Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015     

Dynamic necking of a near α titanium alloy at high strain rates:Experiments and modelling

The tensile behaviour of near α Ti3Al2.5 V alloy, conceived for applications in aerospace and automotive engineering, is characterized from quasi-static to high strain rates. The material is found to present noticeable strain rate sensitivity. The dynamic true strain rate in the necking cross-section reaches values up to ten times higher than the nominal strain rate. It is also observed that beyond necking the dynamic true stress-strain curves present limited rate dependence. The experimental results at different strain rates are used to determine a suitable constitutive model for finite element simulations of the dynamic tensile tests. The model predicts the experimentally macroscopic force-time response, true stress-strain response and effective strain rate evolution with good agreement.