Objective and Subjective Rationality in a Multiple Prior Model

A decision maker (DM) is characterized by two binary relations. The first reflects choices that are rational in an “objective” sense: the DM can convince others that she is right in making them. The second relation models choices that are rational in a “subjective” sense: the DM cannot be convinced that she is wrong in making them. In the context of decision under uncertainty, we propose axioms that the two notions of rationality might satisfy. These axioms allow a joint representation by a single set of prior probabilities and a single utility index. It is “objectively rational” to choose f in the presence of g if and only if the expected utility of f is at least as high as that of g given each and every prior in the set. It is “subjectively rational” to choose f rather than g if and only if the minimal expected utility of f (with respect to all priors in the set) is at least as high as that of g. In other words, the objective and subjective rationality relations admit, respectively, a representation à la Bewley (2002) and à la Gilboa and Schmeidler (1989). Our results thus provide a bridge between these two classic models, as well as a novel foundation for the latter.     

Using Real‐Time Decision Tools to Improve Distributed Decision‐Making Capabilities in High‐Magnitude Crisis Situations*

Multi‐organizational collaborative decision making in high‐magnitude crisis situations requires real‐time information sharing and dynamic modeling for effective response. Information technology (IT) based decision support tools can play a key role in facilitating such effective response. We explore one promising class of decision support tools based on machine learning, known as support vector machines (SVM), which have the capability to dynamically model and analyze decision processes. To examine this capability, we use a case study with a design science approach to evaluate improved decision‐making effectiveness of an SVM algorithm in an agent‐based simulation experimental environment. Testing and evaluation of real‐time decision support tools in simulated environments provides an opportunity to assess their value under various dynamic conditions. Decision making in high‐magnitude crisis situations involves multiple different patterns of behavior, requiring the development, application, and evaluation of different models. Therefore, we employ a multistage linear support vector machine (MLSVM) algorithm that permits partitioning decision maker response into behavioral subsets, which can then individually model and examine their diverse patterns of response behavior. The results of our case study indicate that our MLSVM is clearly superior to both single stage SVMs and traditional approaches such as linear and quadratic discriminant analysis for understanding and predicting behavior. We conclude that machine learning algorithms show promise for quickly assessing response strategy behavior and for providing the capability to share information with decision makers in multi‐organizational collaborative environments, thus supporting more effective decision making in such contexts.     

Missing consequences in multiattribute utility theory

This paper addresses how to deal with decision alternatives with missing consequences in multicriteria decision-making problems. We propose disregarding the attributes for which a decision alternative provides no consequence by redistributing their respective weights throughout the objective hierarchy in favor of a straightforward idea: the assignation of the respective attribute range as a default value for missing consequences due to possible uncertainty about the decision alternative consequences. In both cases, decision alternatives are evaluated by means of an additive multi-attribute utility model. An illustrative example of the restoration of radionuclide contaminated aquatic ecosystems is shown.     

Value of Information in Closed Loop Supply Chains

We explore the value of information (VOI) in the context of a firm that faces uncertainty with respect to demand, product return, and product recovery (yield). The operational decision of interest in matching supply with demand is the quantity of new product to order. Our objective is to evaluate the VOI from reducing one or more types of uncertainties, where value is measured by the reduction in total expected holding and shortage costs. We start with a single period model with normally distributed demands and returns, and restrict the analysis to the value of full information (VOFI) on one or more types of uncertainty. We develop estimators that are predictive of the value and sensitivity of (combinations of) different information types. We find that there is no dominance in value amongst the different types of information, and that there is an additional pay‐off from investing in more than one type. We then extend our analysis to the multi‐period case, where returns in a period are correlated with demands in the previous period, and study the value of partial information (VOPI) as well as full information. We demonstrate that our results from the single period model (adapted for VOPI) carry‐over exactly. Furthermore, a comparison with uniformly distributed demand and return show that these results are robust with respect to distributional assumptions.     

