Elaborations on Multiattribute Utility Theory Dominance

ELABORATIONS ON MULTIATTRIBUTE UTILITY THEORY DOMINANCE By David L. Vairo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University. Virginia Commonwealth University, 2019. Major Director: Dissertation director’s name, Dr. Jason Merrick, Supply Chain Management and Analytics Multiattribute Utility Theory (MAUT) is used to structure decisions with more than one factor (attribute) in play. These decisions become complex when the attributes are dependent on one another. Where linear modeling is concerned with how factors are directly related or correlated with each other, MAUT is concerned with how a decision maker feels about the attributes. This means that direct elicitation of value or utility functions is required. This dissertation focuses on expanding the types of dominance forms used within MAUT. These forms reduce the direct elicitation needed to help structure decisions. Out of this work comes support for current criticisms of gain/loss separability that is assumed as part of Prospect Theory. As such, an alternative to Prospect Theory is presented, derived from within MAUT, by modeling the probability an event occurs as an attribute

Cumulative Prospect Theory for Parametric and Multiattribute Utilities

In cumulative prospect theory models, different behavior concerning gains and losses is per-mitted. For gains different decision weights are assigned than for losses, and the shape of utility can reveal loss aversion. Decision analyses concentrate on both, the capacities, which determine the decision weights, and the nature of utility. This paper focuses on linear/exponential, power and multilinear utility for decision models under uncertainty. Simple preference axioms are for-mulated for a representation by a cumulative prospect theory function. All models share the following axioms: weak ordering, continuity, monotonicity and tail independence. We first show that in their presence constant absolute (proportional) risk aversion implies linear/exponential (power) utility. Then, in the multiattribute case, considering (mutual) utility independence, it is shown that the utility function is (additive/multiplicative) multilinear.mathematical economics and econometrics ;

Using Multiattribute Utility Copulas in Support of UAV Search and Destroy Operations

The multiattribute utility copula is an emerging form of utility function used by decision analysts to study decisions with dependent attributes. Failure to properly address attribute dependence may cause errors in selecting the optimal policy. This research examines two scenarios of interest to the modern warfighter. The first scenario employs a utility copula to determine the type, quantity, and altitude of UAVs to be sent to strike a stationary target. The second scenario employs a utility copula to examine the impact of attribute dependence on the optimal routing of UAVs in a contested operational environment when performing a search and destroy mission against a Markovian target. Routing decisions involve a tradeoff between risk of UAV exposure to the enemy and the ability to strike the target. This research informs decision makers and analysts with respect to the tactics, techniques, and procedures employed in UAV search and destroy missions. An ever increasing UAV operations tempo suggests such research becoming increasingly relevant to the warfighter

A dynamic choice model of hybrid behavior in the attribute-space

This paper presents a dynamic choice model in the attribute space considering rational consumers that discount the future. In light of the evidence of several state-dependence patterns, the model is further extended by considering a utility function that allows for the different types of behavior described in the literature: pure inertia, pure variety seeking and hybrid. The model presents a stationary consumption pattern that can be inertial, where the consumer only buys one product, or a variety-seeking one, where the consumer buys several products simultane-ously. Under the inverted-U marginal utility assumption, the consumer behaves inertial among the existing brands for several periods, and eventually, once the stationary levels are approached, the consumer turns to a variety-seeking behavior. An empirical analysis is run using a scanner database for fabric softener and significant evidence of hybrid behavior for most attributes is found, which supports the functional form considered in the theory.Consumer choice models, state-dependence models, consumption patterns, variety seeking, hybrid behavior

The SIMRAND methodology: Theory and application for the simulation of research and development projects

A research and development (R&D) project often involves a number of decisions that must be made concerning which subset of systems or tasks are to be undertaken to achieve the goal of the R&D project. To help in this decision making, SIMRAND (SIMulation of Research ANd Development Projects) is a methodology for the selection of the optimal subset of systems or tasks to be undertaken on an R&D project. Using alternative networks, the SIMRAND methodology models the alternative subsets of systems or tasks under consideration. Each path through an alternative network represents one way of satisfying the project goals. Equations are developed that relate the system or task variables to the measure of reference. Uncertainty is incorporated by treating the variables of the equations probabilistically as random variables, with cumulative distribution functions assessed by technical experts. Analytical techniques of probability theory are used to reduce the complexity of the alternative networks. Cardinal utility functions over the measure of preference are assessed for the decision makers. A run of the SIMRAND Computer I Program combines, in a Monte Carlo simulation model, the network structure, the equations, the cumulative distribution functions, and the utility functions

Parametric Weighting Functions

This paper provides behavioral foundations for parametric weighting functions under rankdependent utility. This is achieved by decomposing the independence axiom of expected utility into separate meaningful properties. These conditions allow us to characterize rank-dependent utility with power and exponential weighting functions. Moreover, by restricting the conditions to subsets of the probability interval, foundations of rank-dependent utility with parametric inverse-S shaped weighting functions are obtained. --Comonotonic independence,probability weighting function,preference foundation,rank-dependent utility

An Interactive Computer Program for Assessing and Analyzing Preferences Concerning Multiple Objectives

An interactive computer program designed to facilitate the quantification of a decision maker's preferences for multiple objectives in terms of a multiattribute utility function is described. It is meant to alleviate many of the operational difficulties with current procedures for assessing and using multiattribute utility functions. The package includes commands for structuring the utility function, assessing single-attribute component utility functions of the overall multiattribute utility function, identifying the preference trade-offs between attributes, evaluating alternatives, and performing sensitivity analysis. Suggestions for using the program are included

A multicriteria analysis of stated preferences among freight transport alternatives

Stated preferences data can be of different types: choice data, rankings or ratings. In all cases, these data can be used in different ways as inputs of econometric discrete choice models. This allows to estimate the weights of the different attributes characterizing an alternative. For freight transport, an alternative's attributes would be, for example, reliability, safety, frequency, etc., besides time and cost. Depending on the data sample, number of alternatives and number of attributes, it is possible to proceed to an analysis of individual data or of aggregated data. In case one is interested to analyze individual behaviors in depth, the option exists to rely on some kind of multicriteria analysis for deriving individual utility functions (actually, decision functions) rather than on a classic discrete choice model. Such a procedure also can be useful for deriving individual utilities as input in a hybrid model combining individual utilities with group data. Such a multicriteria approach is envisaged in the context of a stated preference experiment that is currently applied to freight shippers in Belgium. The data in this case are rankings of alternatives, and there is multicritera method that is particularly well adapted for such data: the UTA models developed by Jacquet-Lagrèze and Siskos. It is based on the specification of an additive utility made of non-linear partial utility functions that are piecewise linear. This allows the convenient set-up of a linear goal programming problem which estimates all the functions and their weights. The paper intends to present the ranking experiment, and to use some of the preliminary interviews to illustrate this UTA methodology. Also, it will be shown how it can be used to derive equivalent money values for each attributes on the basis of the cost attribute, and how to distinguish valuations in terms of willingness to pay and willingness to accept a compensation.