Knowledge that Transforms

Service systems such as call centers and hospitals typically have strongly time-varying arrivals. A natural model for such an arrival process is a nonhomogeneous Poisson process (NHPP), but that should be tested by applying appropriate statistical tests to arrival data. Assuming that the NHPP has a rate that can be regarded as approximately piecewise-constant, a Kolmogorov–Smirnov (KS) statistical test of a Poisson process (PP) can be applied to test for a NHPP by combining data from separate subintervals, exploiting the classical conditional-uniform property. In this paper, we apply KS tests to banking call center and hospital emergency department arrival data and show that they are consistent with the NHPP property, but only if that data is analyzed carefully. Initial testing rejected the NHPP null hypothesis because it failed to account for three common features of arrival data: (i) data rounding, e.g., to seconds; (ii) choosing subintervals over which the rate varies too much; and (iii) overdispersion caused by combining data from fixed hours on a fixed day of the week over multiple weeks that do not have the same arrival rate. In this paper, we investigate how to address each of these three problems.

The benefits of inventory risk pooling are well known and documented. It has been proven in the literature that the expected costs of a centralized system are increasing in the degree of (positive) dependence of demand in an idealized newsvendor setting. Using the supermodular stochastic order to characterize dependence, we study a general two-tiered supply chain structure, in which both demand and supply yields are random, and prove that the expected costs are increasing in the degrees of positive dependence between demand and supply yield loss factors. Furthermore, using a distributionally robust optimization framework, we prove an analogous result for the case where demand and yield distributions are not precisely known.