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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.

Flexibility has become one of the key concepts in contemporary manufacturing—an important attribute of manufacturing systems that enables companies to become competitive in a very dynamic environment. In particular, flexibility is the piéce de rèsistence of flexible manufacturing systems (FMSs) ( Kochikar & Narendran, 1992). It is this important attribute that distinguishes FMS from the traditional high-volume, process-dedicated production systems like the automated transfer line. Flexibility is defined by some authors as ‘the ability of the manufacturing system to cope with the changes effectively’ ( Gupta & Buzacott, 1989). Due to the great number of different kinds of environmental changes (machine breakdowns, volume changes, introduction of new products), it is very difficult to find a single index characterizing the flexibility of automation ( Azzone & Bertelé, 1991). Consequently, it is necessary to divide the concept of flexibility into elementary concepts that are related to certain kinds of disturbances and elements of a manufacturing system.

A method for representing routing flexibility to be implemented in flexible manufacturing systems has been proposed. The method allows manufacturing sequences and routes to be represented using different formalisms—binary vectors, DNFs, and sets of linear inequalities—and at different levels of detail. These representations enable routing flexibility offered by a flexible manufacturing system design to be exploited effectively. The main contribution of this paper consists in developing a compact representation for all possible manufacturing operation sequences, using information provided by the manufacturing experts. Such representation enables an increase in the manufacturing flexibility by allowing a manufacturing system to select the more convenient course of action according to the current manufacturing system conditions. The routing flexibility model embedded into an analytical and/or simulation model will be able to predict the dynamic behaviour of different FMS configurations under different operational conditions and different logic control. It will be possible to evaluate the influence of flexibility under performance parameters such as throughput of the system, resource utilization and part's lead time under several different operational conditions such as breakdown and maintenance.