Two hybrid flow shop scheduling lines with assembly stage and compatibility constraints

Two hybrid flow shop scheduling lines must be coordinated to assemble batches of terminated products at their last stage. Each product is thus composed of two jobs, each produced in one of the lines. The set of jobs is to be processed in a series of stages to minimize the makespan of the scheduling, but jobs forming a product must arrive at the assembly line simultaneously. We propose a mixed integer linear programming model. Then, based on the model, we propose a pull-matheuristic algorithm. Finally, we present two metaheuristics, a greedy randomized adaptive search procedure and a biased random key genetic algorithm, and compare all the methodologies with real-based instances of a production scheduling problem in the automobile manufacturing industry. The greedy algorithm yields high-quality solutions, while the genetic one offers the best computational times.