灾后不确定需求下应急医疗移动医院鲁棒选址问题研究

我国灾害医学救援主要采用"现场救治"模式，应急医疗移动医院的选址是否合理直接影响救援效率，但各受灾点伤员数量的不确定性增加了决策的困难。本文引入多面体不确定集合刻画伤员数量的不确定性，同时考虑伤员分类及移动医院分型，构建一个以伤员总生存概率最大化为目标的鲁棒选址模型。利用鲁棒优化理论，将模型转化为等价的混合整数规划问题，通过GAMS软件编程并调用CPLEX求解器求解。最后，以四川芦山地震应急医疗救援为例，验证模型和求解方法的可行性和鲁棒性。结果表明，扰动比例和不确定水平对移动医院的选址和伤员的分配方案有显著影响，决策者可根据自己对不确定性风险的偏好程度选择最佳的扰动比例和不确定水平组合，以获得最优的选址分配方案。     

STOCHASTIC COST-VOLUME-PROFIT ANALYSIS WITH A LINEAR DEMAND FUNCTION

In this paper we incorporate a linear demand function to model the price-volume causal relationship into stochastic cost-volume-profit (CVP) analysis. We assume that the objective function is to maximize expected profit; other objective functions are also discussed and compared. A linear stochastic model follows from which probabilistic statements can be easily obtained if the random variables are assumed to be multivariate normal. The basic framework is shown to be a special case of project value maximization where project value is the cash flow of the project discounted for time and risk according to the capital asset pricing model. Moreover, an intertemporal extension that considers inventory is developed. In summary, a new approach to stochastic CVP analysis that incorporates the management decision process in an uncertain environment is developed.     

基于EVA与经营风险偏好的供应链鲁棒优化模型

在由一个制造商和多个外部供应商构成的多产品、多阶段供应链中,将经济增加值（EVA）作为体现价值创造的绩效指标,并考虑决策者的经营风险偏好,采用已知概率的离散情景描述资本成本与需求的波动情况,利用鲁棒随机规划方法,建立了以价值创造为目标的供应链鲁棒优化模型。应用分析的结果表明,模型能够将供应链的绩效与风险管理结合起来,减少资本成本与需求不确定对目标值的影响,得到具有鲁棒性的最优解,而且越是风险厌恶型的决策者越会为了保持较低的经营风险而放弃较大的EVA值。同时,决策者可选择不同的权重系数侧重于解鲁棒或模型鲁棒,保证供应链运作的鲁棒性,实现价值创造的目标。     

工期-质量协调均衡的项目导向型供应链跨组织激励

在假定项目型组织之间平等合作的基础上,从项目价值增值最大化角度,考虑工期-质量目标努力成本关系,构建并剖析工期-质量协调均衡的项目导向型供应链跨组织激励模型,并对模型进行数据模拟和算例分析。结果表明,不论工期-质量目标间努力成本是否存在线性关系,以调整不同控制目标的激励强度为协调手段,实施工期-质量协调激励策略不仅可实现项目导向型供应链项目价值增值的最大化,而且可实现合作双方净收益的帕累托改善,进而使得承包商在工期-质量目标上合理分配资源和努力水平,实现项目工期-质量目标间的协调均衡。     

Strict Uncertainty: A Criterion for Moderately Pessimistic Decision Makers*

This paper proposes a decision rule to rank actions under strict uncertainty, the available information being limited to the states of nature, the set of alternative rows, and the consequence of choosing every row if a given state occurs. This rule is suitable to moderately pessimistic individuals and social groups, these agents being neither maximax nor maximin decision makers but people who assume that the best outcome from the action will not occur. For these decision makers the paper shows the existence of a consistent weight system in which one and only one weight is attached to each state of the world under plausible conditions of domination. Most of the traditional axioms are satisfied by the proposed ranking approach. In the frame of disappointment (measured by ranges of column dispersion), the meaning of some controversial postulates used in the literature is explained. The proposed criterion is a departure from Laplace's (1825) rule and from the remaining standard criteria. Only in the special case of equal column dispersion do both Laplace's rule and the proposed weights lead to the same solution.     

