Fuzzy Decision Analysis for Alternative Selection Using a Fuzzy Annual Worth Criterion

Very often, in industry, discounted cash flow techniques are applied for analyzing and selecting investment alternatives under consideration. These techniques are usually based on the data under certainty or risk. In reality, however, the decision makers are often facing the situation of vague cash flows and discount rates, or even uncertain durations, when evaluating and selecting potential investments. Fuzzy set theory has the capability of capturing vague data and allows mathematical operations. This article proposes a fuzzy equivalent uniform annual worth (fuzzy EUAW) method to assist practitioners in evaluating investment alternatives utilizing the theory of fuzzy sets. Triangular fuzzy numbers (TFNs) are used throughout the analysis to represent the uncertain cash flows and discount rates. Further, fuzzy capital recovery factors and fuzzy sinking fund factor are derived. Using these two factors, the fuzzy equivalent annual worth of each investment alternative can be found. By ranking these fuzzy numbers with the integral value, the optimal investment alternative is selected. A numerical example is provided to illustrate the results of the alternative selection.     

On The Park-Thuesen Index and the Value of Earlier Uncertainty Resolution

In practice, engineering economic analysis involves uncertainty about future cash flows. To deal quantitatively with imprecision or uncertainty, fuzzy set theory is primarily concerned with vagueness in human thoughts and perceptions. As an alternative to conventional cash flow models where cash flows are defined as either crisp numbers or risky probability distributions, we propose an engineering economic decision model in which the uncertain cash flows and discount rates are specified as triangular fuzzy numbers. The present worth formulation of this fuzzy cash flow model is derived. The result of the present worth is also a fuzzy number with nonlinear membership function. The present worth can be approximated by a triangular fuzzy number. Deviation between exact present worth and its approximate form is examined. Finally, the fuzzy project selection is performed by applying different dominance rules. To demonstrate the application of the fuzzy present worth function, a comprehensive numerical example is presented.     

基于CPSO的基础设施模糊投资组合优化模型

针对基础设施效益模糊、难以度量的特点,结合模糊集理论,建立了模糊投资组合优化模型,改进粒子群算法,加入混沌思想,使用混沌粒子群算法(CPSO)求解基础设施的模糊投资组合优化模型。以4个城市投资公司的数据为样本,验证该方法的科学性与有效性。研究结果表明:模糊投资组合优化模型可较好地表征基础设施的模糊效益,提高基础设施投资决策的科学性;混沌寻优思想改进的粒子群算法可求得模糊投资组合优化模型的全局最优解,增强算法的鲁棒性。     

A Review of: “Risk Assessment and Decision Making in Business and Industry: A Practical Guide” By Glenn Roller CRC Press,Boca Raton,Florida, 1999, 239 pp. ISBN 0-8493-0268-4. List: $31.96”

The article surveys contributions to the literature covering the field of probabilistic discounted cash flow (DCF) analysis of individual capital investments from the earliest contributions of the 1960s to today. Such analysis includes the methods of present worth (net present value), annual worth, future worth, internal rate of return, payback period, and benefit:cost ratio. The history and development of the probabilistic case is traced, listing the main assumptions made and any restrictions to applications. The survey will be found useful by those engaged in risk management and decisions associated with investments and budgeting having uncertain outcomes.     

DERIVATION OF AN INTERTEMPORAL CORRELATION COEFFICIENT MODEL BASED ON CASH FLOW COMPONENTS AND PROBABILISTIC EVALUATION OF A PROJECT'S NPV

If the first two moments (mean and variance) of the net present value (NPV) are known, various probabilistic information of possible NPV can be derived. However, in general, it is practically impossible to estimate the variance of lengthy investment projects due to difficulties in estimating all the intertemporal correlation coefficients between cash flows of two different periods. In this paper, we derive an estimation model for the intertemporal coefficients based on cash flow components and show how the model, under a certain assumption, can be used for estimating and deriving probabilistic information.     

