Decision making with interval probabilities

Handling uncertainty by interval probabilities is recently receiving considerable attention by researchers. Interval probabilities are used when it is difficult to characterize the uncertainty by point-valued probabilities due to partially known information. Most of researches related to interval probabilities, such as combination, marginalization, condition, Bayesian inferences and decision, assume that interval probabilities are known. How to elicit interval probabilities from subjective judgment is a basic and important problem for the applications of interval probability theory and till now a computational challenge. In this work, the models for estimating and combining interval probabilities are proposed as linear and quadratic programming problems, which can be easily solved. The concepts including interval probabilities, interval entropy, interval expectation, interval variance, interval moment, and the decision criteria with interval probabilities are addressed. A numerical example of newsvendor problem is employed to illustrate our approach. The analysis results show that the proposed methods provide a novel and effective alternative for decision making when point-valued subjective probabilities are inapplicable due to partially known information.     

Decision making under uncertainty: A semi-infinite programming approach

The subject of this paper is the formulation and discussion of a semi-infinite linear vector optimization problem which extends multiple objective linear programming problems to those with an infinite number of objective functions and constraints. Furthermore it generalizes in some way semi-infinite programming. Besides the statement of some immediately derived results which are related to known results in semi-infinite linear programming and vector optimization, the problem mentioned above is interpreted as a decision model, under risk or uncertainty containing continuous random variables. Thus we treat the case of an infinite number of occuring states of nature. These types of problems frequently occur within aspects of decision theory in management science.     

Decision making in industrial production planning using fuzzy linear programming

Any modern industrial manufacturing unit inevitably faces problemsof vagueness in various aspects such as raw material availability,human resource availability, processing capability and constraintsand limitations imposed by the marketing department. Such acomplex problem of vagueness and uncertainty can be handledby the theory of fuzzy logic. In this paper, a new fuzzy logicbased methodology using a S-curve membership function is usedto solve a fuzzy mix product selection problem in industrialengineering. Profits and satisfaction levels have been computedusing a fuzzy linear programming approach. Since there are severaldecisions to be taken, a performance measure has been definedto identify the decision that achieves a high level of profitwith a high degree of satisfaction.     

兼顾多种决策目标的一类资本结构优化模型

本建立了一个兼顾利润最大化、企业价值最大化、股东财富最大化和经理利益最大化目标的资本结构优化模型，模型最优化条件隐含：在利润最大化前提下，经理利益最大化目标和股东财富最大化目标之间存在冲突，双方冲突协调的结果有利于实现企业价值最大化。     

企业最优投资决策研究

提高企业效益的一个很重要方面是提高企业的投资效益.针对这一问题,运用动态规划的方法,提出了一个决策模型,使该模型得出的投资方案产生最大的贴现现金流(DCF).     

二层次消费与投资决策优化动态规划模型

在动态多阶段情形,投资者面临的环境不仅只有投资环境,还包括消费环境.投资者关于投资与消费的决策具有层次性.因为消费事关人的生存需要,是优先要考虑的问题,且投资的最终目的还是为了消费,所以使消费最大化应是高一层次的目标,而使投资最大化则应是次一级的目标.因此,试图建立一个二层次消费与投资决策优化动态规划模型,以便更好地模拟现实世界的情况.讨论了该模型的动态决策过程和最优解的性质.     

Decision making with imprecise parameters

We analyze the impact of imprecise parameters on performance of an uncertainty-modeling tool presented in this paper. In particular, we present a reliable and efficient uncertainty-modeling tool, which enables dynamic capturing of interval-valued clusters representations sets and functions using well-known pattern recognition and machine learning algorithms. We mainly deal with imprecise learning parameters in identifying uncertainty intervals of membership value distributions and imprecise functions. In the experiments, we use the proposed system as a decision support tool for a production line process. Simulation results indicate that in comparison to benchmark methods such as well-known type-1 and type-2 system modeling tools, and statistical machine-learning algorithms, proposed interval-valued imprecise system modeling tool is more robust with less error.     

连续型动态规划在投资决策中的应用

首先简要介绍了动态规划方法及在投资决策中的应用.然后给出一个具体示例进行分析和计算.     

Decision making under uncertainty with fuzzy targets

This paper discusses the issue of how to use fuzzy targets in the target-based model for decision making under uncertainty. After introducing a target-based interpretation of the expected value on which it is shown that this model implicitly assumes a neutral behavior on attitude about the target, we examine the issue of using fuzzy targets considering different attitudes about the target selection of the decision maker. We also discuss the problem for situations on which the decision maker’s attitude about target may change according to different states of nature. Especially, it is shown that the target-based approach can provide an unified way for solving the problem of fuzzy decision making with uncertainty about the state of nature and imprecision about payoffs. Several numerical examples are given for illustration of the discussed issues.     

Decision making under uncertainty comprising complete ignorance and probability

This paper investigates a model of decision making under uncertainty comprising opposite epistemic states of complete ignorance and probability. In the first part, a new utility theory under complete ignorance is developed that combines Hurwicz–Arrow's theory of decision under ignorance with Anscombe–Aumann's idea of reversibility and monotonicity used to characterize subjective probability. The main result is a representation theorem for preference under ignorance by a particular one-parameter function – the τ-anchor utility function. In the second part, we study decision making under uncertainty comprising an ignorant variable and a probabilistic variable. We show that even if the variables are independent, they are not reversible in Anscombe–Aumann's sense. This insight leads to the development of a new proposal for decision under uncertainty represented by a preference relation that satisfies the weak order and monotonicity assumptions but rejects the reversibility assumption. A distinctive feature of the new proposal is that the certainty equivalent of a mapping from the state space of uncertain variables to the prize space depends on the order in which the variables are revealed. Explicit modeling of the order of variables explains some of the puzzles in multiple-prior model and the models for decision making with Dempster–Shafer belief function.     

