An Assembly Flow-Shop Scheduling Problem with Sequence- Dependent Setup and Transportation times

In this paper, three-stage assembly flowshop scheduling is considered with respect to minimizing bi-objectives, namely mean flow time and mean tardiness. This problem is a model of production systems, which several production operations are done simultaneously and independently, and then produced components are collected and transferred to an assembly stage for the final operation. In this model, by considering sequence-dependent setup time and components transformation times in order to make a real situation for the considered model, a lower bound (LB) is introduced to completion times of all the jobs. Further, due dates are generated randomly in a determined interval for some examples. To validate the proposed model, the Lingo 8.0 software and an enumeration technique that is coded in MATLAB are used. Comparison between the results of the Lingo 8.0 and enumeration technique shows that in larger problems (say n>8, where n is the number of jobs) the results obtained by Lingo do not have the good efficiency and cannot be compared with the enumeration technique in terms of computational time and deviation from the minimum objective function. For example, in some large problems, the objective function values obtained by the Lingo 8.0 software have 20% deviation from their minimum. Therefore, to solve such a hard problem, a meta-heuristic method is required as future research.