On the Max-Plus Linear representation for event-varying systems with buffer and order constraints

This paper extends the existent state-space representation based on max-plus algebra and proposes a new form that can take into account both capacity and order constraints. It is often essential to consider these factors when applying the MPL (max-plus linear) approach to scheduling problems for production or transportation systems. The derived form is a type of augmented state-representation and can contribute to obtaining the earliest start and completion times for processes in installed facilities.