On the Effects of Risk Pooling in Supply Chain Management： Review and Extensions

The primary challenge in supply chain management （SCM） is matching supply with uncertain demand. Risk pooling is an efficient and promising strategy to meet this challenge by reducing the underlying demand uncertainty through aggregation. The main focus of this paper is to analyze the effects of risk pooling under different supply chain settings. There are two main contributions. First, we propose a mathematical framework which serves the multi-purpose of （1） unifying existing models on risk pooling in the literature, （2） providing new facets and insights of understanding existing results on risk pooling, and （3） setting up new ground for extending existing models and results. Second; we investigate one interesting effect of risk pooling, namely, the decreasing marginal return （or supermodularity）. We show that there are decreasing marginal returns in risk pooling practices under certain conditions, specifically when the demand is independent and identically distributed （I.I.D.） and normally distributed.     

Coordinating pricing and inventory control in a fluctuating environment

This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.     

Optimal policies for inventory systems with discretionary sales, random yield and lost sales

We determine replenishment and sales decisions jointly for an inventory system with random demand, lost sales and random yield. Demands in consecutive periods are independent random variables and their distributions are known. We incorporate discretionary sales, when inventory may be set aside to satisfy future demand even if some present demand may be lost. Our objective is to minimize the total discounted cost over the problem horizon by choosing an optimal replenishment and discretionary sales policy. We obtain the structure of the optimal replenishment and discretionary sales policy and show that the optimal policy for finite horizon problem converges to that of the infinite horizon problem. Moreover, we compare the optimal policy under random yield with that under certain yield, and show that the optimal order quantity （sales quantity） under random yield is more （less） than that under certain yield.     

Implicit Sampling, with Application to Data Assimilation

There are many computational tasks, in which it is necessary to sample a given probability density function (or pdf for short), i.e., to use a computer to construct a sequence of independent random vectors x i (i = 1, 2, ··· ), whose histogram converges to the given pdf. This can be difficult because the sample space can be huge, and more importantly, because the portion of the space, where the density is significant, can be very small, so that one may miss it by an ill-designed sampling scheme. Indeed, Markovchain Monte Carlo, the most widely used sampling scheme, can be thought of as a search algorithm, where one starts at an arbitrary point and one advances step-by-step towards the high probability region of the space. This can be expensive, in particular because one is typically interested in independent samples, while the chain has a memory. The authors present an alternative, in which samples are found by solving an algebraic equation with a random right-hand side rather than by following a chain; each sample is independent of the previous samples. The construction in the context of numerical integration is explained, and then it is applied to data assimilation.     

Populations with individual variation in dispersal in heterogeneous environments: Dynamics and competition with simply diffusing populations

We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reactiondiffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".     

Bifurcations and chaos in Duffing equation with damping and external excitations

Duffng equation with damping and external excitations is investigated.By using Melnikov method and bifurcation theory,the criterions of existence of chaos under periodic perturbations are obtained.By using second-order averaging method,the criterions of existence of chaos in averaged system under quasi-periodic perturbations forff=nω+εσ,n=2,4,6(whereσis not rational toω)are investigated.However,the criterions of existence of chaos for n=1,3,5,7-20 can not be given.The numerical simulations verify the theoretical analysis,show the occurrence of chaos in the averaged system and original system under quasiperiodic perturbation for n=1,2,3,5,and expose some new complex dynamical behaviors which can not be given by theoretical analysis.In particular,the dynamical behaviors under quasi-periodic perturbations are different from that under periodic perturbations,and the period-doubling bifurcations to chaos has not been found under quasi-periodic perturbations.     

Optimal policy for brownian inventory models with general convex inventory cost

We study an inventory system in which products are ordered from outside to meet demands, and the cumulative demand is governed by a Brownian motion. Excessive demand is backlogged. We suppose that the shortage and holding costs associated with the inventory are given by a general convex function. The product ordering from outside incurs a linear ordering cost and a setup fee. There is a constant leadtime when placing an order. The optimal policy is established so as to minimize the discounted cost including the inventory cost and ordering cost.     

One-step estimation for varying coefficient models

A one-step method is proposed to estimate the unknown functions in the varying coefficient models, in which the unknown functions admit different degrees of smoothness. In this method polynomials of different orders are used to approximate unknown functions with different degrees of smoothness. As only one minimization operation is employed, the required computation burden is much less than that required by the existing two-step estimation method. It is shown that the one-step estimators also achieve the optimal convergence rate. Moreover this property is obtained under conditions milder than that imposed in the two-step estimation method. More importantly, as only one minimization operation is employed, the full asymptotic properties, not only the asymptotic bias and variance, but also the asymptotic distributions of the estimators can be derived. The asymptotic distribution results will play a key role for making statistical inference.     

