Abstract
The problem of detailed scheduling of complex flexible manufacturing systems is addressed by optimal flow control. A model problem of scheduling parallel machines is considered to obtain necessary setup conditions. Studying the conditions results in a new solution approach that takes advantage of a juggling analogy of the production/setup scheduling. This analogy is used in the paper to direct construction of a solution method. The method searches for a globally optimal schedule by means of both a juggling strategy and a method of global optimization. The results obtained for a model problem are then generalized to systems with complex production and setup operations. Computational examples demonstrate the validity of the approach.
Similar content being viewed by others
References
Bai, S. X., and Elhafsi, M. 1996. Transient and steady-state analysis of a manufacturing system with setup changes. Journal of Global Optimization 8(4): 349–378.
Caramanis, M., Sharifnia, A., Hu, J., and Gershwin, S. 1991. Development of a science base for planning and scheduling manufacturing systems. Proceedings of the 1991 NSF Design and Manufacturing Systems Conference. Austin, Texas, pp. 27–40.
Chase, C., and Ramadge, P. 1992. On real-time scheduling policies for flexible manufacturing systems. IEEE Transactions on Automatic Control 37(4): 491–496.
Chase, C., Serrano, J., and Ramadge, P. 1993. Periodicity and chaos from switched flow systems: Contrasting examples of discretely controlled continuous systems. IEEE Transactions on Automatic Control 38: 70–83.
Dobson, G. 1987. The economic lot scheduling problem: Achieving feasibility using time-varying lot sizes. Operations Research 35: 764–771.
Elhafsi, M., and Bai, S. 1995. Optimal production and setup control of a dynamic two-product manufacturing system: Analytical solution. Journal of Computers and Mathematical Modeling.
Gallego, G. 1990. Scheduling the production of several items with random demands in a single facility. Management Science 36: 1579–1592.
Gibilisco, F., and Love, J. 1996. Scheduling Project Report (MN510), Dept. of Manufacturing Engineering, Boston University.
Hanlon, J., and MacVicar, J. 1996. Scheduling Project Report (MN510), Dept. of Manufacturing Engineering, Boston University.
Hu, J. 1994. Optimal and near-optimal scheduling in flow control problems. Ph.D. Dissertation. Dept. of Mfg. Engineering, Boston University.
Hu, J., and Caramanis, M. 1995. Dynamic set-up scheduling of flexible manufacturing systems: Design and stability of near optimal general round robin policies. Discrete Event Systems, IMA Volumes in Mathematics and its Applications Series (P. R. Kumar and P. P. Varaiya, eds.). Springer-Verlag, pp. 73–104.
Kimemia, J. G., and Gershwin, S. B. 1983. An algorithm for the computer control of a flexible manufacturing system. IIE Transactions 15(4): 353–362.
Khmelnitsky, E., and Kogan, K. 1994. Necessary optimality conditions for a generalized problem of production scheduling. Optimal Control Applications and Methods 15: 215–222.
Khmelnitsky, E., Kogan, K., and Maimon, O. 1995. A maximum principle based method for scheduling in a flexible manufacturing system. Discrete Event Dynamic Systems 5: 343–355.
Khmelnitsky, E., Kogan, K., and Maimon, O. 1996. Optimal flow control for continuous-time scheduling in flexible manufacturing systems. International Transactions in Operational Research 2(4): 331–339.
Khmelnitsky, E., and Caramanis, M. 1998. One-machine n-part-type optimal set-up scheduling: Analytical characterization of switching surfaces. IEEE Transactions on Automatic Control, 43(11): 1584–1588.
Perkins, J. R., and Kumar, P.R. 1989. Stable, distributed, real-time scheduling of flexible manufacturing/assembly/ disassemble. IEEE Transactions on Automatic Control 34(2): 139–148.
Sharifnia, A., Caramanis, M., and Gershwin, S. 1991. Dynamic setup scheduling and flowcontrol in manufacturing systems. Discrete Event Dynamic Systems 1: 149–175.
Yu, G.-X., and Vakili, P. 1996. Periodic and chaotic dynamics of a switched-server system under corridor policies. IEEE Transactions of Automatic Control 15(4).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khmelnitsky, E. Setup Scheduling of Manufacturing Systems as the Art of Juggling. Discrete Event Dynamic Systems 9, 241–260 (1999). https://doi.org/10.1023/A:1008349414383
Issue Date:
DOI: https://doi.org/10.1023/A:1008349414383