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This paper and its companion (Part 2) deal with modelling and optimization of the flexible job-shop problem (FJSP). The FJSP is a generalised form of the classical job-shop problem (JSP) which allows an operation to be processed on several alternatives machines. To solve this NP-hard combinatorial problem, this paper proposes a customised Genetic Algorithm (GA) which uses an array of real numbers as chromosome representation so the proposed GA is called a real-coded GA (RCGA). The novel chromosome representation is designed to produces only feasible solutions which can be used to effectively explore the feasible search space. This first part of the papers focuses on the modelling of the problems and discusses how the novel chromosome representation can be decoded into a feasible solution. The second part will discuss genetic operators and the effectiveness of the RCGA to solve various test bed problems from literature.

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