The two stage assembly flow-shop scheduling problem with batching and delivery

This paper investigates the two-stage assembly flow shop scheduling problem with a batched delivery system where there are m independent machines at the first stage doing the components of a job and multiple identical assembly machines at the second stage, each of which can assemble the components and complete the job. The objective is to schedule the jobs, to form them into batches so as to minimize the sum of tardiness plus delivery costs. To the best of our knowledge, the assembly flow shop scheduling problem with this objective function has not been addressed so far. A mathematical model for this problem is presented. However, due to the fact that this model happens to be a mixed integer nonlinear programming model and cannot guarantee to reach the solution at reasonable time we developed the imperialist competitive algorithm (ICA) and a hybrid algorithm (HICA) by incorporating the dominance relations. Computational results show that HICA performs better than ICA with respect to the value of the objective function, However the runtime of the ICA is less than HICA.