Abstract
This paper is concerned with optimal production planning on a single failure-prone flexible machine that produces N distinct part types. The machine is flexible in the sense that no setup is required for switching from production of one part type to another. We consider the problem of controlling production rates to minimize the expected long-run average cost of product surpluses over time. We assume constant unit holding and shortage costs and constant demand rates for the part types. Moreover, the costs are assumed to be the same for all products. We provide an explicit optimal solution for the problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akella, R. and Kumar, P.R., “Optimal Control of Production Rate in a Failure Prone Manufacturing System,” IEEE Transactions on Automatic Control, Vol. AC-31, No. 2, pp. 116-126 (1986).
Bielecki, T. and Kumar, P.R., “Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems,” Operations Research, Vol. 36, No. 4, pp. 532-546 (1988).
Feller, W., An Introduction to Probability Theory and Its Applications, 3rd ed., Vol. 1, John Wiley and Sons, New York (1968).
Gershwin, S.B., Manufacturing Systems Engineering, Prentice-Hall, Englewood Cliffs, NJ (1994).
Hsu, G.H., Stochastic Service Systems, Academic Press, Beijing (1988).
Liberopoulos, G. and Hu, J.Q., “On the Ordering of Optimal Hedging Points in a Class of Manufacturing Flow Control Models,” IEEE Transactions on Automatic Control, Vol. AC-40, No. 3, pp. 282-286 (1995).
Presman, E., Sethi, S.P., Zhang, H., and Zhang, Q., “Optimality of Zero-Inventory Policies for an Unreliable Manufacturing System Producing Two Part Types,” Dynamics of Continuous, Discrete and Impulsive Systems, to appear (1998).
Sethi, S.P. and Zhang, Q., Hierarchical Decision Making in Stochastic Manufacturing Systems, Birkhäuser Boston, Cambridge, MA (1994).
Sethi, S.P., Suo, W., Taksar, M., and Yan, H., “Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost,” Journal of Discrete Event Dynamic Systems: Theory and Applications, Vol. 8, pp. 37-54 (1998).
Sharifnia, A., “Production Control of a Manufacturing System with Multiple Machine States,” IEEE Transactions on Automatic Control, Vol. AC-33, No. 7, pp. 600-626 (1988).
Srivatsan, N., “Synthesis of Optimal Policies in Stochastic Manufacturing Systems,” Ph.D thesis, Operations Research Center, Massachusetts Institute of Technology, Cambridge (1993).
Srivatsan, N. and Dallery Y., “Partial Characterization of Optimal Hedging Point Policies in Unreliable Two-Part-Type Manufacturing Systems,” Operations Research, Vol. 46, No. 1, pp. 36-45 (1998).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Sethi, S.P., Zhang, H. Average-Cost Optimal Policies for an Unreliable Flexible Multiproduct Machine. International Journal of Flexible Manufacturing Systems 11, 147–157 (1999). https://doi.org/10.1023/A:1008011204617
Issue Date:
DOI: https://doi.org/10.1023/A:1008011204617