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Boolean Methods in Operations Research and Related Areas

Econometrica 1972 40(4), 777
In classical analysis, there is a vast difference between the class of problems that may be handled by means of the methods of calculus and the class of problems requiring combinatorial techniques.With the advent of the digital computer, the distinction begins to blur, and with the increasing emphasis on problems involving optimization over structures, tIlE' distinction vanishes.What is necessary for the analytic and computational treatment of significant questions arising in modern control theory, mathematical economics, scheduling theory, operations research, bioengineering, and so forth is a new and more flexible mathematical theory which subsumes both the cla8sical continuous and discrete t 19orithms.The work by HAMMER (IVANESCU) and RUDEANU on Boolean methods represents an important step in this dnectlOn, and it is thus a great pleasure to welcome it into print.It will certainly stimulate a great deal of additional research in both theory and application.

Restricted Bargaining for Organizations with Multiple Objectives

Econometrica 1968 36(2), 397
In this paper we show that a bargaining game will yield a negotiated solution with certain reasonable properties if the rules of the game are appropriately restricted. The basic idea is to provide an incentive for all the components to engage in a process of concessions until the point where some agreement is reached. The incentive consists of the threat of a preannounced imposed solution which will be enforced if no settlement can be reached. ORGANIZATIONAL DECISION MAKING is characterized by a multiplicity of partially conflicting objectives, all of which are desirable to some extent. Although the presence of multiple goal structures has been recognized for a long time in economic theory, the assumption of a unique goal of profit maximization has been made in nearly every analytical study of firm behavior, except in a few recent contributions.2 There are many reasons for this apparent lack of interest in the problem of multiple objectives and the failure to introduce them explicitly in models of firm behavior, though most of these are probably related to the difficulty of handling such objectives in a satisfactory way. For instance, a utility-if one exists-will generally fail to be a scalar function; more often it will be a multidimensional function.3 Furthermore, one must face the problem of aggregating the preferences of individual members into a group ordering which satisfies certain reasonable requirements.4 Several approaches have been developed to deal with the problem of resource allocation under multiple objectives; however, none are really satisfactory. Such