Modeling a bi-criteria two stage assembly flow shop scheduling problem with sequence dependent setup times

In this paper, we address a two-stage assembly flow shop scheduling problem with sequence dependent setup times, which minimizes makespan (C_max) and maximum tardiness (T_max) as objectives. In this problem, there are n products to be produced; each product has m unique parts to be processed concurrently on m parallel machines at first stage, with each part on a specified machine. At the second stage final products are made by assembling m parts on a single machine. Sequence dependent setup times in both stages are considered as an important presumption to declare a more realistic problem. First, the problem is formulated by a non-linear mathematical model and a lower bound for the problem is proposed and some instances of different and fairly small size problems are generated and solved using Lingo 8.0 optimization software. Finally, the obtained results are compared with those of total enumeration and concluding remarks are made.