Algebraic expression of system configurations and performance metrics for mixed-model assembly systems

One of the challenges in the design and operation of a mixed model assembly system (MMAS) is the high complexity of the station layout configuration due to the various tasks that have to be performed to produce different product variants. It is therefore desirable to have an effective way of representing complex system configurations and analyzing system performances. By overcoming the drawbacks of two widely used representation methods (block diagrams and adjacency matrix), this article proposes to use algebraic expressions to represent the configuration of an MMAS. By further extending the algebraic configuration operators, algebraic performance operators are defined for the first time to allow systematic evaluation of system performance metrics, such as quality conforming rates for individual product types at each station and process capability for handling complexity induced by product variants. Therefore, the benefits of using the proposed algebraic representation are not only their effectiveness in achieving a compact storage of system configurations but also its ability to systematically implement computational algorithms for automatically evaluating various system performance metrics. Examples are given in the article to illustrate how the proposed algebraic representation can be effectively used in assisting the design and performance analysis of an MMAS.