Level workforce planning for multistage transfer lines

In this article, we define two different workforce leveling objectives for serial transfer lines. Each job is to be processed on each transfer station for c time periods (e.g., hours). We assume that the number of workers needed to complete each operation of a job in precisely c periods is given. Jobs transfer forward synchronously after every production cycle (i.e., c periods). We study two leveling objectives: maximin workforce size ( W _ m ) and min range (R). Leveling objectives produce schedules where the cumulative number of workers needed in all stations of a transfer line does not experience dramatic changes from one production cycle to the next. For W _ m and a two‐station system, we develop a fast polynomial algorithm. The range problem is known to be NP‐complete. For the two‐station system, we develop a very fast optimal algorithm that uses a tight lower bound and an efficient procedure for finding complementary Hamiltonian cycles in bipartite graphs. Via a computational experiment, we demonstrate that range schedules are superior because not only do they limit the workforce fluctuations from one production cycle to the next, but they also do so with a minor increase in the total workforce size. We extend our results to the m‐station system and develop heuristic algorithms. We find that these heuristics work poorly for min range (R), which indicates that special structural properties of the m‐station problem need to be identified before we can develop efficient algorithms.