Modeling a Flow-Shop with Setup Times in Dioid Algebra

Abstract

This paper aims at proposing a model for flow-shops with setup times in dioid algebra. Since this algebra is efficient and generic, the absence of a general systematic technique available for such systems using this tool is a strong motivatioui for investigating the issue. (Min, +) constraints are developed to handle resource sharing of flow-shops. In particular, the part that can be modeled by a Timed Event Graph induce (Min, +)-linear equations which are constrained regarding to the resource availability. The proposed algebraic model is proved to describe exactly the exhaustive set of possible behaviors of dealt systems. An example of flow-shop with setup times is modeled using our approach.