The service facility startup and capacity model and its application to the National Cranberry case

This paper provides formal modeling for and analytical aid to the startup and capacity problem facing Receiving Plant 1 of National Cranberry Cooperative. The analysis is based on a finite-horizon, single-facility queueing system with general variability. Using marginal analysis, we derive simple formulae that the optimal starting time and processing capacity should satisfy. These formulae lead to the comparative statics results showing that the starting time should be optimally delayed or the processing capacity optimally decreased when the operating cost increases, when the waiting cost decreases, when the cumulative arrival process decreases, or when the capacity of storage increases. We then demonstrate that three important performance measures, the expected waiting, tardiness, and operating costs, are jointly convex with respect to two control variables, starting time and processing capacity, in a generalized version of the model. Therefore, in the applications that involve minimizing these measures, the simple formulae derived from first-order conditions are necessary and sufficient for optimality. The applications for the model in service and manufacturing operations are numerous.