Production Planning Models using Max-Plus Algebra

Abstract

The chapter presents a novel building block approach to developing models of manufacturing systems. The approach is based on max-plus algebra. Within this algebra, manufacturing schedules are modeled as a set of coupled linear equations. These equations are solved to find performance metrics such as the make span. The chapter develops a generic modeling block with three inputs and three outputs. It is shown that this structure can model any manufacturing system. It is also shown that the structure is hierarchical, that is, a set of blocks can be reduced to a single block with the same three inputs and three output structure. Basic building blocks, like machining operations, assembly, and buffering are derived. Job shop, flow shop, and cellular system applications are given. Extensions of the theory to buffer allocation and stochastic systems are also outlined. Finally, several numerical examples are given throughout the development of the theory.