| The dissertation presents a novel hierarchical block-diagram modeling framework for manufacturing systems. A block can be a single manufacturing operation, a single machine, a single part or a factory. Each block has three inputs and three outputs and is represented by a set of linear max-plus algebraic equations. A complex manufacturing system can be modeled as a network of basic manufacturing blocks. Routing of parts and resources through the block diagram graphically corresponds to machine-flow and resource-flow interconnection of blocks and is mathematically modeled by part-flow and machine-flow interconnection matrices, respectively. A formula for composing a network of manufacturing blocks into a single manufacturing block is derived. The model can be used for: (a) performance evaluation, (b) deadlock detection, (c) structural analysis, (d) scheduling, (e) design, and (f) control of manufacturing systems.;The dissertation develops an elegant analysis tool called a matrix signal flow graph (MSFG) over max-plus algebra (also called a synchronous MSFG) for these models. New topological methods for evaluating gains of synchronous MSFGs are presented. Synchronous MSFG provide a straightforward way to covert the graphical block-diagram representation of the system to the max-plus algebraic view.;The dissertation also shows that in the case of a permutation flow shop, an inverse Monge matrix represents the resulting algebraic equations for the system. The dissertation proves that the class of inverse Monge matrices is closed under max-plus algebraic multiplication, and provides an efficient algorithm for computing an eigenvector of an inverse Monge matrix. These properties allow for efficient computation of performance characteristics of permutation flow shops. |
