Economics Insights @ CBS

This paper establishes connections between two derivative estimation techniques: infinitesimal perturbation analysis (IPA) and the likelihood ratio or score function method. We introduce a systematic way of expanding the domain of the former to include that of the latter, and show that many likelihood ratio derivative estimators are IPA estimators obtained in a consistent manner through a special construction. Our extension of IPA is based on multiplicative smoothing.

Customers, in a Poisson stream at rate A, enter an infinite-server queue. Customer service times are independent and uniformly distributed on [0, s], s > 0. Gated service is performed in stages as follows. A stage begins with all customers transferred from the queue to the servers. The servers then begin serving these customers, all simultaneously. The stage ends when the service of all customers is complete. At this point, the next stage begins if the queue is nonempty.

We consider inventory systems with several distinct items. Demands occur at constant, item specific rates. The items are interdependent because of jointly incurred fixed procurement costs: The joint cost structure reflects general economies of scale, merely assuming a monotonicity and concavity (submodularity) property. Under a power-of-two policy each item is replenished with constant reorder intervals which are power-of-two multiples of some fixed or variable base planning period.