Time-Optimal Coordination of Flexible Manufacturing Systems Using Deterministic Finite Automata and Mixed Integer Linear Programming

Automation and flexibility are often mentioned as key concepts in modern production industry. To increase the level of flexibility, deterministic finite automata (DFA) can be used to model, specify and verify the production systems. Often, it is also desirable to optimize some production criteria, such as for example the cycle time of a manufacturing cell. In this paper, a method for automatic conversion from DFA to a mixed integer linear programming (MILP) formulation is first presented. This conversion is developed for a number of DFA structures that have shown to be useful in practical applications. Special attention is paid to reducing the search region explored by the MILP solver. Second, a conversion from the MILP solution to a DFA supervisor is described. This allows to combine the advantages of DFA modeling with the efficiency of MILP and supervisory control theory to automatically generate time-optimal, collision-free and non-blocking working schedules for flexible manufacturing systems.