供应提前期和需求不确定下库存系统的随机比较

本文研究供应提前期和需求不确定下包含最小化成本和最大化利润的一致化报童问题中随机比较实现的充分条件,并通过随机比较定量刻画提前期和需求不确定性对库存系统决策和利润的影响。首先引入报童收益函数,给出其优化前后满足随机占优及拉普拉斯变换序的充分条件。进一步,在周期需求服从指数分布的情形下,定量刻画固定提前期与提前期服从几何分布两种情况的随机单调性。最后,将上述结论应用到报童模型中,得到提前期需求对一致化报童问题的随机单调性。     

需求依赖销售努力库存系统的随机比较

研究需求依赖销售努力库存系统中需求不确定性对系统最优订货量、利润和销售努力的影响.对一般需求模型给出期望利润关于订货量和努力水平为联合凹的充分条件,证明期望利润函数的超模性质.对加乘需求模型证明系统最优利润和最优努力水平都可由一类与需求分布有关的广义TTT变换来表示.通过引入定义在不同支撑分布集合上一阶、二阶和三阶随机占优,得到广义TTT变换之差与二阶和三阶随机占优之间的关系式,建立了比较库存系统最优利润或努力水平的理论基础.在一阶和二阶随机占优意义下对加乘需求模型得到比较系统最优利润和努力水平的充分条件或充分必要条件.进一步,证明存在一类需求分布当系统关键比(或市场价格)足够大时系统最优利润和努力水平随需求可变性的增加而增加.最后给出几个数值例子验证了研究结果.     

过度自信和需求不确定性对多报童模型的影响

研究在竞争条件下过度自信和需求不确定性对库存决策的影响.通过引入一个均值相等且方差缩小的变换来定量刻画决策者的过度自信偏好,得到系统最优订货量关于报童数量和过度自信系数的单调性.进一步,研究需求不确定性对系统的影响,证明随机大的需求导致较高的最优订货量.当需求分布为均匀分布时,对割准则序意义下系统最优订货量进行比较.     

一类二阶非线性时滞微分方程的振动性

利用广义的Riccati变换、积分均值等方法,讨论了一类二阶非线性时滞微分方程的振动性,建立了方程所有解振动的充分条件,改进和推广了已有文献中的某些结论,并给出了两个数值实例说明主要结果.     

报童问题及其商业拓展的两类利润期望模型

基于会计利润与经济利润的不同意义和经济利润在经济管理中的重要性,明确区分并解释了离散型随机需求量报童问题及其商业拓展的这两类利润期望,得出了随机需求量取值个数有限的报童问题及其商业拓展的会计利润期望模型和经济利润期望模型及其利润期望最大化进货量的计算关系式;着重区分了相应的显性成本期望和隐性成本期望;指出求解此类问题运筹学的处理方法与经济学原理并不相悖.     

可追加订购的报童问题

研究带有追加 (两次 )订购的报童模型 ,分析了此模型与经典 (一次订购 )报童模型的收益关系 ,服务水平评价 ,订购量与需求均值、方差、价格等的灵敏度及发现了在适当的条件下 ,最大追加订购量 M的最优解存在 ,且给出了求解的方法 .     

Banach空间中的广义Dunkl-Williams常数及其性质

本文给出了广义Dunkl-Williams常数与一些著名几何常数例如凸系数、光滑系数、James常数之间的关系,从而得到一些蕴含不动点性质的充分条件,另外通过广义Dunkl-Williams常数的上下界的估计给出了Banach空间一致非方的刻画.     

广义正态分布次序统计量的随机序比较（英文）

本文研究了广义正态分布的次序统计量的随机序关系,通过参数矩阵和参数向量优化序给出了随机序关系成立的充分条件,并证明这些条件在某些情形下也是必要条件.     

基于预期的损失厌恶的“报童式”推理

利用Koszegi与Rabin的参照依赖效用函数对报童问题进行了研究,不仅求得基于预期的损失厌恶报童的最优订货量而且讨论了它的性质.研究发现,基于预期的损失厌恶的报童的订货量要低于利润最大化的报童的订货量,而且,基于预期的损失厌恶的报童的订货量随预期利润、损失厌恶程度的增加而减少.     

随机模糊需求报童问题

考虑到需求的随机模糊性,建立了随机模糊需求报童的利润模型。利用可信性测度理论给出了其期望利润模型,并揭示了期望利润函数的凹性,证明了最优订货量的存在性和唯一性。结合随机模糊模拟技术和随机扰动近似算法设计了求解最优订货量的混合算法。最后,通过数值算例说明了算法的有效性。     

Stability and monotonicity in newsvendor situations

This study considers a supply chain that consists of n retailers, each of them facing a newsvendor problem, and a supplier. Groups of retailers might increase their expected joint profit by joint ordering and inventory centralization. However, we assume that the retailers impose some level of stock that should be dedicated to them. In this situation, we show that the associated cooperative game has a non-empty core. Afterwards, we concentrate on a dynamic situation, where several model cost parameters and the retailers’ dedicated stock levels can change. We investigate how the profit division might be affected by these changes. We focus on four monotonicity properties. We identify several classes of games with retailers, where some of the monotonicity properties hold. Moreover, we show that pairs of cooperative games associated with newsvendor situations do not necessarily satisfy these properties in general, when changes in dedicated stock levels are in concern.     