Economic Evaluation of Scale Dependent Technology Investments

We study the effect of financial risk on the economic evaluation of a project with capacity decisions. Capacity decisions have an important effect on the project̂s value through the up‐front investment, the associated operating cost, and constraints on output. However, increased scale also affects the financial risk of the project through its effect on the operating leverage of the investment. Although it has long been recognized in the finance literature that operating leverage affects project risk, this result has not been incorporated in the operations management literature when evaluating projects. We study the decision problem of a firm that must choose project scale. Future cash flow uncertainty is introduced by uncertain future market prices. The firm's capacity decision affects the firm's potential sales, its expected price for output, and its costs. We study the firm's profit maximizing scale decision using the CAPM model for risk adjustment. Our results include that project risk, as measured by the required rate of return, is related to the inverse of the expected profit per unit sold. We also show that project risk is related to the scale choice. In contrast, in traditional discounted cash flow analysis (DCF), a fixed prescribed rate is used to evaluate the project and choose its scale. When a fixed rate is used with DCF, a manager will ignore the effect of scale on risk and choose suboptimal capacity that reduces project value. S/he will also misestimate project value. Use of DCF for choosing scale is studied for two special cases. It is shown that if the manager is directed to use a prescribed discount rate that induces the optimal scale decision, then the manager will greatly undervalue the project. In contrast, if the discount rate is set to the risk of the optimally‐scaled project, the manager will undersize the project by a small amount, and slightly undervalue the project with the economic impact of the error being small. These results underline the importance of understanding the source of financial risk in projects where risk is endogenous to the project design.     

COMPARATIVE EVALUATION OF INFORMATION UNDER TWO BUSINESS OBJECTIVES

Information economics models evaluate the value of information under the assumption that decision makers wish to maximize their expected payoff. This assumption has been criticized for not being realistic enough since decision makers usually consider more than one business objective and might be satisficers rather than optimizers. This paper attempts to apply an information economics model to decision situations where two business performance criteria, expected payoff and risk, are considered. In order to overcome the difficulty of unknown trade-off between the two criteria, one criterion is used as an objective to be optimized, while the other is set as a constraint. This may be interpreted as a combination of optimizing and satisficing approaches. It is shown how an information system can be evaluated in terms of both expected payoff and risk. The model suggests the trade-off between the two criteria as an additional trait of an information system. In the last part of the paper, a numerical example illustrates how a comparative evaluation of information structures is performed when risk minimization and expected payoff maximization are concurrently used as business performance criteria.     

A Decision-Theoretic Valuation of Information in Sealed-Bid Auctions for Items of Known Value

This paper considers the question of how much time and effort should be spent in preparing a bid for a single item of known value sold at a first-price sealed-bid auction. A decision-theoretic approach to this bid decision summarizes the decision maker's knowledge of the competitive environment through his or her subjective probability distribution of the highest competing bid. Research activities such as collecting and analyzing bid histories are efforts to obtain additional information that reduces the uncertainty in the highest competing bid. The decision-theoretic concepts of expected value of perfect and imperfect information are used to place an economic value on such research activities. The results presented allow the decision maker to quantify the expected value of imperfect information when the uncertainty is normally distributed. The results show that additional research is most valuable prior to auctions the bidder expects to win.     

Information sharing in supply chains

Supply chain is defined as a system of suppliers, manufacturers, distributors, retailers and customers where material, financial and information flows connect participants in both directions. Most supply chains are composed of independent agents with individual preferences. It is expected that no single agent has the power to optimise the supply chain. Supply chain management is now seen as a governing element in strategy and as an effective way of creating value for customers. The so-called bullwhip effect, describing growing variation upstream in a supply chain, is probably the most famous demonstration that decentralised decision making can lead to poor supply chain performance. Information asymmetry is one of the most powerful sources of the bullwhip effect. Information sharing of customer demand has an impact on the bullwhip effect. Information technology has lead to centralised information, shorter lead times and smaller batch sizes. The analysis of causes of the bullwhip effect has lead to suggestions for reducing the bullwhip effect in supply chains by strategic partnership. Supply chain partnership leads to increased information flows, reduced uncertainty, and a more profitable supply chain. The cooperation is based on contacts and formal agreements. Information exchange is very important issue for coordinating actions of units. New business practices and information technology make the coordination even closer. Information sharing and strategic partnerships of units can be modelled by different network structures.     

