Journal of Intelligent Manufacturing, 8, 5, 435-447
Département de Microtechnique, Institut de Microtechnique, EPFL, CH-1015 Lausanne, Switzerland Cited By (since 1996): 3 Export Date: 6 December 2012 Source: Scopus CODEN: JIMNE Language of Original Document: English Correspondence Address: Hongler, M.-O.; Département de Microtechnique, Institut de Microtechnique, EPFL, CH-1015 Lausanne, Switzerland References: Akella, R., Kumar, P.R., Optimal control of production rate in a failure prone manufacturing system (1986) IEEE Transactions on Automation and Control, AC-31, pp. 116-126; Bielicki, T., Kumar, P.R., Optimality of zero-inventory policies for unreliable manufacturing systems (1988) Operations Research, 36, pp. 532-541; Buzacott, J.A., Shanthikumar, J.G., (1993) Stochastic Models of Manufacturing Systems, , Prentice Hall; Carrascosa, M., (1995) Variance of the Output in a Deterministic Two Machine Lines, , Master's Thesis, MIT, Laboratory for Manufacturing and Productivity, Report LMP-95-010; Ciprut, Ph., Hongler, M.-O., Salama, Y., (1997) On the Variance of the Production Output of Transfer Lines, , preprint, Dept, de Microtechnique EPF-Laussane; Ciprut, Ph., Hongler, M.-O., Salama, Y., (1997) Hedging Point for Non-Markovian Piecewise Deterministic Production Processes, , preprint, Dept de Microtechnique EPF-Lausanne; Cohen, J.W., (1982) The Single Server Queue, , North Holland; Coillard, P., Proth, J.-M., (1983) Rev. Belge Inform. et de Rech. Op., 24, pp. 1-23; Dallery, Y., Gerschwin, S.B., Manufacturing flow lines systems. A review of models and analytical results (1993) Queueing Systems: Theory and Applications, 12, pp. 3-94; Dubois, D., Forestier, J.-P., Productivité et encours moyens d'un ensemble de deux machines séparées par une zone de stockage (1981) RAIRO Automated Systems Analysis and Control, 16, pp. 105-132; Georgescu-Roegen, N., (1976) The Entropy Law and the Economic Process, , Harvard University Press; Gerschwin, S.B., Variance of the output of a tandem production system (1993) Proceedings of 2nd International Workshop Held in Triangle Park, North Carolina, 1992, , Queueing Networks with Finite Capacity, Onvural, R. and Akyldiz, I. (eds); Gerschwin, S.B., (1993) Manufacturing System Engineering, , Prentice Hall; Glansdorff, P., Prigogine, I., (1971) Structure Stabilité, Fluctuations, , Masson; Hongler, M.-O., Chaotic and Stochastic Behavior in Automatic Production Lines (1994) Lecture Notes in Physics, , New Series m: Monographs m22, Springer-Verlag, Heidelberg; Hongler, M.-O., Domine, E., On the variability of the throughput and the random time to complete a fixed batch with failure prone machines (1994) Proceedings of European Workshop on Integrated Manufacturing Systems Engineering, pp. 375-382. , Grenoble; Hongler, M.-O., Salama, Y., Continuous versus discrete flow of parts in a production dipole. Exact transient analysis (1995) Proceedings of Conference on Emerging Technology and Factory Automation (ETFA 95), , Paris; Hu, J.-Q., Production rate control for failure prone production systems with no backlog permitted (1995) IEEE Transactions on Automation Control, AC-40, pp. 291-295; Hu, J.-Q., Xiang, D., The queueing equivalence to a manufacturing system with failures (1993) IEEE Transactions on Automation and Control, AC-38, pp. 499-502; Hu, J.-Q., Xiang, D., Structural properties of optimal production controllers in failure prone manufacturing systems (1994) IEEE Transactions on Automation and Control, AC-39, pp. 640-642; Kimenia, J.G., Gerschwin, S.B., An algorithm for the computer control of production in flexible manufacturing systems (1983) IIE Transactions, 15, pp. 353-362; Miller, R.G., Continuous time stochastic storage processes with random linear inputs and outputs (1963) Journal of Mathematics and Mechanics, 12, pp. 275-291; Pinsky, M.A., (1991) Lectures on Random Evolution, , World Scientific Press; Ross, S.M., (1982) Stochastic Processes, , John Wiley; Schlesinger, (1995) Random Walks in Random Environments, 1. , Oxford University Press, Section 5.3.2; Seshadri, V., (1993) The Inverse Gaussian Distribution, , Oxford Science Publications; Sethi, S.P., Zhang, Q., (1994) Hierarchical Decision Making in Stochastic Manufacturing Systems, , Birkhauser; Takacs, L., On certain sojourn time problems in the theory of stochastic processes (1957) Acta Mathematica Academiae Scientianim Hungarincae, 8, pp. 169-191; Terracol, C., David, R., Performance d'une ligne composée de machines et de stocks intermédiaires (1987) APII, 21, pp. 239-262; Winjgaard, J., The effect of interstage buffer storage on the output of two unreliable production units in series with different production rates (1979) AIIE Transactions, 11, pp. 42-47
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Scopus: 2-s2.0-0031248321

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