Enrique Ballestero

A theorem connecting utility function optimization and compromise programming

The aim of this paper is to determine conditions under which the Lagrangian maximum of a utility function and compromise programming lead to close solutions.

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 (1 825) 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. Subject Areas: Decision Analysis, Disappointment, Domination, and Unce&n& INTRODUCTION According to certain common definitions, strict uncertainty means almost complete lack of knowledge about an outcome. Regarding this type of uncertainty, the authors distinguish between complete and partial ignorance (Arrow & Hurwicz, 1972). Under complete ignorance the probabilities are totally unknown while under partial ignorance they are virtually but not totally unknown. More precisely, in the case of partial ignorance, the individual’s vague beliefs about them are sufficient to assign superior positions to some states of the world with respect to the remaining states. However, “complete ignorance” might be an inappropriate terminology, as the decision maker (DM) has sufficient information on the states of the world (with exception of their probabilities), and he can predict the consequence xij *Thanks are given to the reviewers for their helpful suggestions which have greatly improved the presentation and accuracy of the paper. The English editing by Dr. Keith Stuart is appreciated.

Weighting in compromise programming: A theorem on shadow prices

This paper attempts to justify a weighting system proposed as a normalizer in the literature by proving that weights inversely proportional to the ideal are good shadow prices in economic scenarios.

Project finance: a multi-criteria approach to arbitration

Large investment projects in sectors such as transportation and natural resources require some risk allocation agreements to be financed at low interest rates. Focusing on these agreements made between the project company (or the sponsors) and other participants (the host government, the client, the supplier, the constructor, or the lenders) I propose a multi-criteria normative model to conduct the bargain decision-making process in a rational way. This model is based on compromise programming (CP) and it is specially designed for arbitration when the bargain process becomes deadlocked. Plausible theoretical and practical results are obtained, and a numerical example is developed.

Multiple Criteria Decision Making: Some Connections with Economic Analysis

Multiple Criteria Decision Making (MCDM) has been perhaps the fastest growing area of Decision Analysis in the last twenty years. However, despite its popularity and wide range of applications, there are very few research efforts connecting MCDM with economics. In this context, this paper shows the potentiality of Compromise Programming, a popular MCDM approach, in tackling some basic problems in economics.

Multiattribute Utility Approaches

The most traditional or classic approach in multi-criteria decisional problems consists in defining a utility function comprising all the relevant attributes. This multiattribute utility function is optimised subject to the constraints of the problem. Such methodology is known as Multiattribute Utility Theory (MAUT). Let us start its presentation by introducing the individual utility functions, which reflects decision-maker’s preferences for the attributes relevant to a certain decisional problem.

Multiple Criteria Decision Making: An Introduction

The basic traditional structure underlying any decision-making problem can be summarised as follows. The existence of limited resources (understanding the term resource in a broad sense), generates the constraints of the problem. The value of the decision variables satisfying the constraints define what is known as the feasible or attainable set. This set can either be continuous (infinite number of solutions) or discrete (finite number of solutions). Once the feasible set is established, the subsequent step consists in defining a criterion function which suitably reflects the preferences of decision maker by associating a number to each feasible solution. Finally, by resorting to more or less sophisticated mathematical techniques, the “best” or “optimal” solution is obtained.

A First Linkage: CP and Bi-Attribute Utility

The basic traditional structure underlying any choice problem in economics can be summarised as follows:

Multiobjective Optimisation Methods

Max\;\;Z=Z(x_{1},x_{2})\;\;subject\;to\;T(x_{1},x_{2})=k