Confidence Intervals for Data-Driven Inventory Policies with Demand Censoring

We revisit the classical dynamic inventory management problem of Scarf (1959b) from the perspective of a decision-maker who has n historical selling seasons of data and must make ordering decisions for the upcoming season. We develop a nonparametric estimation procedure for the (*S; s*) policy that is consistent, then characterize the finite-sample properties of the estimated (*S; s*) levels by deriving their asymptotic confidence intervals. We also consider having at least some of the past selling seasons of data censored from the absence of backlogging, and show that the intuitive procedure of first correcting for censoring in the demand data yields inconsistent estimates. We then show how to correctly use the censored data to obtain consistent estimates and derive asymptotic confidence intervals for this policy using Stein’s method. We further show the confidence intervals can be used to effectively bound the difference between the expected total cost of an estimated policy and that of the optimal policy. We validate our results with extensive computations on simulated data. Our results extend to the repeated newsvendor problem and the base-stock policy problem by appropriate parameter choices

On the Stability of Positive Semigroups

International audienceThe stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive andpossibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to a class of time-varying positive semigroups. In the context of time-homogeneous models, the regularity conditions discussed in the present article appear to be necessary and sufficient condition for the existence of leading eigenvalues. We review and illustrate the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and signal processing

Heat Transfer

Over the past few decades there has been a prolific increase in research and development in area of heat transfer, heat exchangers and their associated technologies. This book is a collection of current research in the above mentioned areas and describes modelling, numerical methods, simulation and information technology with modern ideas and methods to analyse and enhance heat transfer for single and multiphase systems. The topics considered include various basic concepts of heat transfer, the fundamental modes of heat transfer (namely conduction, convection and radiation), thermophysical properties, computational methodologies, control, stabilization and optimization problems, condensation, boiling and freezing, with many real-world problems and important modern applications. The book is divided in four sections : "Inverse, Stabilization and Optimization Problems", "Numerical Methods and Calculations", "Heat Transfer in Mini/Micro Systems", "Energy Transfer and Solid Materials", and each section discusses various issues, methods and applications in accordance with the subjects. The combination of fundamental approach with many important practical applications of current interest will make this book of interest to researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modelling, inverse problems, implementation of recently developed numerical methods in this multidisciplinary field as well as to experimental and theoretical researchers in the field of heat and mass transfer