Flexible Decision Making

A decision is defined to be flexible decision if (1) the Decision Maker (DM) has bounded rationality, and (2) the preference of the DM, the constraints of the decision problem, and/or the goals the DM seeks for are flexible. The motif of this paper is flexible decision which accords with reality. Based on the concept of flexible decision, this paper studies 3 problems. They are multiobjective decision making, resource allocation and one kind of cooperative game. In order to solve the flexible decision problem, the methods used in this paper include maximin method, set inclusion method, interactive method and interval analysis method.In order to solve the multiobjective flexible decision problem, this paper presents the interactive maximin method. Though the method is used by others, it remains unsolved about how to adjust satisfying solution according to DM's preference. In fact, the adjusted solution may be not in agreement with DM's requirement if some rules are not applied. So this paper studies the principles of adjustment, and gives the interactive maximin method suitable for flexible decision making. The set inclusion method and interval analysis method are integrated with the interactive maximin method to solve linear and some nonlinear flexible decision problems.The resource allocation problem is multiobjective flexible decision problem. And this kind of decision problem consists many DMs, including one leader DM and many follower DMs. The leader DM uses the technique of large scale system decomposition and coordination to look for allocation scheme according to the information provided by follower DMs. To solve this kind of decision problem, this paper presents the flexible decision method that cooperates large scale system decomposition, coordination and incentive control. This method consists of two parts as follows:(1) The maximin method of multiobjective flexible decision. There are many existing algorithms that solve the maximin or minimax programming without constraint or with linear constraints. Some of the algorithms need the 2nd order differential information of objective functions. In resource allocation problem, however, the constraints may be nonlinear, the leader DM can only get the 1st order differential information of the functions. So, according to the characteristics of resource allocation problem, this paper gives the iterating algorithm by means of piecewise linearization. The algorithm is proved to be convergent.(2) Incentive control that induces the follower DMs to tell the truth. Although some incentive strategies in resource allocation problem are given by other researchers, the strategies are not in keeping with the basic principles of management science, and can not be applied to real problem. According to the real situation of China, this paper designs "Contract Mechanism" (CM) which is - inducible for the true information and encourage follower DMs to work hard. As the incentive strategy, the CM overcomes the disadvantages that other strategies have and is suitable for flexible decision problem.This paper also studies the bargaining method for one kind of cooperative game. In the cooperative game, the constraint of DMs' cooperative behavior is flexible, the preferences of DMs are flexible. Thus the problem is the flexible decision problem. The flexible decision method of bargaining for the kind of cooperative game is presented. The solution by the method is egalitarian and efficient. Under some condition, it is the lexicographic maximin solution.At the end of the paper, a summary is made, the future research development is discussed...