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.

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

Published in
Journal of Intelligent Manufacturing

Volume
8

Issue
5

Pages
435-447

Date
1997

ISSN
09565515

Note
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