Abstract
The maximum principle analysis conducted in the previous chapter yields qualitative information about the extremal behavior of flexible manufacturing systems. Until now we examined typical elements (regimes) of optimal “scheduling trajectories” and the production conditions necessary for their appearance. It was easy to predict that the analytical information would be insufficient for developing the optimal schedule for the large class of FMS modeled and studied in the previous chapters. The calculation of the optimal schedule can be done analytically only for special cases of small-dimensional manufacturing systems. For example, assuming constant demand rate and linear or quadratic surplus/backlog cost dependencies, the limit cycles and transition corridors can be found analytically for one-machine, two-product scheduling problems. In section 7.2, we present an analytical solution approach to solving one-machine, multiple-part-type problems under constant-in-time demand.
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Bibliography
Caramanis, M., A. Sharifnia, J. Hu and S. Gershwin, 1991, “Development of a Science Base for Planning and Scheduling Manufacturing Systems” in Proceedings ofthe 1991 NSF Design and Manufacturing Systems Conference, Austin, Texas, 27–40.
Chase, C. and P. Ramadge, 1992, “On Real-Time Scheduling Policies for Flexible Manufacturing Systems”, IEEE Transactions on Automatic Control, 37(4), 491–496.
Connolly, S., Y. Dallery and S. Gershwin, 1992, “A Real-time Policy for Performing Setup Changes in a Manufacturing System”, in Proceedings of the 31 st IFEE Conference on Decision and Control , Tucson, Arizona.
Dobson, G., 1987, “The Economic Lot Scheduling Problem: Achieving Flexibility Using Time-Varying Lot Sizes”, Operations Research, 35, 764–771.
Elhafsi, M. and S. Bai, 1996, “Transient and Steady-State Analysis of a Manufacturing System with Setup Changes”. Journal ofGlobal Optimization, 8, 349–378.
Hu, J, 1994, “Optimal and Near-Optimal Scheduling in Flow Control Problems”, Ph.D. Dissertation, Dept. of Mfg. Engineering, Boston University.
Hu, J. and M. Caramanis, 1995, “Dynamic Set-Up Scheduling of Flexible Manufacturing Systems: Design and Stability of Near Optimal General Round Robin Policies”, in Discrete Event Systems, IMA Volumes in Mathematics and its Applications Series, P.R. Kumar and P.P. Varaiya Editors, Springer-Verlag, 73–104.
Kimemia, J. G. and S. B. Gershwin, 1983, “An Algorithm for the Computer Control of a Flexible Manufacturing Svstern” IIE Transactions 15(4)353–362.
Khmelnitsky, E, K. Kogan and O. Maimon, 1995, “A Maximum Principle-Based Combined Method for Scheduling in a Flexible Manufacturing System”, Discrete Event Dynamic Systems, 5, 343–355.
Khmelnitsky, E, K. Kogan and O. Maimon, 1997, “Maximum Principle-based Methods for Production Scheduling with Partially Sequence-dependent Setups”, International Journal ofProduction Research, 35(10), 2701–2712.
Milyutin, AA., N. Osmolovsky, S. Chukanov and A. Ilyutovich, 1993, Optimal Control in Linear Systems, Nauka, Moscow (in Russian).
Perkins, J. R. and P. R. Kumar, 1989, “Stable, Distributed, Real-Time Scheduling of Flexible Manufacturing/Assembly/Disassemble”, IEFE Transactions on Automatic Control, 34(2), pp. 139–148.
Sharifnia, A., M. Caramanis and S. Gershwin, 1991, “Dynamic Setup Scheduling and Flow Control in Manufacturing Systems”, Discrete Event Dynamic Systems, 1, 149–175.
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© 1998 Springer Science+Business Media Dordrecht
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Maimon, O., Khmelnitsky, E., Kogan, K. (1998). Solution Methods. In: Optimal Flow Control in Manufacturing Systems. Applied Optimization, vol 18. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2834-7_7
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DOI: https://doi.org/10.1007/978-1-4757-2834-7_7
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