基于后悔理论和概率犹豫模糊集的多属性决策方法

由于决策环境的不确定性以及决策问题的复杂性,决策者越来越难以处理不确定型多属性决策的相关问题.针对决策者评估时具有犹豫性和偏好性以及风险规避和后悔规避等特点,提出了一种基于后悔理论和概率犹豫模糊集的多属性决策方法.运用概率犹豫模糊集对专家的评价信息进行表述和处理,在权重属性完全未知的情况下,使用CRITIC法确定属性权重;通过定义决策者对方案的感知效用函数,计算各个方案的总感知效用值并进行排序.最后,通过算例对该方法进行验证分析.结果表明:方法可以更好地刻画决策者的实际心理,决策结果更加客观和科学.     

上升线性需求条件下考虑资金时间价值的变质性物品生产库存模型

变质性物品生产库存系统的研究具有重要实际意义.本文研究了变质性物品生产库存系统在上升趋势线性需求条件下,考虑资金的时间价值,在有限计划时间水平内,如何确定最优生产周期,各周期最优生产率,以及最优库存安排策略.通过本文的研究,得到了一些有用的结论.     

不确定性对混合CVaR约束库存系统的影响

运用应用概率中的随机占优研究需求不确定性对混合CVaR约束库存系统最优订购量和最优利润的影响。引入刻画决策者风险态度的“风险偏好系数”,得到系统最优订购量和最优利润关于风险偏好系数的单调性。研究表明随机大需求总会导致系统较高的最优订购量和最优利润;在割准则序意义下,最优订购量可能随需求可变性的增加而增加也可能随需求可变性的增加而减少;在二阶随机占优且风险偏好系数大于等于1的情况下系统最优利润具有随机单调性,然而当风险偏好系数小于1时最优利润在二阶随机占优意义下的结论不一定成立,我们通过一个数值例子来说明。     

基于合格值自适应后悔理论和证据理论的区间多属性决策方法

针对属性值和权重都用区间描述的不确定性多属性决策问题,文章提出了一种基于合格值自适应后悔理论和证据理论的决策方法.该方法定义属性合格参考值,表示决策者对方案的接受度在该值以下呈现快速下降趋势.之后依据后悔理论,定义基于属性合格参考值的后悔效用函数,改善传统后悔效用函数灵活性弱和对风险规避行为的描述能力不够强的缺点.之后扩展出基于区间的效用计算方法,并基于区间最优点得到感知效用值矩阵.然后将感知效用值转化为基本概率分配函数并据此进行基于权重的证据合成.该方法还通过设定偏好态度系数以反映决策者对评价高低的倾向性.最后,通过算例分析说明了该方法的可行性,合理性和稳定性.     

基于混合CVaR的供应链回购策略优化与协调研究

研究了风险中性供应商与混合CVaR约束零售商构成的两级供应链模型中回购契约协调问题.混合CVaR是由最小化CVaR和最大化CVaR通过加权平均的方式得到的,它包括风险规避,风险中性和风险追求三种特殊情形.引入一个刻画决策者风险态度的"风险偏好系数",证明当风险偏好系数大于1时混合CVaR与前景理论中的损失规避均能刻画决策者对损失的敏感性高于对收益的敏感性.得到零售商最优订货量和最优利润关于风险偏好系数的单调性;证明无论风险偏好系数大于等于1或小于1,回购契约都能实现供应链协调,并推导出实现系统协调时最优契约参数之间的关系.最后结合数值例子验证了供应链回购契约机制的有效性.     

价格竞争下风险规避对闭环供应链决策的影响研究

基于零售商销售价格与回收价格竞争情形,构建了一个可持续的闭环供应链.考虑决策者风险规避行为,研究了闭环供应链成员的定价决策问题.利用博弈论,在风险中性与风险规避特性下分别探讨了批发价格,零售价格和回收价格的最优决策,并建立了它们的表达式.研究结论表明,仅当零售商具有风险规避时,制造商决策不受零售商的影响,而仅当制造商具有风险规避时,零售商决策会受制造商的影响.同时,当二者都具有风险规避特性时,他们之间的决策会相互影响.     

医院医疗器械—麻醉包库存策略

麻醉包对于医院来说是一种重要的医疗物品,具有需求量大,一旦缺货则损失严重等特点,为此研究了黑龙江省某医院麻醉包的库存问题.以存储费用为标准来评价和优选库存策略,共建立了四大库存模型,分别是经济批量EOQ库存模型;需求离散条件下多周期有准备成本库存模型;需求服从正态分布条件下多周期有准备成本库存模型和蒙特卡罗仿真库存控制模型.其中,三个模型得出了结果,通过证明,一个模型不符合医院实际情况.通过比较上述三个模型求得的最优化库存策略与医院实际使用的库存策略,建议采取蒙特卡罗仿真库存控制模型求解得出的结果作为医院方最优库存策略.     

