Separation of Time Scales and a Hierarchical Approach to Design and Management

We consider the design and management concerns of a service firm whose customers are long-term, take up space, and require occasional assistance; consulting services, nursing homes, and and residential rehabilitation facilities are our motivating examples. These firms must determine and pay for space capacity as well as staffing levels. The space capacity determines how many clients -- or members -- that the firm can accommodate at any given time. The staffing levels determine how quickly members' needs are addressed once they arise.

Through the heuristic investigation of two time and space scalings, we uncover a separation of time scales whereby the internal dynamics of the membership -- involving the arising and resolution of occasional needs -- evolve very fast on the time scale on which the membership size changes by significant amounts. The separation of time scales suggests a decoupling of the system-wide total potential membership process from the internal process that distinguishes between content members and those awaiting attention from the staff. The managerial insight is that staffing and facility decisions can safely be considered separately.