Dynamic Set-Up Scheduling of Flexible Manufacturing Systems: Design and Stability of Near Optimal General Round Robin Policies
Dynamic set-up scheduling is an important issue when a Flexible Manufacturing System (FMS) recovers from a failure or other disruption induced excursion from its economic-lot size steady state cycle. In fact, FMSs usually spend more time recovering from disruptions than being in steady state. We present recent results on the structure of optimal and near optimal policies for dynamic set-up scheduling that minimize backlog costs for a given vector of demands for each of many part types. When different part-types are nonhomogeneous or differ significantly in importance or value, non-Round Robin (general Round Robin) set-up change policies may be needed. Theoretical considerations and numerical solution results are used to deduce structural properties of the optimal policies (not necessarily Round Robin) and design near optimal policies that are tractable for high dimensional systems. The near optimal policies are based on primary and secondary set-up change hyper plane surfaces (thresholds). Primary switching surfaces (PSSs) are of dimension n — 1 (for n part-type systems) and when encountered indicate that the current set-up must be changed. Secondary switching surfaces (SSSs) are of lower dimension and indicate what set-up to change to. Stability issues as well as issues on convergence to a limit cycle are raised and analyzed, and sufficient conditions are obtained. A procedure for designing primary and secondary hyper plane set-up switching surfaces is proposed and implemented.
Key wordsDiscrete Event Systems Hybrid Systems Flexible Manufacturing Systems Scheduling Optimal Policies Set-ups
Unable to display preview. Download preview PDF.
- Michael Caramanis, Ali Sharifnia, Junjie Hu, AND Stanley Gershwin. “Development of a Science Base for Planning and Scheduling Manufacturing Systems”. NSF Grantees conference, Austin, TX, Januaray 1991.Google Scholar
- Junjie Hu AND Michael Caramanis. “Near Optimal Set-up Scheduling for Flexible Manufacturing Systems”. Proceedings of the Third International Conference on Computer Integrated Manufacturing, RPI, Troy, NY, May 20–22 1992.Google Scholar
- Harold J. Kushner. “Numerical Methods for Stochastic Control Problems in Continuous Time”. Technical Report LCDS #89-11, Division of Applied Mathematics, Lefschetz Center for Dynamical Systems, Brown University, Providence, Rhode Island 02912, May 1989.Google Scholar
- Guo-Xiang Yu AND Pirooz Vakili. “Periodic and Chaotic Dynamics of a Switched Server System under Corridor Policies”. Submitted to IEEE Trans-actions on Automatic Control, March 1994.Google Scholar