Analysis of algorithms for two-stage flowshops with multi-processor task flexibility

In this article we introduce a 2-machine flowshop with processing flexibility. Two processing modes are available for each task: namely, processing by the designated processor, and processing simultaneously by both processors. The objective studied is makespan minimization. This production environment is encountered in repetitive manufacturing shops equipped with processors that have the flexibility to execute orders either individually or in coordination. In the latter case, the product designer exploits processing synergies between two processors so as to execute a particular task much faster than a dedicated processor. This type of flowshop environment is also encountered in labor-intensive assembly lines where products moving downstream can be processed either in the designated assembly stations or by pulling together the work teams of adjacent stations. This scheduling problem requires determining the mode of operation of each task, and the subsequent scheduling that preserves the flowshop constraints. We show that the problem is ordinary NP-complete and obtain an optimal solution using a dynamic programming algorithm with considerable computational requirements for medium and large problems. Then, we present a number of dynamic programming relaxations and analyze their worst-case error performance. Finally, we present a polynomial time heuristic with worst-case error performance comparable to that of the dynamic programming relaxations.