Complexity of Workforce Scheduling in Transfer Lines

Consider a production system that consists of m assembly stations arranged in series. All jobs enter the assembly line at station 1 and proceed with subsequent stations in the same order as in a ßow shop. Each job spends a Þxed amount of time c in each station, known as the production cycle. This production system is synchronous or paced because jobs move one station forward synchronously, every c time units. To ensure that all required work is performed in precisely c periods, the appropriate number of workers is assumed to be known for every task in each station. Hence, each job is speciÞed by an m-tuple of workforce requirements. We are interested in “level” workforce schedules where workforce size ßuctuations are minimal during the production horizon. In this article we deÞne level workforce scheduling objectives and analyze the complexity status of the associated problems. We Þnd that most of these problems are NP-complete even when m = 2.