A Computationally Efficient Method for Optimal Input-Flow Control of Timed-Event Graphs Ensuring a Given Production Rate

Abstract

We focus in this paper on input control of manufacturing systems modelled by timed-event graphs and max-plus algebra. We propose a method for controlling the inflow of material into a production system, and the parameters of a feedback controller are computed, delaying the material input and determining its input rate. The proposed method aims to minimize system inventory to meet demand specifications, allowing the controller to obtain the best control, which delays the occurrence of input events, and delaying the input of raw material in the system as much as possible. The proposed method guarantees that the controller is optimal and proceeds according to just-in-time production planning strategy. It can also be synthesized through efficient computation (polynomial time). In addition, we show that the proposed method outperforms feedback synthesis using model reference techniques.