Abstract
A continuous time dynamic model of discrete scheduling problems for a large class of manufacturing systems is considered in the present paper. The realistic manufacturing based on multi-level bills of materials, flexible machines, controllable buffers and deterministic demand profiles is modeled in the canonical form of optimal control. Carrying buffer costs are minimized by controlling production rates of all machines that can be set up instantly. The maximum principle for the model is studied and properties of the optimal production regimes are revealed. The solution method developed rests on the iterative approach generalizing the method of projected gradient, but takes advantage of the analytical properties of the optimal solution to reduce significantly computational efforts. Computational experiments presented demonstrate effectiveness of the approach in comparison with pure iterative method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akella, R., Choong, Y. F., and Gershwin, S. B. 1984. Performance of hierarchical production scheduling policy.IEEE Trans. Components Hybrids Mfg. Technol. CHMT-7: 225–240.
Akella, R., and Kumar, P. R. 1986. Optimal control of production rate in a failure-prone manufacturing system.IEEE Trans. on Automatic Control. AC-31: 116–126.
Akella, R., Maimon, O., and Gershwin, S. B. 1990. Value function approximation via linear programming for FMS scheduling.Int. J. Prod. Res. 28(9): 1459–1470.
Dielecki, T., and Kumar, P. R. 1988. Optimality of zero-inventory policies for unreliable manufacturing systems.Operations Research 36: 532–541.
Bryson, A. E., and Ho, Y.-C. 1969.Applied Optimal Control. Waltham: Ginn and Company.
Burden, R. L., and Faires, J. D. 1989.Numerical Analysis. Boston: PWS-KENT.
Dubovitsky, A. Y., and Milyutin, A. A. Theory of the maximum principle.Methods of Theory of Extremum Problems in Economy, pp. 6–47.
Gershwin, S. B., Akella, R., and Choong, Y. F. 1985. Short term scheduling of an automated manufacturing facility.IBM J. of Res. and Development 29: 392–400.
Ilyutovich, A., and Khmenlnitsky, E. 1991.A Numerical Method for an Optimal Control Problem with Constraints on State Variables, Based on the Maximum Principle. Moscow: VNIISI Publishing.
Khmelnitsky, E., and Kogan, K. Necessary optimality conditions for a generalized problem of production scheduling.Optimal Control Applications and Methods, 15.
Kimemia, J. G., and Gershwin, S. B. An algorithm for the computer control of a flexible manufacturing system.IIE Transactions 15: 353–362.
Maimon, O., and Gershwin, S. B. 1988. Dynamic scheduling and routing for flexible manufacturing systems that have unreliable machines.Operations Research 36: 279–292.
Sharifnia, A. 1988. Optimal production control of a manufacturing system with machine failures.IEEE Trans. on Automatic Control 33(7): 620–625.
Sousa, J. B., and Pereira, F. L. 1992. A hierarchical framework for the optimal flow Control in manufacturing systems.Proceedings of the Third International Conference on Computer Integrated Manufacturing, Troy, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khmelnitsky, E., Kogan, K. & Maimon, O. A maximum principle based combined method for scheduling in a flexible manufacturing system. Discrete Event Dyn Syst 5, 343–355 (1995). https://doi.org/10.1007/BF01439152
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01439152