Scheduling workforce and workflow in a high volume factory

We define a high volume factory to be a connected network of workstations, at which assigned workers process work-in-progress that flows at high rates through the workstations. A high rate usually implies that each worker processes many pieces per hour, enough so that work can be described as a deterministic hourly flow rate rather than, say, a stochastic number of discrete entities. Examples include mail processing and sorting, check processing, telephoned order processing, and inspecting and packaging of certain foods. Exogenous work may enter the factory at any workstation according to any time-of-day profile. Work-in-progress flows through the factory in discrete time according to Markovian routings. Workers, who in general are cross-trained, may work part time or full time shifts, may start work only at designated shift starting times, and may change job assignments at mid shift. In order to smooth the flow of work-in-progress through the service factory, work-in-progress may be temporarily inventoried (in buffers) at work stations. The objective is to schedule the workers (and correspondingly, the workflow) in a manner that minimizes labor costs subject to a variety of service-level, contractual and physical constraints. Motivated in part by analysis techniques of discrete time linear time-invariant systems, an object-oriented linear programming model is developed. Using exogenous input work profiles typical of large US mail processing facilities, illustrative computational results are included.