Max-plus Modeling of Manufacturing Flow Lines

Max-plus algebra can be used to model manufacturing flow lines using linear state-space-like equations which can be used in analysis and control. This paper presents a method for easy and quick generation of the max-plus equations for manufacturing flow lines of any size or structure. The generated equations can model flow lines with infinite as well as finite buffer sizes.A flow line to be modeled is initially assumed to have infinite buffers for all stations. The line model equations are then generated as a combination of serial and merging stations after identifying the different stages using an adjacency matrix for the flow line. In the generated equations, the dynamics of the system are captured in two matrices that are function of the processing times of the different stations in the line. After generating these equations, extra terms are added to account for the finite buffers where for each buffer size, a matrix is added multiplied by the vector of system parameters delayed by the buffer size plus one.The method is intuitive and easy to understand and code in software and thus can facilitate quick analysis of different configurations of manufacturing flow lines and assessing what if scenarios. This can also allow quick on-line reconfiguration of controllers for frequently reconfiguring flow lines.