基于损失规避行为的最优保险投资与再保策略选择

保险公司决策者一方面通过投资来实现保险资金的保值增值,另一方面通过再保险业务来控制承保风险.保险投资市场假定是由两种资产构成:一种是无风险资产,另一种是风险资产.与已有研究不同,文章基于累积前景理论,假定保险公司决策者具有损失规避异质性的非理性行为人.保险公司的盈余过程用跳跃扩散过程来刻画,保险公司的决策目标是最大化最终财富的"S"型期望效用,借助于鞅理论将动态的最大化问题转化为静态问题,通过求解静态优化问题得到了最优投资和再保险策略的解析表达式.数值模拟分析了最优策略的动态性质.     

具有两类需求服务的随机库存系统控制策略研究

研究具有两类顾客排队需求服务的随机库存系统.系统采取(s,Q)补货策略且当库存水平下降到安全库存s时,到达的第二类顾客以概率P得到服务.首先,建立库存水平状态转移方程并通过递推算法求解获得库存水平稳态概率分布和系统稳态指标;接下来,构建库存成本函数;最后,采用数值试验的方法研究该库存系统的最优控制策略并考察系统参数的敏感性.     

基于不同风险偏好的退货可再销报童模型研究

考虑退货可再销售的情况下,应用条件风险价值(CVaR),构建纳入不同风险偏好的报童模型,并给出了不同环境下的最优订货量.通过解析和数值仿真,进一步分析了决策者的风险偏好水平、产品退货率以及残值对最优订货量决策的影响.研究结果表明:最优订货量随着决策者风险追逐偏好水平的增加而增加,随着风险规避偏好水平的增加而减小;最优订货量随着退货率的增加而减小,随着产品残值的增加而增加.结合订货决策的实际特点,给出了不同环境下的最优订货量,为决策者提供了全面且动态的决策建议.     

Loss-averse newsvendor problem with supply risk

Modeling the manufacturer as a newsvendor, in this paper we study the ordering decisions of a loss-averse newsvendor with supply and demand uncertainties. Using the stylized newsvendor models, we analyse several key issues, including the effect of the newsvendor’s loss aversion, the effect of demand uncertainty, and the effect of supply uncertainty on the decision maker’s optimal decision under the procurement model, in which the decision maker only pays for the actual quantity received. Through our analysis, we find the following facts: the optimal order quantity decreases with respect to the degree of loss-aversion; the supply uncertainty induces the decision maker to order more than that in a deterministic environment; a stochastically larger demand always results in a larger order quantity and a larger expected utility; the optimal expected utility decreases in the demand volatility while the optimal order quantity may increase or decrease. Moreover, with numerical experiments, we demonstrate that the supply risk negatively affects the utility more than the demand risk does.     

Inventory Problems with Partially Observed Demands and Lost Sales

This paper considers the case of partially observed demand in the context of a multi-period inventory problem with lost sales. Demand in a period is observed if it is less than the inventory level in that period and the leftover inventory is carried over to the next period. Otherwise, only the event that it is larger than or equal to the inventory level is observed. These observations are used to update the demand distributions over time. The state of the resulting dynamic program consists of the current inventory level and the current demand distribution, which is infinite dimensional. The state evolution equation for the demand distribution becomes linear with the use of unnormalized probabilities. We study two demand cases. First, the demands evolve according to a Markov chain. Second, the demand distribution has an unknown parameter which is updated in the Bayesian manner. In both cases, we prove the existence of an optimal feedback ordering policy. Permanent address of J. Adolfo Minjárez-Sosa: Departamento de Matemáticas, Universidad de Sonora, Hermosillo, Sonora, México. This project was partially supported by NSF Grant 0509278, ARPATP Grant 009741-0019-2006, and CONACYT (Mexico) Grant 46633-F.     