Decision making,new information,ranking and structure

The rank of a set of alternatives can change if a new criterion is introduced into the set of criteria, but it can also change if the importances of the criteria depend on the number of alternatives and on the strength of their ranking. As a result a new alternative may change the relative order of the previous set. This is allowed to happen by making paired comparisons of alternatives with respect to criteria. It is particularly useful in a complex structure where the importances of the criteria are not well established. If on the other hand they are, then the alternatives can be scored with respect to intensities of the criteria and a new alternative would not change the relative rank of the old ones. Copies and near copies of alternatives can be treated by applying the same weight to them or by comparing them with the others respectively. Near copies are identified by a % variation measure.     

A Gridding Method for Bayesian Sequential Decision Problems

This article introduces a numerical method for finding optimal or approximately optimal decision rules and corresponding expected losses in Bayesian sequential decision problems. The method, based on the classical backward induction method, constructs a grid approximation to the expected loss at each decision time, viewed as a function of certain statistics of the posterior distribution of the parameter of interest. In contrast with most existing techniques, this method has a computation time which is linear in the number of stages in the sequential problem. It can also be applied to problems with insufficient statistics for the parameters of interest. Furthermore, it is well-suited to be implemented using parallel processors.     

Interactive fuzzy decision making method for solving bilevel programming problem

In this paper, an interactive fuzzy decision making method is proposed for solving bilevel programming problem. Introducing a new balance function, we consider the overall satisfactory balance between the leader and the follower. Then, a satisfactory solution can be obtained by the proposed method. Finally, numerical examples are reported to illustrate the feasibility of the proposed method.     

Decision model and analysis for investment interest expense deduction and allocation

Investment income tax planning requires informed, strategic choices. One must determine the amount of qualified dividends and net long-term capital gain to be included in investment income (against which investment interest expense can be deducted). This choice also determines the residual qualified dividends and net long-term capital gain which enjoy a reduced tax rate. Another important decision is whether all or some of this interest expense should be deducted in the current year or carried forward. This paper puts forward a new approach to formulate these questions as a generalized resource allocation problem which permits analysis of the interdependence between, and the tax consequences of, the above decisions. The commonly used approach – deducting investment interest expense sooner rather than later – we consider myopic since the benefit of deferring some of the deduction is not leveraged. Presented here is a tax planning guideline (a necessary and sufficient condition for optimality) to realize a more forward-looking strategy. We also show that, for certain income structures, the tax savings by deducting a one-dollar investment interest expense may be more than the tax rate on the dollar of investment income that is offset.     

双层规划的递阶交互决策有效化方法

本文讨论了协调集上双层规划问题解的性质,所得结论表明上层将所得利益全部让给下层,或下层将所得利益全部让给上层.当决策者不满足此种有效化方式时,必须寻找体现递阶结构的有效化方法.本文给出了一种保持递阶结构的递阶交互决策有效化方法.该方法适用于下层有多个平行子问题的双层线性规划.     

Location and sizing of facilities on a line

The location-allocation problem in its basic form assumes that the number of new facilities to be located is known and the capacities are unlimited. When the locations of the facilities and demand points (or customers) are restricted to the real line, the basic model may be solved efficiently by dynamic programming. In this note, we show that when the number of facilities and their capacities are included in the decision process, the problem may actually be easier to solve.     

Decision making under uncertainty with unknown utility function and rank-ordered probabilities

We consider the ranking of decision alternatives in decision analysis problems under uncertainty, under very weak assumptions about the type of utility function and information about the probabilities of the states of nature. Namely, the following two assumptions are required for the suggested method: the utility function is in the class of increasing continuous functions, and the probabilities of the states of nature are rank-ordered. We develop a simple analytical method for the partial ranking of decision alternatives under the stated assumptions. This method does not require solving optimization programs and is free of the rounding errors.     

Forward differential dynamic programming

The dynamic programming formulation of the forward principle of optimality in the solution of optimal control problems results in a partial differential equation with initial boundary condition whose solution is independent of terminal cost and terminal constraints. Based on this property, two computational algorithms are described. The first-order algorithm with minimum computer storage requirements uses only integration of a system of differential equations with specified initial conditions and numerical minimization in finite-dimensional space. The second-order algorithm is based on the differential dynamic programming approach. Either of the two algorithms may be used for problems with nondifferentiable terminal cost or terminal constraints, and the solution of problems with complicated terminal conditions (e.g., with free terminal time) is greatly simplified.     

A multiple criteria decision making approach to manure management systems in the Netherlands

The intensification of livestock operations in the last few decades has resulted in an increased social concern over the environmental impacts of livestock operations and thus making appropriate manure management decisions increasingly important. A socially acceptable manure management system that simultaneously achieves the pressing environmental objectives while balancing the socio-economic welfare of farmers and society at large is needed. Manure management decisions involve a number of decision makers with different and conflicting views of what is acceptable in the context of sustainable development. This paper developed a decision-making tool based on a multiple criteria decision making (MCDM) approach to address the manure management problems in the Netherlands. This paper has demonstrated the application of compromise programming and goal programming to evaluate key trade-offs between socio-economic benefits and environmental sustainability of manure management systems while taking decision makers’ conflicting views of the different criteria into account. The proposed methodology is a useful tool in assisting decision makers and policy makers in designing policies that enhance the introduction of economically, socially and environmentally sustainable manure management systems.