Netzausbauplanung unter Berücksichtigung probabilistischer Einflussgrößen

The present network expansion planning is performed by simulating extreme scenarios in order to proof the security of energy supply. This procedure is associated with high investment costs for equipment which is only needed a few hours per year. Planners have to consider uncertainties and prediction errors for the creation of the extreme scenarios due to the long economic life time of the equipment. The consideration of these influencing factors becomes very complex due to increased utilization of renewable energy sources and frequent changes in the unit commitment of conventional power plants. In contrast to classic load flow methods probabilistic load flow calculation considers the static behaviour of the loads, renewable energies and the power plants instead of only discrete values of nodal powers. These characteristics can be described by probabilistic density functions of load and generation mapped with a probabilistic load flow calculation into a probabilistic density function of the state variables of the energy system (as nodal voltages or line currents). This article presents an overview about existing methods of probabilistic load flow calculations and introduces a newly developed method. The characteristics and the applicability of these methods are verified and the computational burden is analysed exemplarily. Necessary extensions for the mapping of real energy systems and possible approaches for this are presented. The potential and the impact of probabilistic network expansion planning are discussed.     

Neural network application for fuzzy multi-criteria decision making problems

In this paper, a fuzzy multi-criteria decision making model is presented based on a feed forward artificial neural network. This model is used to capture and represent the decision makers' preferences. The topology of the neural network model is developed to train the model. The proposed model can use historical data and update the database information for alternatives over time for future decisions. Basically, multi-criteria decision making problems are formulated, and neural network is used to learn the relation among criteria and alternatives and rank the alternatives. We do not use any utility function for the modeling; however, a unique method is proposed for eliciting the information from decision makers. The proposed model is applicable for a wide variety of multi-attribute decision making problems and can be used for future ranking or selection without managers' judgment effort. Simulation of the managers' decisions is demonstrated in detail and the design and implementation of the model are illustrated by a case study.     

The Maximum Prospective Value Criterion

In this paper the authors analyze the logic of the capital budgeting decision in two different settings. First it is assumed that the decision-maker has complete information about both his current and future investment opportunities in which case the decision problem reduces basically to a computing problem. Second it is assumed that the decision maker has complete information about his current investment opportunities and a knowledge of his expectations about future investment opportunities.

The authors analyze the logic underlying the selection of the capital growth (discount) rate that should be used in determining whether a marginal increment of investment should be accepted or rejected. If the marginal increment were rejected, the unused cash would typically be invested temporarily in a highly liquid investment at a relatively low interest rate with the prospect that a better than marginal investment would absorb the funds at the next decision time.

The analysis led to the formulation of a capital-budgeting decision criterion, called the Maximum Prospective Value Criterion, which is presented in this article. As its name implies, the criterion is designed to select the set of investments that has the maximum prospective value, given the decision-maker's expectations about his future investment opportunities. This criterion relates the capital-budgeting decision to the opportunity-cost and marginal-analysis concepts of classical economics. The present-worth criterion of engineering economy is shown to be a special case of the Maximum Prospective Value Criterion, and the minimum at tractive rate of return of engineering economy when properly selected appears to be closely related to the capital growth rate on the marginal increment of investment.     

Fuzzy Present Value Analysis Model For Evaluating Information System Projects

In this article, the economic evaluation of information system projects using present value is analyzed based on triangular fuzzy numbers. Information system projects usually have numerous uncertainties and several conditions of risk that make their economic evaluation a challenging task. Each year, several information system projects are cancelled before completion as a result of budget overruns at a cost of several billions of dollars to industry. Although engineering economic analysis offers tools and techniques for evaluating risky projects, the tools are not enough to place information system projects on a safe budget/selection track. There is a need for an integrative economic analysis model that will account for the uncertainties in estimating project costs, benefits, and useful lives of uncertain and risky projects. In this study, we propose an approximate method of computing project present value using the concept of fuzzy modeling with special reference to information system projects. This proposed model has the potential of enhancing the project selection process by capturing a better economic picture of the project alternatives. The proposed methodology can also be used for other real-life projects with high degree of uncertainty and risk.     

An economic analysis of the optimal information security investment in the case of a risk-averse firm

This paper presents an analysis of information security investment from the perspective of a risk-averse decision maker following common economic principles. Using the expected utility theory, we find that for a risk-averse decision maker, the maximum security investment increases with, but never exceeds, the potential loss from a security breach, and there exists a minimum potential loss below which the optimal investment is zero. Our model also shows that the investment in information security does not necessarily increase with increasing level of risk aversion of the decision maker. Relationships between vulnerability and investment effectiveness and two broad classes of security breach probability functions are examined, leading to interesting insights that can be used as guidelines for managers to determine the optimal level of security investment for certain types of security threats faced by risk-averse firms. Future research directions are discussed based on the limitations and possible extensions of this study.     

