Group Decision Problem Under Competitive Situation and its Interactive Solution by Optimization-Satisfaction Approach

Abstract

This paper concerns a group decision problem for competitive system where plural decision-makers exist. The group must choose the alternative that is “best for the group” in some sense. The problem is formulated as follows. Each decision-maker is guaranteed with the satisfaction condition such that his objective function should be always kept below a certain permissible level, regardless of whatever opponents’ decisions may be taken. All decision-makers then cooperate together and seek a group preference solution to minimize a group’s objective function under the satisfaction condition. Hence a two-level optimization problem whose constraints include maximizations by the opponents is presented.Our primary aim is to develop a method for solving the described problem by means of usual non-linear programming. The second is to find methods to aggregate group preference. The group preference solution is obtained by using paired comparisons of alternatives and the Borda's rating method. Utilizing mathematical programming techniques and a computer-assisted system, the group decision problem under competitive situation can be solved in man-machine interaction scheme.