Optimal production and rationing decisions in supply chains with information sharing

This paper considers a two-echelon capacitated supply chain with two non-identical retailers and information sharing. We characterize the optimal inventory policies. We also study the benefits of the optimal stock rationing policy over the first come first served (FCFS) and the modified echelon-stock rationing (MESR) policies.     

Growth of Lévy trees

We construct random locally compact real trees called Lévy trees that are the genealogical trees associated with continuous-state branching processes. More precisely, we define a growing family of discrete Galton–Watson trees with i.i.d. exponential branch lengths that is consistent under Bernoulli percolation on leaves; we define the Lévy tree as the limit of this growing family with respect to the Gromov–Hausdorff topology on metric spaces. This elementary approach notably includes supercritical trees and does not make use of the height process introduced by Le Gall and Le Jan to code the genealogy of (sub)critical continuous-state branching processes. We construct the mass measure of Lévy trees and we give a decomposition along the ancestral subtree of a Poisson sampling directed by the mass measure. T. Duquesne is supported by NSF Grants DMS-0203066 and DMS-0405779. M. Winkel is supported by Aon and the Institute of Actuaries, EPSRC Grant GR/T26368/01, le département de mathématique de l’Université d’Orsay and NSF Grant DMS-0405779.     

随机环境中分枝过程的等价定理

给定了随机环境中分枝过程(BPRE)的精确定义,讨论了有关的可测性问题和BPRE的基本性质．在此基础上,证明了BPRE的一个等价定理．     

Allocating unfunded liability in pension valuation under uncertainty

This paper studied the cost allocation for the unfunded liability in a defined benefit pension scheme incorporating the stochastic phenomenon of its returns. In the recent literature represented by Cairns and Parker [Insurance: Mathematics and Economics 21 (1997) 43], Haberman [Insurance: Mathematics and Economics 11 (1992) 179; Insurance: Mathematics and Economics 13 (1993) 45; Insurance: Mathematics and Economics 14 (1994) 219; Insurance: Mathematics and Economics 14 (1997) 127], Owadally and Haberman [North American Actuarial Journal 3 (1999) 105], the fund level is modeled based on the plan dynamics and the returns are generated through several stochastic processes to reflect the current realistic economic perspective to see how the contribution changed as the cost allocation period increased. In this study, we generalize the previous constant value assumption in cost amortization by modeling the returns and valuation rates simultaneously. Taylor series expansion is employed to approximate the unconditional and conditional moments of the plan contribution and fund level. Hence the stability of the plan contribution and the fund size under different allocation periods could be estimated, which provide valuable information adding to the previous works.     

On a Polynomial Fractional Formulation for Independence Number of a Graph

In this paper we characterize the local maxima of a continuous global optimization formulation for finding the independence number of a graph. Classical Karush-Kuhn-Tucker conditions and simple combinatorial arguments are found sufficient to deduce several interesting properties of the local and global maxima. These properties can be utilized in developing new approaches to the maximum independent set problem.     

Growth kinetics of iron boride layers: Dimensional analysis

Dimensional analysis is presented as a powerful tool in the study of the paste boriding process. In particular, a dimensional method is used to study the growth kinetics of the boride layers FeB and Fe₂B. Experiments were performed in AISI 1045 steel and AISI M2 steel, to test the suggested model. Samples of 1045 steel were prepared and treated using boron paste thickness of 3-5 mm, at temperatures of 1193, 1223 and 1273 K, with 2, 4 and 6 h of treatment time. The M2 specimens had boron paste thickness of 3 and 4 mm and temperatures of 1223, 1253 and 1273 K for 2 and 6 h. Results indicate that the growth of boron layers obeys power laws of the form y = αx^β, where α and β constants are a function of the material and the interface of interest. Validation of the model was carried out using experimental data with an average error percentage of 7.6% for Fe₂B in 1045 steel, 15.8% for FeB and 3.4% for Fe₂B in M2 steel.     

随机环境下的对称零程过程的大偏差原理

利用相对熵方法及鞅方法给出了随机环境下的对称零程过程的经验测度的收敛速度函数.     

Parking Capacity and Pricing in Park'n Ride Trips: A Continuous Equilibrium Network Design Problem

In this paper we consider the problem of designing parking facilities for park'n ride trips. We present a new continuous equilibrium network design problem to decide the capacity and fare of these parking lots at a tactical level. We assume that the parking facilities have already been located and other topological decisions have already been taken.The modeling approach proposed is mathematical programming with equilibrium constraints. In the outer optimization problem, a central Authority evaluates the performance of the transport network for each network design decision. In the inner problem a multimodal traffic assignment with combined modes, formulated as a variational inequality problem, generates the share demand for modes of transportation, and for parking facilities as a function of the design variables of the parking lots. The objective is to make optimal parking investment and pricing decisions in order to minimize the total travel cost in a subnetwork of the multimodal transportation system.We present a new development in model formulation based on the use of generalized parking link cost as a design variable.The bilevel model is solved by a simulated annealing algorithm applied to the continuous and non-negative design decision variables. Numerical tests are reported in order to illustrate the use of the model, and the ability of the approach to solve applications of moderate size.     

Liouville theorem and coupling on negatively curved Riemannian manifolds

By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds with Ricci curvatures bounded below by a negative function. Indeed, for these manifolds we prove that all harmonic functions (maps) with certain growth are constant. In particular, the well-known Liouville theorem due to Cheng for sublinear harmonic functions (maps) is generalized. Moreover, our results imply the Brownian coupling property for a class of negatively curved Riemannian manifolds. This leads to a negative answer to a question of Kendall concerning the Brownian coupling property.     

Observation of hydrogen induced intermediate borides in PrFeB based alloys by Mössbauer effect spectroscopy

In the present work, a quantitative analysis of the phase compositions by Mössbauer effect spectroscopy of solid and conventional hydrogen disproportionated Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys was carried out. Significant amounts of intermediate borides t-Fe₃B and Pr(Fe, Co)₁₂B₆ were detected after solid hydrogen disproportionation treatment in Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys, respectively. After conventional hydrogenation–disproportionation–desorption–recombination treatment these phases were not detected and in no case residual Pr₂Fe₁₄B-phase was found. It was observed that the amount of intermediate borides after disproportionation can be correlated with the degree of texture after recombination at various temperatures.