RANKING MUTUALLY EXCLUSIVE PROJECTS: THE ROLE OF DURATION

This paper develops a new measure of cash-flow timing called “return duration.” Numerically quite close to Macaulay duration, return duration is a straightforward function of a project's net present value (NPV) and internal rate of return (IRR). When comparing mutually exclusive projects, differences in return duration can explain ranking conflicts between NPV and IRR. The paper also clarifies the conditions under which a manager should consider duration or generalized NPV before making investment decisions when faced with such ranking conflicts.     

The use of ranking formulae in R & D projects

Abstract . Numerous ranking formulae have been proposed in the literature for use in the evaluation and selection of R& D projects, but their rate of adoption has been relatively slow. This situation appears to be changing in the U.K. and a considerable amount of effort is being expended to improve the methods of obtaining estimates for the variables which appear in the formulae. This paper argues that the most commonly quoted formulae do not adequately represent the practical situation and are likely to introduce bias into the system as well as tending to make estimating more difficult. A modified ranking index derived from a decision tree type of analysis is suggested as a more useful estimate of the worth of a project, but it is concluded that any such formulae will always have serious limitations because they must inevitably ignore important characteristics of the research process.     

Average Internal Rate of Return and Investment Decisions: A New Perspective

The internal rate of return (IRR) is often used by managers and practitioners for investment decisions. Unfortunately, it has serious flaws: (1) multiple real-valued IRRs may arise; (2) complex-valued IRRs may arise; (3) the IRR is, in general, incompatible with the net present value (NPV) in accept/reject decisions; (4) the IRR ranking is, in general, different from the NPV ranking; (5) the IRR criterion is not applicable with variable costs of capital. The efforts of economists and management scientists in providing a reliable project rate of return have generated over the decades an immense bulk of contributions aiming to solve these shortcomings. This article offers a complete solution to this long-standing unresolved issue by changing the usual perspective: the IRR equation is dismissed and the evaluator is allowed to describe the project as an investment or a borrowing at his discretion. This permits showing that any arithmetic mean of the one-period return rates implicit in a project reliably informs about a project's profitability and correctly ranks competing projects. With such a measure, which we call average internal rate of return, complex-valued numbers disappear and all the above-mentioned problems are wiped out. The economic meaning is compelling: it is the project return rate implicitly determined by the market. The traditional IRR notion may be found as a particular case.     

炼油企业伦理决策模型初探

炼油企业要正确进行投资决策，不仅要注重经济分析，而且还应注重伦理分析。由此提出了炼油企业伦理决策的思路和方法，给出了炼油企业伦理决策的指标体系，建立了相应的炼油企业伦理决策数学模型，并且进行了实例分析。计算结果表明所提出的模型是合理、实用的。     

Risk Allowance in Original Capital Investments*

In engineering economy studies, the total risk capital is often not the original capital investment. If a firm remains profitable in the future, a portion of a completely unsuccessful investment can be recovered (1) through income-tax saving as a result of the depreciation cash flows, and (2) through possible reuse of the idle depreciating facilities.

To allow for income-tax savings, the authors propose that the present worth of the guaranteed depreciation cash flow be discounted at the cost of capital and subtracted from the total initial investment to give a better measure of the risk capital. The operating profit, depreciation-free net income, can then be treated in an appropriate fashion using probabilities or a higher discount rate to account for future uncertainties in forecasting market volume, price, manufacturing costs, etc. The application of this principle has been illustrated through a number of ex amples. The results indicate the value of distinguishing between the depreciation and operational cash flow in evaluating high-risk projects in which the yield criterion is used and in mutually exclusive evaluations in which capital investment and depreciation life vary.

