Banach空间中微分方程解的存在与唯一性

在一般Banach空间中,作者讨论了微分方程的初值问题u=f(t,u),u(0)=x0.在比文[6]中弱Carathodory条件更弱的情况下,不仅放宽了[6]中的一个重要不等式条件,还去掉了另一与之相关的不等式限制,仍获得了初值问题解的存在与唯一性及解的迭代逼近.对周期边值问题也获得了类似结果.     

Manufacturer-buyer coordination for newsvendor-type-products with two ordering opportunities and partial backorders

In a recent paper [Weng, Z.K., 2004. Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model. European Journal of Operational Research 156, 148–161], a newsvendor-type coordination model was developed for a single-manufacturer single-buyer channel with two ordering opportunities. This paper further extends the model to the case where the excess demand after the first order is partially backlogged and both parties share the manufacturing setup cost of the second order (if happened). We show that the decentralized system would perform best if the manufacturer covers utterly the second production setup cost, which is opposite to that obtained in Weng (2004). Another extension in the present paper is that in the centralized system, the second order decision is made by the buyer based on the channel’s benefit rather than based on the buyer’s benefit as in Weng (2004). It is proved that the expected profit of the system in our paper is always larger than that in Weng (2004). In order to maximize the expected profit of the channel, two coordinated policies are proposed to achieve perfect coordination: a two-part-tariff policy for the special case that the buyer pays all the manufacturing setup cost, and a revised revenue-sharing contract for the case that two parties share the manufacturing setup cost.     

Analysis of GI<Superscript><Emphasis Type="Italic">X</Emphasis></Superscript>/<Emphasis Type="Italic">M</Emphasis>(<Emphasis Type="Italic">n</Emphasis>)//<Emphasis Type="Italic">N</Emphasis> systems with stochastic customer acceptance policy

We investigate GI ^X /M(n)//N systems with stochastic customer acceptance policy, function of the customer batch size and the number of customers in the system at its arrival. We address the time-dependent and long-run analysis of the number of customers in the system at prearrivals and postarrivals of batches and seen by customers at their arrival to the system, as well as customer blocking probabilities. These results are then used to derive the continuous-time long-run distribution of the number of customers in the system. Our analysis combines Markov chain embedding with uniformization and uses stochastic ordering as a way to bound the errors of the computed performance measures.      

一类增算子不动点定理及其应用

利用锥理论和非对称迭代方法,讨论了不具有连续性和紧性条件的增算子方程解的存在唯一性.作为其应用着重讨论了非增算子方程解的存在唯一性,并给出了迭代序列收敛于解的误差估计,改进和推广了某些已知结果.     

Almost sure comparison of birth and death processes with application to M/M/s queueing systems

Given conditions, which concern the infinitesimal parameters of two birth and death processes, the processes are constructed on the same probability space such that one process is almost surely larger than the other. Application is made to M/M/s queueing systems. Stochastic comparisons of queue length and virtual waiting time in two M/M/s systems are obtained.     

一类混合单调算子的不动点定理

运用锥理论与迭代方法,讨论了在较弱条件下一类混合单调算子的不动点的存在唯一性,所得结果是某些已有结果的本质改进和推广.     

K型区间删失数据下参数的置信限

基于K型区间删失数据,利用样本空间排序法给出参数优良的置信下限和计算置信下限的递推公式.     

A two-level supply chain with partial backordering and approximated Poisson demand

We consider a two-level supply chain with a number of identical, independent ‘retailers’ at the lower echelon and a single supplier at the upper echelon controlled by continuous review inventory policy (R, Q). Each retailer experiences Poisson demand with constant transportation times. We assume constant lead time for replenishing supplier orders from an external warehouse to the supplier and unsatisfied retailer orders are backordered in the supplier. We assume that the unsatisfied demand is partially backordered in the identical retailers. The partially backordering policy is implemented in the identical retailers using an explicit control parameter ‘b’ which limits the maximum number of backorders allowed to be accumulated during the lead time. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations, the optimal value of b in the identical retailers and the related accuracy is assessed through simulation.     

Convex Ordering for Random Vectors using Predictable Representation

We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends the results proved in Klein et al. (Electron J Probab 11(20):27, 2006) in the one-dimensional case. We also study a geometric interpretation of convex ordering for discrete measures in connection with the conditions set on the jump heights and intensities of the considered processes. The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 7200108).