Derivation Algorithm of State-Space Equation for Production Systems Based on Max-Plus Algebra

This paper proposes a new algorithm for determining an optimal control input for production systems. In many production systems, completion time should be planned within the due dates by taking into account precedence constraints and processing times. To solve this problem, the max-plus algebra is an effective approach. The max-plus algebra is an algebraic system in which the max operation is addition and the plus operation is multiplication, and similar operation rules to conventional algebra are followed. Utilizing the max-plus algebra, constraints of the system are expressed in an analogous way to the state-space description in modern control theory. Nevertheless, the formulation of a system is currently performed manually, which is very inefficient when applied to practical systems. Hence, in this paper, we propose a new algorithm for deriving a state-space description and determining an optimal control input with several constraint matrices and parameter vectors. Furthermore, the effectiveness of this proposed algorithm is verified through execution examples.