An interactive approach to multiple criteria optimization with multiple decision-makers

In this article we propose a formal man-machine interactive approach to multiple criteria optimization with multiple decision makers. The approach is based on some of our earlier research findings in multiple criteria decision making. A discrete decision space is assumed. The same framework may readily be used for multiple criteria mathematical programming problems. To test the approach two experiments were conducted using undergraduate Business School students as subjects in Finland and in the United States. The context was, respectively, a high-level Finnish labor-management problem and the management-union collective bargaining game developed at the Krannert Graduate School of Management, Purdue University. The results of the experiments indicate that our approach is a potentially useful decision aid for group decision-making and bargaining problems.     

Generalized implicit enumeration using bounds on variables for solving linear programs with zero-one variables

In an earlier paper [1] we put forth a framework that helps to tie together a number of approaches for solving integer programming problems. We outlined there how Balas' Additive Algorithm can be explained and generalized in terms of the framework. In the present paper we review Balas' algorithm, and our earlier framework, and present an algorithm generalizing Balas' scheme. In addition, some examples are presented and future research to be done is discussed.     

Programming with linear fractional functionals

Charnes and Cooper [1] showed that a linear programming problem with a linear fractional objective function could be solved by solving at most two ordinary linear programming problems. In addition, they showed that where it is known a priori that the denominator of the objective function has a unique sign in the feasible region, only one problem need be solved. In the present note it is shown that if a finite solution to the problem exists, only one linear programming problem must be solved. This is because the denominator cannot have two different signs in the feasible region, except in ways which are not of practical importance.