只有输出的广义样本区间DEA模型

在应用多个绩效指标综合评价决策单元有效性时，决策者常常把这些决策单元与另外预先指定的标准（样本单元）进行比较。由于客观事物的复杂性和不确定性导致样本单元和决策单元的指标信息有时必须用区间数的形式给出。针对区间数指标信息的综合评价问题，本文通过分解的方法讨论样本单元和决策单元指标信息为区间数时用广义DEA模型评价决策单元有效性的方法，并相应地构建了只有输出的广义区间DEA模型。同时，对模型的含义、求解以及性质等进行了分析。之后，探讨了该方法在决策单元有效性分类和排序中的应用。最后，通过实例表明该方法的可行性和有效性。     

Decision Making Under Risk: A Comparison of Bayesian and Fuzzy Set Methods

A classical decision problem is considered where a decision maker is to choose one of a number of actions each offering different consequences. The outcome from a choice of action is uncertain because it depends on the existing state of Nature. Also, the outcome, once an action and state of Nature are specified, may be a vector or a random vector. The decision maker employs both Bayesian methods and fuzzy set techniques to handle the uncertainties. The decision maker is also allowed to use multiple, possibly conflicting, goals in order to determine his best strategy. The Bayesian method produces a set of undominated strategies to choose from, whereas the fuzzy set technique usually produces a unique optimal strategy.     

AN APPROACH TO COST—VOLUME—PROFIT ANALYSIS UNDER UNCERTAINTY*

Cost-Volume-Profit analysis is a tool of cost accountants aiding in the choice of an optimal course of action in the solution of a managerial problem. C-V-P is a limited analysis since all the needs of management in determining the optimal strategy are not fulfilled. Factors pertinent to the choice of the optimal strategy under uncertainty are variables, although traditional C-V-P treats these factors as constants. Hence, an approach to C-V-P where pertinent factors necessary for decision making are considered as variables is more desirable than traditional C-V-P. By introducing uncertainty, it is also beneficial to broaden C-V-P to fulfill the following desire of management. Should management choose a course of action based only on its own estimates of the decision parameters or is it advisable to postpone a terminal decision until additional research into the decision parameters is accomplished? Broadened C-V-P solves this problem with the aid of Bayesian Decision Theory for the choice of the optimal course of action in the face of uncertainty.     

A SIMPLE PROOF THAT DOLLAR AVERAGING IS A MAXIMIN INVESTMENT STRATEGY

Dollar averaging is a strategy for investment timing which hedges against purchases at the market high by investing fixed amounts at regular intervals. This note gives a simple proof that it is a maximin strategy. This result complements Pye's [2] finding that dollar averaging is a minimax regret strategy. In addition to its theoretical value, the result is an excellent classroom illustration of a real-life application of the maximin criterion.     

A COMPARISON OF WEIGHTING METHODS IN POWER PLANT SITING*

The insufficient attention that too often is paid to the characteristics required of attribute weights prevents multiattribute decision rules from accurately representing preferences. The weighting summation or linear model requires weights to be proportional to the relative value of unit changes in their attribute value functions. Only then will weights accurately reflect the trade-offs decision makers are willing to make. A number of methods of choosing weights are critiqued from this perspective. Applications of weighting methods in power plant siting are surveyed, and a siting study of western Maryland is presented. Two weighting methods were used, one deriving weights from trade-offs made by decision makers and the other asking decision makers to choose weights on a scale of 0 to 10. The locations picked by the two methods differ strikingly.     

α-鲁棒随机截流选址问题的模型和算法

由于选址决策的长期性,相关参数会随着时间而变化,所以选址问题存在很多不确定因素。本文通过不同的情景来处理截流问题中流量的不确定性,并结合随机优化和鲁棒优化,提出α-鲁棒随机截流选址模型。该模型规定了在各情景下的相对后悔值不超过α的条件下,使截得的流量的期望值最大,该条件称为α-鲁棒约束。本文将该模型建立成为一个线性0-1整数规划,并给出了改进型贪婪算法和拉格朗日启发式算法。最后,本文使用这两种算法对不同规模的截流选址问题进行了研究。