A copula-based approximation to Markov chains

The Markov chain is well studied and widely applied in many areas.For some Markov chains,it is infeasible to obtain the explicit expressions of their corresponding finite-dimensional distributions and sometimes it is time-consuming for computation.In this paper,we propose an approximation method for Markov chains by applying the copula theory.For this purpose,we first discuss the checkerboard copula-based Markov chain,which is the Markov chain generated by the family of checkerboard copulas.This Markov chain has some appealing properties,such as self-similarity in copulas and having explicit forms of finite-dimensional distributions.Then we prove that each Markov chain can be approximated by a sequence of checkerboard copula-based Markov chains,and the error bounds of the approximate distributions are provided.Employing the checkerboard copula-based approximation method,we propose a sufficient condition for the geometric β-mixing of copula-based Markov chains.This condition allows copulas of Markov chains to be asymmetric.Finally,by applying the approximation method,analytical recurrence formulas are also derived for computing approximate distributions of both the first passage time and the occupation time of a Markov chain,and numerical results are listed to show the approximation errors.     

OPTIMAL DELAUNAY TRIANGULATIONS

The Delaunay triangulation, in both classic and more generalized sense, is studied in this paper for minimizing the linear interpolation error (measure in L^P-norm) for a given function. The classic Delaunay triangulation can then be characterized as an optimal triangulation that minimizes the interpolation error for the isotropic function ‖x‖^2 among all the triangulations with a given set of vertices. For a more general function, a functiondependent Delaunay triangulation is then defined to be an optimal triangulation that minimizes the interpolation error for this function and its construction can be obtained by a simple lifting and projection procedure. The optimal Delaunay triangulation is the one that minimizes the interpolation error among all triangulations with the same number of vertices, i.e. the distribution of vertices are optimized in order to minimize the interpolation error. Such a function-depend entoptimal Delaunay triangulation is proved to exist for any given convex continuous function.On an optimal Delaunay triangulation associated with f, it is proved that △↓f at the interior vertices can be exactly recovered by the function values on its neighboring vertices.Since the optimal Delaunay triangulation is difficult to obtain in practice, the concept of nearly optimal triangulation is introduced and two sufficient conditions are presented for a triangulation to be nearly optimal.     

数量折扣契约下基于成本分担的供应链突发事件协调应对

突发事件会增加供应链成本,如何进行成本分担是决定供应链能否协调应对突发事件的重要因素.用参数分别描述市场需求剧增时增加的生产成本和市场需求剧减时发生的多余产品处理成本,在数量折扣契约基础上,研究突发事件发生后制造商的最优批发价格和零售商的最优订货量,分析其影响因素比较突发事件发生前后包括市场剧增与市场剧减两种情况下的差异,并给出了数值算例.结果表明,成本分担系数和市场需求分布及其变化都会影响最优批发价格和最优订货量,只要根据市场需求变化相应调整契约参数并合理分担由突发事件增加的成本,通过数量折扣契约供应链就能够协调应对突发事件.     

回购契约下闭环供应链对突发事件的协调应对

在回购契约下,可以实现闭环供应链的协调。然而突发事件发生造成零售商面临的需求分布变化时,闭环供应链的销售活动将受到影响,闭环供应链的协调将被打破;但是闭环供应链的废旧品回收活动却不受突发事件的影响。为此,给出了闭环供应链对突发事件的最优应对策略,并调整了原来的回购契约使其能协调应对突发事件,并且使调整后的回购契约也能实现突发事件前闭环供应链的协调。     

突发事件下需求信息不对称时的供应链协调应对

协调供应链系统使其具有抗突发事件性的研究是供应链管理的核心议题之一。为了分析突发事件下需求信息不对称时的供应链协调问题,考虑由一个制造商和一个零售商组成的供应链,在随机市场需求下,首先分析了数量折扣契约对供应链的协调作用;然后探讨了突发事件导致市场需求发生变化且变化后的需求信息是不对称信息时数量折扣契约对供应链的协调作用,研究表明:基准的数量折扣契约对突发事件下的供应链不再发挥协调作用,为此,给出了供应链应对突发事件的最优应对策略,并调整了原来的数量折扣契约使其具有抗突发事件性。最后,应用一个算例对比加以说明。     

信息不对称下多因素波动的应急数量弹性契约

考虑突发事件导致市场需求大幅波动、市场价格随机波动,构建生产成本信息不对称时应急供应链的数量弹性契约模型,寻找最优定价及订货策略;与完全信息情形对比,分析突发事件的信息共享及其对供应链最优决策的影响程度。研究发现,在生产成本信息不对称情形下,突发事件发生时,虽然零售商设计的数量弹性契约可以有效体现真实生产成本,但对供应链协调不起作用。同时,如果市场需求规模缩减,制造商表现出隐藏信息行为,可以促使供应链整体效益增加。最后通过算例验证了这些结论。     

Demand disruption and coordination of the supply chain with a dominant retailer

This paper develops two coordination models of a supply chain consisting of one manufacturer, one dominant retailer and multiple fringe retailers to investigate how to coordinate the supply chain after demand disruption. We consider two coordination schedules, linear quantity discount schedule and Groves wholesale price schedule. We find that, under the linear quantity discount schedule, the manufacturer only needs to adjust the maximum variable wholesale price after demand disruption. For each case of the disrupted amount of demand, the higher the market share of the dominant retailer, the lower its average wholesale price and the subsidy will be under the linear quantity discount schedule, while the higher its fraction of the supply chain’s profit will be under Groves wholesale price schedule. When the increased amount of demand is very large and production cost is sufficiently low, linear quantity discount schedule is better for the manufacturer. However, when the production cost is sufficiently large, Groves wholesale price schedule is always better. We also find that the disrupted amount of demand largely affects the allocation of the supply chain’s profit.     

