Cyclic job scheduling in paced assembly lines with cross-trained workers

Paced or synchronous assembly lines allow concurrent manufacturing of a mix of products by repetitive production of a minimal product set (MPS). We refer to the associated production schedules as cyclic. We consider a paced assembly line where every job (or order) visits all m assembly stations in the same sequence and spends the same amount of time (known as the production cycle) at each station, by using the appropriate number of workers. Hence, associated with each job is an m-tuple of workforce requirements. Our objective is to find a cyclic schedule of jobs such that the total required workforce size is minimized. Assuming that each worker is cross-trained to work at a number of stations, we show that the problem is strongly NP-complete. In light of this result, we develop lower bounds, heuristic algorithms and an optimal branch-and-bound procedure. Our computational experiments show that our algorithms are computationally efficient and exhibit near-optimal performance. We also compare the savings in workforce size among systems with various levels of cross training.