Modeling and Performance Analysis of Manufacturing Systems Using Max-Plus Algebra

In response to increased competition, manufacturing systems are becoming more complex in order to provide the flexibility and responsiveness required by the market. The increased complexity requires decision support tools that can provide insight into the effect of system changes on performance in an efficient and timely manner. Max-Plus algebra is a mathematical tool that can model manufacturing systems in linear equations similar to state-space equations used to model physical systems. These equations can be used in providing insight into the performance of systems that would otherwise require numerous time consuming simulations. This research tackles two challenges that currently hinder the applicability of the use of max-plus algebra in industry. The first problem is the difficulty of deriving the max-plus equations that model complex manufacturing systems. That challenge was overcome through developing a method for automatically generating the max-plus equations for manufacturing systems and presenting them in a form that allows analyzing and comparing any number of possible line configurations in an efficient manner; as well as giving insights into the effects of changing system parameters such as the effects of adding buffers to the system or changing buffers sizes on various system performance measures. The developed equations can also be used in the operation phase to analyze possible line improvements and line reconfigurations due to product changes. The second challenge is the absence of max-plus models for special types of manufacturing systems. For this, max-plus models were developed for the first time for modeling mixed model assembly lines (MMALs) and re-entrant manufacturing systems. The developed methods and tools are applied to case studies of actual manufacturing systems to demonstrate the effectiveness of the developed tools in providing important insight and analysis of manufacturing systems performance. While not covering all types of manufacturing systems, the models presented in this thesis represent a wide variety of systems that are structurally different and thus prove that max-plus algebra is a practical tool that can be used by engineers and managers in modeling and decision support both in the design and operation phases of manufacturing systems

Makespan Minimization in Re-entrant Permutation Flow Shops

Re-entrant permutation flow shop problems occur in practical applications such as wafer manufacturing, paint shops, mold and die processes and textile industry. A re-entrant material flow means that the production jobs need to visit at least one working station multiple times. A comprehensive review gives an overview of the literature on re-entrant scheduling. The influence of missing operations received just little attention so far and splitting the jobs into sublots was not examined in re-entrant permutation flow shops before. The computational complexity of makespan minimization in re-entrant permutation flow shop problems requires heuristic solution approaches for large problem sizes. The problem provides promising structural properties for the application of a variable neighborhood search because of the repeated processing of jobs on several machines. Furthermore the different characteristics of lot streaming and their impact on the makespan of a schedule are examined in this thesis and the heuristic solution methods are adjusted to manage the problem’s extension