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This paper explores the classic single-item newsvendor problem under a novel setting which combines temporal dependence and tractable robust optimization. First, the demand is modeled as a time series which follows an autoregressive process AR(p), p ≥ 1. Second, a robust approach to maximize the worst-case revenue is proposed: a robust distribution-free autoregressive forecasting method, which copes with non-stationary time series, is formulated. A closed-form expression for the optimal solution is found for the problem for p = 1; for the remaining values of p, the problem is expressed as a nonlinear convex optimization program, to be solved numerically. The optimal solution under the robust method is compared with those obtained under two versions of the classic approach, in which either the demand distribution is unknown, and assumed to have no autocorrelation, or it is assumed to follow an AR(p) process with normal error terms. Numerical experiments show that our proposal usually outperforms the previous benchmarks, not only with regard to robustness, but also in terms of the average revenue.

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In this article we describe a method for carrying out Bayesian estimation for the double Pareto lognormal (dPlN) distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the $\mathit{dPlN}/M/1$ and $M/\mathit{dPlN}/1$ queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the $\mathit{Pareto}/M/1$ system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS336 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org