Coordinating a three-echelon fresh agricultural products supply chain considering freshness-keeping effort with asymmetric information

This paper studies the coordination problem of a three-echelon supply chain system consisting of one supplier, third-party logistics service providers (TPLSP) and one retailer that provides seasonal fresh agricultural products to customers. The market demand for the retailer is assumed to be influenced by the retail price, the product's freshness and other random variables. Both quantity and quality losses are viewed as endogenous variables of the freshness-keeping effort, which is decided by the TPLSP. Dynamic game models for both the decentralized decision mode and the centralized decision mode are developed, and asymmetric demand information is considered in the decentralized decision mode. The analysis shows that decentralized decision making could result in the distortion of the order quantity and selling price and could ultimately result in a loss of supply chain profit. The TPLSP is motivated to exaggerate the demand, which could seriously damage the supplier's interests. Based on an analysis of the major influencing factors in the supply chain system, a coordination contract based on cost and revenue sharing (RS) is designed for the two transaction processes in the three-echelon supply chain system. We illustrate the proposed models with a numerical study and conduct a sensitivity analysis of some of the key parameters in the models. It is proven that with the designed contract, the sales volume can be significantly expanded, all the supply chain members can benefit from Pareto improvement, and both the retailer and the TPLSP have no incentive to exaggerate the market demand.     

基于质量分级的生鲜农产品供应链的定价与保鲜策略研究

为了有效降低生鲜农产品损耗,保障流通与销售过程中生鲜农产品的品质及安全,解决消费者对生鲜农产品品质及其新鲜度的高追求与生鲜农产品冷链物流成本过高导致保鲜投入不足之间的矛盾,文中以价格和新鲜度为市场需求的主要影响因素,分别在产销地均不分级、销地分级和产地分级三种质量分级模式下,构建了供应商和零售商的利润函数,采用stackelberg博弈求解得到各自的最优定价策略和最优保鲜策略.对不同质量分级模式下的定价策略和保鲜策略进行对比分析显示,产地分级模式下的定价策略有利于增加市场需求及市场主体的利润;产地分级模式下的保鲜策略在控制损耗的效果和控制保鲜的成本上都优于其他模式.     

目标回扣契约下供应链对突发事件的协调应对

本文的目的就是要研究当突发事件造成需求的市场分布发生变化时,供应链如何运用目标回扣契约进行协调应对.通过设置目标回扣契约参数,分别获得了需求突发下,集权供应链和分权供应链协调的条件.并且,研究结果表明,当突发事件造成需求的市场规模变化不是很大时,分权供应链仅通过调整目标回扣契约就能实现供应链的协调应对;当突发事件造成市场规模变化很大时,则需要采取调整目标回扣契约和改变生产计划两种策略来协调应对.这些结论,为供应链应急管理提供了一种新的应对策略.     

考虑零售商促销策略的供应链融资及运营策略研究

当零售商的促销策略影响商品市场需求时,本文将促销分摊决策嵌入到经典报童模型,在银行信用与商业信用两种不同的融资模式下,对供应商及供应链整体的利润进行分析。研究发现:当零售商的行为对市场需求有影响时,商业信用在一定程度上减少了供应链的融资成本,增加了供应链的利润;核心企业的融资策略与自身成本及促销分摊策略有关;商业信用对供应链资本配置及零售商的激励,受供应商生产成本及激励策略的影响;商业信用在一定程度上减少了双重边际化效应。     

Random yield supply chain with a yield dependent secondary market

This paper considers a simple supply chain with one supplier and one retailer where the supplier’s production is subject to random yield and the retailer faces uncertain demand. There exists a secondary market for acquiring or disposing products by the supplier. We study both the centralized and decentralized systems. In the decentralized system, a no risk sharing contract and a risk sharing minimum commitment contract are analyzed. The supply chain with the risk sharing contract is further analyzed with a constant secondary market price and a yield dependent secondary market price. We present both the supplier’s and the retailer’s optimal strategies and provide insights for managers when making decisions under random yield risk and demand uncertainty. We find that the secondary market generally has a positive impact on supply chain performance and the actual effect of random yield risk on the supply chain performance depends on cost parameters and supply chain contract settings. Under certain conditions, reducing yield randomness may weaken the double marginalization effect and improve the chain performance. From the numerical study, we also show that there exists an optimal commitment level for the supply chain.