Bi-level genetic algorithms for a two-stage assembly flow-shop scheduling problem with batch delivery system

In this paper, an integrated production and distribution scheduling on a two-stage assembly flow-shop setting with a batch delivery system is addressed. The objective is to schedule the jobs in the two-stage assembly flow-shop and groups the completed products into a suitable number of batches for delivery with the minimum number of weighted tardy jobs and sum of delivery costs. After extending a mixed-integer linear programming (MILP) model, we proposed a bi-level genetic algorithm to solve the addressed problem that the first level of its chromosome is supposed to determine the sequence of the processing jobs, and the second level of it is responsible for allocating jobs to batches independently. To offer the more efficient algorithm, we change the structure of the proposed GA. Therefore, by applying the hierarchical decision-making approach, we present a bi-level improved genetic algorithm (IGA) in which according to the determined sequence in the first level, batches are determined. The proposed algorithms are evaluated based on computational experiments. The experiments reveal that IGA, which has the decreased decision-making space for the second level, outperforms GA. Moreover, to validate the proposed model and the efficiency of the proposed algorithms, a real-life example is presented and solved.