The Multistage Service Facility Start-Up and Capacity Model

In service industries, operations are often split into the “front office” and the “back room.” The front office deals directly with customers, whereas the back room engages in manufacturing-like operations. While such an arrangement may enjoy many benefits including reduced customer participation and back room efficiency, it gives rise to the possibility of communication and coordination problems between the front office and the back room. To address such coordination problems, we work from one popular piece of case material in operations management, the National Cranberry Cooperative (NCC) case, and develop and analyze a service facility start-up and capacity model based on a finite-horizon, multistage queueing system. The model allows for general variability that can be either stationary or nonstationary, predictable or unpredictable. We derive the relationships between job start and finish times and primitive parameters and control variables using a sample path construction. We then show that two performance measures, the expected waiting and operating costs, have desirable convexity properties with respect to the control variables; namely, the starting time and the processing capacity of each stage. We also show how to perform marginal analysis on start-up times. Numerical examples based on the NCC case are presented and discussed. The model can be extended and applied to many service and manufacturing situations.