需求可变性降低对均值CVaR约束销售努力决策库存系统的影响

本文运用Levy提出的变换研究需求可变性降低对风险偏好零售商的库存决策、销售努力决策和期望效用的影响,用均值CVaR刻画零售商的风险偏好特性,它包括风险厌恶、风险追求,也具有损失规避的特性。首先,运用该变换定量刻画需求可变性的降低,证明该变换蕴含经典随机占优中的割准则序和二阶随机占优等。其次,给出系统的最优订货量、最优期望效用和最优销售努力水平,得到它们关于风险偏好系数的单调性,并给出降低需求可变性对期望效用的影响。第三,针对风险中性、风险厌恶(最大化CVaR)和风险追求(最小化CVaR)这三种特殊情况得到相应的结果,并给出企业在库存决策和促销决策的管理启示。最后,通过数值例子验证了得到的研究结果并给出相应的管理启示。     

An Incomplete Information Inventory Model with Presence of Inventories or Backorders as Only Observations

In many real-life contexts, inventory levels are only incompletely observed due to non-observation of demand, discrepancies in transmitting sales data, transaction errors, spoilage, misplacement, or theft of inventory. We study a periodic review inventory system, where the demand is not observed and the unmet demand is backordered. As a result, the inventory manager cannot tell the exact quantities of inventories or backorders. However, by looking at the shelf, he knows whether the inventory is positive or nonpositive. Only with this information, the inventory manager must determine the order quantity in each period that would minimize the expected total discounted cost over an infinite-horizon. The dynamic programming formulation of this problem has an infinite-dimensional state space. We use the concept of unnormalized probability to establish the existence of an optimal feedback policy and the uniqueness of the solution of the dynamic programming equation when the periodic cost has linear growth.     

Optimal investment under operational flexibility, risk aversion, and uncertainty

Traditional real options analysis addresses the problem of investment under uncertainty assuming a risk-neutral decision maker and complete markets. In reality, however, decision makers are often risk averse and markets are incomplete. We confirm that risk aversion lowers the probability of investment and demonstrate how this effect can be mitigated by incorporating operational flexibility in the form of embedded suspension and resumption options. Although such options facilitate investment, we find that the likelihood of investing is still lower compared to the risk-neutral case. Risk aversion also increases the likelihood that the project will be abandoned, although this effect is less pronounced. Finally, we illustrate the impact of risk aversion on the optimal suspension and resumption thresholds and the interaction among risk aversion, volatility, and optimal decision thresholds under complete operational flexibility.     

Confidence-based optimisation for the newsvendor problem under binomial,Poisson and exponential demand

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist—e.g. based on maximum likelihood estimators—or Bayesian strategies.     

需求中断下具有提前期的双渠道供应链的风险规避决策

讨论了由一个制造商和一个零售商所组成的双渠道供应链在需求中断下具有提前期的双渠道供应链的风险规避问题.给出了在需求中断前后的最优价格、最优提前期和最优生产决策.研究表明决策变化量是需求中断量的线性函数,在集中式下最优的决策和销售量与供应链的市场份额和需求中断有关,模型的最优生产体现了一定的稳健性.对于提前期来说,当市场份额较大时,最优提前期关于风险规避系数呈正比例,当市场份额较小时,最优提前期关于风险规避系数呈反比例.     

An optimal investment and consumption model with stochastic returns

We consider a financial market consisting of a risky asset and a riskless one, with a constant or random investment horizon. The interest rate from the riskless asset is constant, but the relative return rate from the risky asset is stochastic with an unknown parameter in its distribution. Following the Bayesian approach, the optimal investment and consumption problem is formulated as a Markov decision process. We incorporate the concept of risk aversion into the model and characterize the optimal strategies for both the power and logarithmic utility functions with a constant relative risk aversion (CRRA). Numerical examples are provided that support the intuition that a higher proportion of investment should be allocated to the risky asset if the mean return rate on the risky asset is higher or the risky asset return rate is less volatile. Copyright © 2008 John Wiley & Sons, Ltd.     

Optimal portfolio, consumption and retirement decision under a preference change

We investigate an optimal portfolio, consumption and retirement decision problem in which an economic agent can determine the discretionary stopping time as a retirement time with constant labor wage and disutility. We allow the preference of the agent to be changed before and after retirement. It is assumed that the agent's coefficient of relative risk aversion becomes higher after retirement. Under a constant relative risk aversion (CRRA) utility function, we obtain the optimal policies in closed-forms using martingale methods and variational inequality methods. We give some numerical results of the optimal policies. We also consider the relation between the level of disutility and the labor wage with the optimal retirement wealth level.     

Beneficial changes in dependence structures and two-moment decision models

We analyze the comparative static effects of beneficial changes in the dependence structure between risks. In a quasi-linear decision model with an endogenous risk and a dependent background risk, a mean-variance decision maker will choose a lower level of risky activities upon an increase in the coefficient of correlation of the risks if, and only if, the elasticity of risk aversion is larger than −0.5. For elliptical distributions, the elasticity condition is equivalent to relative prudence being smaller than 1.