One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

A class of Markov chains we call successively lumbaple is specified for which it is shown that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains. Each of the latter chains has a(typically much) smaller state space and this yields significant computational improvements. We discuss how the results for discrete time Markov chains extend to semi-Markov processes and continuous time Markov processes. Finally, we will study applications of successively lumbaple Markov chains to classical reliability and queueing models.

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

The purpose of this study is two-fold. First, we investigate further properties of the second-order regular variation (2RV). These properties include the preservation properties of 2RV under the composition operation and the generalized inverse transform, among others. Second, we derive second-order expansions of the tail probabilities of convolutions of non-independent and identically distributed (i.i.d.) heavy-tail random variables, and establish second-order expansions of risk concentration under mild assumptions. The main results extend some ones in the literature from the i.i.d. case to non-i.i.d. case.

We analyze the asymptotic number of items chosen in a selection procedure. The procedure selects items whose rank among all previous applicants is within the best 100p percent of the number of previously selected items. We use analytic methods to obtain a succinct formula for the first-order asymptotic growth of the expected number of items chosen by the procedure.

The normalized importance sampling estimator allows the target density f to be known only up to a multiplicative constant. We indicate how it can be derived by a delta method-based approximation of a Rao–Blackwellized acceptance rejection estimator. Using additional terms in the delta method then results on a new estimator that also only requires f to be known only up to a multiplicative constant. Numerical examples indicate that the new estimator usually outperforms the normalized importance sampling estimator in terms of mean square error.

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

We consider the problem of dynamic multi-skill routing in call centers. Calls from different customer classes are offered to the call center according to a Poisson process. The agents are grouped into pools according to their heterogeneous skill sets that determine the calls that they can handle. Each pool of agents serves calls with independent exponentially distributed service times. Arriving calls that cannot be served directly are placed in a buffer that is dedicated to the customer class. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on approximate dynamic programming techniques. In particular, we perform one-step policy improvement using a polynomial approximation to relative value functions. We compare the performance of this method with decomposition techniques. Numerical experiments demonstrate that our method outperforms leading routing policies and has close to optimal performance.

This paper introduces two statistics that assess whether (or not) a sequence sampled from a stationary time-homogeneous Markov chain on a finite state space is reversible. The test statistics are based on observed deviations of transition sample counts between each pair of states in the chain. First, the joint asymptotic normality of these sample counts is established. This result is then used to construct two chi-squared-based tests for reversibility. Simulations assess the power and type one error of the proposed tests.