A further reduction in original risk capital investment may be justified if the investment still has alternate use value should the project fail; that is, in addition to the depreciation tax credit from an idle piece of equipment. The application of this principle to a mutually exclusive decision involving a grass roots plant versus a plant located as a part of an integrated facility is illustrated. Interestingly, while most decision-makers tend to be conservative with regard to reducing risk capital, ignoring the reuse potential is inconsistent in this situation as it will tend to favor the investment with the greater risk, i.e., the grass roots location.     

Adjustments within discount rates to cater for uncertainty—Guidelines

Deterministic discounted cash flow (DCF) analysis is a well-accepted technique in engineering appraisals. Common practice is to incorporate all uncertainty influences within a single variable—namely, the discount rate—which also represents the time value of money. Commentary already exists in the literature that such a practice is expedient but not rational and has shortcomings. This article examines the error involved in this practice and provides guidelines and precautions for using blanket or constant discount rates in dealing with uncertainties. It shows the adjustments necessary for any given investment scenario. This is done through establishing equivalence of the expected utility of deterministic and probabilistic present worth, allowing a rate adjustment to be calculated. Numerical studies look at the relationship or trends of this rate adjustment to the key analysis variables. Generally, it is found that the rate adjustment should be decreased as the timing of a cash flow's occurrence increases, increased as the variance of the cash flow increases, kept almost as an additive constant as the base rate increases, and increased as the investor's level of risk aversion increases. The article provides practitioner-friendly usable guidelines for adjusting rates, something that is unavailable elsewhere in the literature.     

EXPLOITING UNCERTAINTY—INVESTMENT OPPORTUNITIES AS REAL OPTIONS: A NEW WAY OF THINKING IN ENGINEERING ECONOMICS

A new trend in corporate planning is to exploit uncertainty by taking investment opportunities as real options. This options approach is to complement the conventional net present value (NPV) criterion in evaluating risky investments. In this paper, we take a broad look at the real options approach to various engineering economic decision problems, laying out how it provides an immediate and important perspective on value creation in an uncertain world. Unlike financial options, real options analysisdeals with investments in real assets, which is one of the primary interest areas in engineering economics. For that reason, we believe that any advancement in the real options decision framework will benefit the field of engineering economics.     

Irreversibility, sunk costs and investment under incomplete information

Despite its importance to economic growth, the investment behavior of firms remains poorly understood. Existing models ignore irreversibility and the opportunity to wait for new information. Even if some recent literature accounts for these two characteristics, these models ignore information costs. This paper presents a framework for the valuation of investment opportunities accounting for information costs regarding the project cash‐flows.
We develop some basic models of irreversible investment to illustrate the option‐like characteristics of investment opportunities under incomplete information. We show how optimal investment rules can be obtained using option pricing theory under incomplete information. It is possible to value real options and investment decisions using our approach in a context of incomplete information. Simulations are provided to illustrate our main results.     

Application of fuzzy decision making in part-machine grouping

In this study, fuzzy set theory (FST) is used to set out the cell layout. A new algorithm which will consider both design and manufacturing attributes and operation sequences as factors, is proposed to formulate the problem. The structure of the algorithm is based on fuzzy decision making system (FDMS). Hence three factors mentioned above are determined as input variables and fuzzified using membership function concept. Then the pairwise comparison of the analytical hierarchy process (AHP), which ensures the consistency of the designer`s decisions when assigning the importance of one factor over another, is used to find the weights of these factors. Applying IF–THEN decision rules, parts relationship chart (PRC) is generated. After these steps, the traditional cell formation procedure is applied. Finally the proposed method is scored by performance measures such as machine investment, the amount of work load deviations within cell and between cells and the number of skippings. Also the comparison with Aktürk's study (International Journal of Production Research 34 (8) (1996) 2299–2315) in respect to these performance measures is presented.     

基于粗糙集的银行存货质押业务投资决策研究

针对银行在存货质押业务筛选中缺乏有效方法,将决策粗糙集引入到存货质押业务筛选中,在考虑延迟决策最优投入的情况下,建立了一个基于期望损失最小下阈值和先验概率对比的决策模型。模型中根据投资决策下的收入和支出来确定损失函数,从而确定决策阈值,通过历史数据构建信息表确定先验概率,经阈值和先验概率二者对比,得出银行针对业务的最优决策,算例分析显示模型对银行业务投资决策有一定的借鉴意义。