Multiple shift workforce lower bounds

Previous lower bounds on workforce size have been derived from the consideration that the number of working shifts which can be provided by the workers over a given period of time must be at least as large as the number of working shifts required by the staffing demands over that period. None of those bounds incorporates the effect of constraints on the changing of shifts in a multiple shift manpower scheduling problem. This paper utilizes a network model of the problem to model its multiple shift aspect and provide new lower bounds on workforce size. For some common special cases of constraints these lower bounds can be calculated by hand. For some common special cases of demands the multiple shift lower bounds degenerate to the single shift lower bounds.