Analysis of Max-Plus Algebraic Model for Intelligent Manufacturing Systems Based on Heap Method

Max-plus algebra is a mathematical method with special operational rules that can describe the temporal logic characteristics of discrete event systems and optimize the intelligent manufacturing system. The heap model in the max-plus algebra is an intuitive dynamic system description method that can be used to model various Tetris like systems. Each block in the model can be used to identify a single work-piece in the intelligent manufacturing process, with the goal of manufacturing a set of products in a specific order, thereby minimizing the total manufacturing time. In this paper, the heap method based on max-plus algebra is used to model and analyse discrete manufacturing processes involving multiple devices and tasks. The research addresses both rigid heaps, which do not impose restrictions on the order of processing objects, and complex rigid heaps, which also allow for flexible processing object order. To enhance the analytical accuracy in scenarios involving machining tasks comprising intricate stacks of rigid heaps, an enhanced 3D heap modelling method is proposed. This approach aims to improve the production scheduling outcome. Moreover, by investigating non-rigid heaps with limited processing object order, the proposed method is compared with the simulated annealing algorithm in the field of production scheduling, and further analysis was conducted. Finally, a comprehensive analysis is presented to identify the applicable fields for the proposed method.