The Impact of Forecast Errors on Staffing Decisions for Service Centers

Providing the right staffing levels is of paramount importance in most service centers. Excess capacity is costly, yet a lack of sufficient capacity leads to unacceptably low service levels which may be even costlier. When determining staffing levels for a service center it is, therefore, essential to develop forecasting for the expected load on the system. Although in practice these forecasts are not perfect, they are often taken to be so. In this paper we explore the impact of ignoring forecast uncertainty, and develop an approach that explicitly incorporates the effects of forecast errors. We model the service center as a queuing system in which the arrival rate is a random variable with known distribution. The manager sets the number of servers to minimize a cost function that includes a variety of terms related to the performance of the system. We show that both the optimal number of servers and the optimal value of the cost function are quite sensitive to the variance of the arrival rate, so the performance of the service center could be significantly suboptimal if a manager ignores forecast uncertainty. In addition we show that the decision and the optimal value of the cost function are quite insensitive to uncertainty in other parameters such as the waiting and reneging costs. Although the optimal value of the cost function is also quite sensitive to the shape of the prior distribution for the arrival rate, a manager can make a near-optimal staffing decision knowing only the first two moments of the distribution of forecast errors