Parametric analysis of Mixed-Model Assembly Lines using max-plus algebra

Mixed-Model Assembly Lines (MMALs) are widely used in industries where high variety of products is required in addition to low cost and high responsiveness. When a certain product mix is demanded and different variants require different assembly times on different stations, the sequence of variants on the line highly affects the line performance. Although assembly tasks in MMALs are usually manual, most sequencing algorithms assume deterministic times for these tasks rendering the obtained results unreliable. Max-plus algebra is a mathematical tool that can model discrete event systems in linear equations analogous to traditional state space dynamic equations. Modeling MMALs with max-plus equations would enable comparing sequences over ranges of values of assembly times thus increasing the robustness and reliability of obtained results. MMALs with both closed and open stations are modeled using max-plus algebra and the produced models are used to compare possible sequences and to analyze various performance measures of the lines while varying some system parameters. Two numerical examples are presented to demonstrate different analyses that can be performed using the developed model. In the first example, three possible sequences where compared and regions of optimality for each sequence determined. In the second example, the effect of changing launching rate of work units on line performance is studied.