State space representation of routing flexibility

This paper describes a state space representation for sequencing and routing flexibility in manufacturing systems. Routing flexibility is represented using five different stages as follows: (i) Precedence Graph of Operations; (ii) State Transition Graph of Manufacturing Operation Sequences; (iii) State Transition Graph of Manufacturing Operation Routes; (iv) Disjunctive Normal Form (DNF) Representation of Manufacturing Sequences; and (v) DNF Representation of Manufacturing Routes. Each representation is able to represent sequencing and routing flexibility at different levels of detail. The third representation is capable of enumerating all possible manufacturing operation routes that can be applied to a certain part, being the most complete representation. Bounds for computation of some of the representations are presented to help users select the most suitable for a specific problem context. The efficacy of the representation is demonstrated through its application to problems such as job route selection and routing flexibility measure.