James S. Dyer

Measurable Multiattribute Value Functions

This paper presents a theory of measurable multiattribute value functions. Measurable value functions are based on the concept of a “preference difference” between alternatives and provide an interval scale of measurement for preferences under certainty. We present conditions for additive, multiplicative, and more complex forms of the measurable multiattribute value function. This development provides a link between the additive value function and multiattribute utility theory.

Simulation techniques for the sensitivity analysis of multi-criteria decision models

This paper presents a simulation approach for high dimensional sensitivity analysis of the weights of multi-criteria decision models. This approach allows simultaneous changes of the weights and generates results that can easily be analyzed statistically to provide insights into multi-criteria model recommendations. In this study we consider three cases: no information, order information, and partial information regarding the weights. Our approach also allows investigation of sensitivity to the form of multi-criteria decision models. The simulation procedures we propose can also be used to aide in the actual decision process, particularly when the task is to select a subset of superior alternatives.

Attribute weighting methods and decision quality in the presence of response error: A simulation study

This paper uses a simulation approach to investigate how different attribute weighting techniques affect the quality of decisions based on multiattribute value models. The weighting methods considered include equal weighting of all attributes, two methods for using judgments about the rank ordering of weights, and a method for using judgments about the ratios of weights. The question addressed is: How well does each method perform when based on judgments of attribute weights that are unbiased but subject to random error? To address this question, we employ simulation methods. The simulation results indicate that ratio weights were either better than rank order weights (when error in the ratio weights was small or moderate) or tied with them (when error was large). Both ratio weights and rank order weights were substantially superior to the equal weights method in all cases studied. Our findings suggest that it will usually be worth the extra time and effort required to assess ratio weights. In cases where the extra time or effort required is too great, rank order weights will usually give a good approximation to the true weights. Comparisons of the two rank-order weighting methods favored the rank-order-centroid method over the rank-sum method.

Maut — Multiattribute Utility Theory

In this chapter, we provide a review of multiattribute utility theory. We begin with a brief review of single-attribute preference theory, and we explore preference representations that measure a decision maker’s strength of preference and her preferences for risky alternatives. We emphasize the distinction between these two cases, and then explore the implications for multiattribute preference models. We describe the multiattribute decision problem, and discuss the conditions that allow a multiattribute preference function to be decomposed into additive and multiplicative forms under conditions of certainty and risk. The relationships among these distinct types of multiattribute preference functions are then explored, and issues related to their assessment and applications are surveyed.

Using Binomial Decision Trees to Solve Real-Option Valuation Problems

Traditional decision analysis methods can provide an intuitive approach to valuing projects with managerial flexibility or real options. The discrete-time approach to real-option valuation has typically been implemented in the finance literature using a binomial lattice framework. Instead, we use a binomial decision tree with risk-neutral probabilities to approximate the uncertainty associated with the changes in the value of a project over time. Both methods are based on the same principles, but we use dynamic programming to solve the binomial decision tree, thereby providing a computationally intensive but simpler and more intuitive solution. This approach also provides greater flexibility in the modeling of problems, including the ability to include multiple underlying uncertainties and concurrent options with complex payoff characteristics.

The Reliability of Subjective Probabilities Obtained Through Decomposition

The use of decomposition as a procedure for improving the consistency of subjective probability encoding is discussed. Using a psychometric measurement model, an expression is developed that describes the random error associated with decomposition estimates as a function of characteristics of the component assessments. Decomposition is compared to direct assessment in terms of the percent change in measurement error that can be attributed to the use of decomposition. Potential benefits of decomposition are specified and recommendations made on how to utilize decomposition as an approach for error control.

Discrete time modeling of mean-reverting stochastic processes for real option valuation

Abstract In this paper the recombining binomial lattice approach for modeling real options and valuing managerial flexibility is generalized to address a common issue in many practical applications, underlying stochastic processes that are mean-reverting. Binomial lattices were first introduced to approximate stochastic processes for valuation of financial options, and they provide a convenient framework for numerical analysis. Unfortunately, the standard approach to constructing binomial lattices can result in invalid probabilities of up and down moves in the lattice when a mean-reverting stochastic process is to be approximated. There have been several alternative methods introduced for modeling mean-reverting processes, including simulation-based approaches and trinomial trees, however they unfortunately complicate the numerical analysis of valuation problems. The approach developed in this paper utilizes a more general binomial approximation methodology from the existing literature to model simple homoskedastic mean-reverting stochastic processes as recombining lattices. This approach is then extended to model dual correlated one-factor mean-reverting processes. These models facilitate the evaluation of options with early-exercise characteristics, as well as multiple concurrent options. The models we develop in this paper are tested by implementing the lattice in binomial decision tree format and applying to a real application by solving for the value of an oil and gas switching option which requires a binomial model of two correlated one-factor commodity price models. For cases where the number of discrete time periods becomes too large to be solved using common decision tree software, we describe how recursive dynamic programming algorithms can be developed to generate solutions.

Decision Analysis and Real Options: A Discrete Time Approach to Real Option Valuation

In this paper we seek to enhance the real options methodology developed by Copeland and Antikarov (2001) with traditional decision analysis tools to propose a discrete time method that allows the problem to be specified and solved with off the shelf decision analysis software. This method uses dynamic programming with an innovative algorithm to model the project’s stochastic process and real options with decision trees. The method is computationally intense, but simpler and more intuitive than traditional methods, thus allowing for greater flexibility in the modeling of the problem.

A Multiattribute Utility Analysis of Alternatives for the Disposition of Surplus Weapons-Grade Plutonium

This paper describes an application of multiattribute utility theory to support the selection of a technology for the disposition of surplus weapons-grade plutonium by the Department of Energy (DOE). This analysis evaluated 13 alternatives, examined the sensitivity of the recommendations to the weights and assumptions, and quantified the potential benefit of the simultaneous deployment of several technologies. The measures of performance that were identified through the creation of a hierarchy of objectives helped to organize the information collected during the evaluation process, and the results of the analysis were presented to DOE on several occasions. This analysis supported the final DOE recommendation to pursue a strategy of the parallel development of two of the most preferred technologies.

An Actual Application of Collective Choice Theory to the Selection of Trajectories for the Mariner Jupiter/Saturn 1977 Project

This paper describes the use of decision analysis to facilitate a group decision-making problem in the selection of trajectories for the two spacecraft of the Mariner Jupiter/Saturn 1977 Project. This NASA project includes the participation of some eighty scientists, divided by specialization among eleven science teams. A set of thirty-two candidate trajectory pairs was developed by the Project, in collaboration with the science teams. Each science team then ordinally ranked and assigned cardinal utility function values to the trajectory pairs. The scientists used these data and statistics derived from collective choice rules in selecting the preferred trajectory pair.