On Equivalent Equilibrium Problems

We give sufficient conditions for the equivalence between two equilibrium problems. In particular we deduce that, under suitable assumptions, an equilibrium problem has an equivalent reformulation as a generalized variational inequality. Such conditions are satisfied when the equilibrium bifunction is lower semicontinuous, coercive and quasiconvex with respect to the second variable. We also show that the equivalent generalized variational inequality inherits the same generalized monotonicity properties of the original nonconvex equilibrium problem.     

A benchmark solution for the risk-averse newsvendor problem

In this paper, we derive the first order conditions for optimality for the problem of a risk-averse expected-utility maximizer newsvendor. We use these conditions to solve a special case where the utility function is any increasing differentiable function, and the random demand is uniformly distributed. This special case has a simple closed form solution and therefore it provides an insightful and practical interpretation to the optimal point. We show some properties of the solution and also demonstrate how it can be used for assessing the newsvendor utility function parameters.     

Monotonicity properties of wholesale price contracts

This paper contributes to the supply chain contracts literature in economics and operations by performing qualitative sensitivity analysis of a wholesale price contract in a two-echelon supply chain setting. Order-theory tools are used to derive sufficient conditions for monotonicity of contract parameters.The upstream supplier is modeled as a Stackelberg leader. The supplier is assumed to have complete information about the costs and revenue function of the downstream retailer. It is shown that an equilibrium wholesale price weakly increases with an increase in the supplier production cost rate, but it may increase or decrease with an increase in the retailer cost rate. As either the supplier production cost or the retailer cost increases, the supplier profit decreases weakly. Additional sensitivity analysis is performed assuming certain properties of the retailer revenue function.Several well-known results in the supply chain contracting literature can be considered as special cases of the more general theorems developed here. In particular, this paper reexamines the analysis of a newsvendor supply chain problem by Lariviere and Porteus [Lariviere, M.A., Porteus, E.L., 2001. Selling to the newsvendor: An analysis of price-only contracts. Manufacturing & Service Operations Management 3, 293–305]. This paper generalizes and extends their work, by establishing properties of the newsvendor demand distribution that guarantee monotonicity of the contract parameters, without requiring a unique contract solution.     

The stochastic ordering of mean-preserving transformations and its applications

The stochastic variability measures the degree of uncertainty for random demand and/or price in various operations problems. Its ordering property under mean-preserving transformation allows us to study the impact of demand/price uncertainty on the optimal decisions and the associated objective values. Based on Chebyshev’s algebraic inequality, we provide a general framework for stochastic variability ordering under any mean-preserving transformation that can be parameterized by a single scalar, and apply it to a broad class of specific transformations, including the widely used mean-preserving affine transformation, truncation, and capping. The application to mean-preserving affine transformation rectifies an incorrect proof of an important result in the inventory literature, which has gone unnoticed for more than two decades. The application to mean-preserving truncation addresses inventory strategies in decentralized supply chains, and the application to mean-preserving capping sheds light on using option contracts for procurement risk management.     

Monotonieeigenschaften des Steffensen-Verfahrens

Steffensen's method is slightly generalized by introducing a real parameter. In this way one can get different monotonicity properties, depending on the choice of this parameter. These monotonicity statements give the possibility of bracketing the solution of a given problem. In a special case they even ensure the convergence and the existence of a solution. Furthermore there are given sufficient conditions, which show that Steffensen's method converges at least as quickly as Newton's method. A numerical example shows the efficiency of the theorems and compares Steffensen's and Newton's method.

     

Optimality of monotonic policies for two-action Markovian decision processes,with applications to control of queues with delayed information

We consider a discrete-time Markov decision process with a partially ordered state space and two feasible control actions in each state. Our goal is to find general conditions, which are satisfied in a broad class of applications to control of queues, under which an optimal control policy is monotonic. An advantage of our approach is that it easily extends to problems with both information and action delays, which are common in applications to high-speed communication networks, among others. The transition probabilities are stochastically monotone and the one-stage reward submodular. We further assume that transitions from different states are coupled, in the sense that the state after a transition is distributed as a deterministic function of the current state and two random variables, one of which is controllable and the other uncontrollable. Finally, we make a monotonicity assumption about the sample-path effect of a pairwise switch of the actions in consecutive stages. Using induction on the horizon length, we demonstrate that optimal policies for the finite- and infinite-horizon discounted problems are monotonic. We apply these results to a single queueing facility with control of arrivals and/or services, under very general conditions. In this case, our results imply that an optimal control policy has threshold form. Finally, we show how monotonicity of an optimal policy extends in a natural way to problems with information and/or action delay, including delays of more than one time unit. Specifically, we show that, if a problem without delay satisfies our sufficient conditions for monotonicity of an optimal policy, then the same problem with information and/or action delay also has monotonic (e.g., threshold) optimal policies.