Investigation of Autonomy and Coordination

1. Investigation of Autonomy and Coordination Xiaobing Zhao Computer Integrated Manufacturing (CIM) Lab Systems and Industrial Engineering The University of Arizona

2. Introduction • Shop Floor Control: • Hierarchical: Master/slave • Heterarchical: Pure distributed • Hybrid: Combination COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

3. Introduction Hierarchical Hybrid Heterarchical COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

4. Comparison COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

5. Hybrid SFC System • Higher level agents (Coordination) Coordinate and optimize the overall performance of the system. • Within lower level (Autonomy), agents exhibit properties of pure distributed systems, such as p2p and autonomous decision-making. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

6. Autonomy and coordination • Autonomy: the degree of freedom that the agent can make their own decisions. • Coordination: The ability of a set of entities to develop mutually acceptable plans and execute it. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

7. Tradeoff between coordination and autonomy • To implement coordination, the autonomy of lower level agents may be reduced in favor of higher level agents. • Reduction of autonomy will undermine the property of quick reaction to disturbances. • There is tradeoff between coordination and autonomy. To what degree that the lower level agents should be autonomy will depend on the degree of disturbances. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

8. Coordination • Two main ways to implement coordination: • 1. Decomposition of overall optimization function The optimization can be guaranteed through distributing the overall goal among lower level agents. • 2. Rules Rules will be constraints to the lower agents. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

9. Example Assumptions: • The higher level agent need solve a time consuming nonlinear function to obtain a schedule and impossible to be computed in real time. • The high level agent have come up with a schedule based on known information (there will be unknown disturbances in the system). • Through the analysis of the nonlinear function, we can obtain the cost (earliness-tardiness penalties) of change of the schedule. • In this example we only consider the rush order disturbance. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

10. Rule • All the jobs shall be executed on the machine and in the sequence given by the schedule, unless other agents can explicitly proof that they have an alternative schedule with a guaranteed better performance. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

11. Single-machine schedule under the rush order disturbances (from reference 2) • Rush orders arrive intermittently through the time horizon, and we can estimate their processing time and earliness-tardiness penalties. • Jobs have distinct processing times according to the schedule, changing of the schedule will cause earliness-tardiness penalties. • The time horizon is discretized into time slots of unit length. • For each machine the overall objective now become only minimize the overall penalties. • Each job should process in the machine for contiguous time slots equal to its processing time (sub-rule). COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

12. Model Notation COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering A example from reference 2.

13. Overall Objective function • minimize the overall penalty COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

14. Lagrangian relaxation • A careful examination of the formulation reveals the only constraint set that links the jobs together with the machine is (2). Constraints (1) and (3) can be combined by restricting the time when the job can begin processing from its arrival time to processing time before the time horizon ends. If constraint set (2) is relaxed, and can be decomposed to job and machine agents, the resulting functions is as follows. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

15. Lagrangian relaxation COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

16. Agent objectives COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

17. Auction • The machine make a task announcement similar to an auction whenever it is idle and available. Each job will bid for the time slots on the machine as computed by solving its own subproblem. Because these bids might have an overlap in terms of time desired, the capacity constraints of the machine would be violated. Machine agent will use the bids to solve its own subproblem to determine the price vector. • If more than one job demands the same time slot, the price of the slot can be increased. On the other hand, if we increase the price too much so that all the bidders decide not to bid for the slot as they find it too expensive, then the price needs to be reduced to sell the slot. At each round of bidding, checking the overlap of time slots or objects desired by jobs would determine the direction in which the prices need to be adjusted for each time unit. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

18. Coordination and autonomy • When there is no disturbance, the penalties of changing schedule will force the lower level agents to come up the same schedule as the higher level agents give them. • When there are disturbances, the lower level agents will consider the situation and come up a improved schedule. • How much the original schedule will be changed will depend on the degree of disturbances. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

19. Deal with Sub-rule • If the lower level agent objective function is very simple like this one. We also can consider add a disturbance detector to the system, whenever the disturbance detector find a very urgent job comes (the lateness penalty for the job is greater than a threshold value), the cell controller will make the machine agent to make a auction immediately, even the machine is busy (by setting the value of Xik=1). In this auction, only compare the rework cost of current job and the urgent job penalty. Which cost is bigger will win the auction. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering

20. References • 1. Luc Bongaerts, Hendrik Van Brussel, Paul Valckenaers, Co-operative reactive scheduling: schedule execution using perturbation analysis, International symposium on non-linear dynamic in production processes and systems, Hannover, 17-18 September 1997- reference PMA: PMA97P61. • 2. POOJA DEWAN and SANJAY JOSHI, Dynamic single-machine scheduling under distributed decision-making, INT. J. PROD. RES., 2000, VOL. 38, NO. 16, 3759-3777. • 3. KASKAVELIS, C.A. and CARAMANIS,M. C., 1997, A Lagrangian relaxation based algorithm for scheduling multiple part production systems. Department of Industrial Engineering, Boston University, working paper. • 4. SHAW,M., 1988, A distributed knowledge-based approach to exible automation: the contract net framework. International Journal of Flexible Manufacturing Systems, 1, 85- 104. • 5. Michael Mock, Edgar nett, On the coordination of Autonomous Systems, 5TH IEEE workshop on object-oriented real-time dependable systems, Monterey, California, 1999. COMPUTER INTEGRATED MANUFACTURING LAB Department of Systems and Industrial Engineering