Solution of Multi-objective Management Problem by Means of Probabilistic Multi-objective Optimization Approach

This paper presents the application of probabilistic multi-objective optimization method (PMOO) in enterprise production management, which involves the simultaneous optimization of "high long-term profit target" and "small investment amount". PMOO method is an effective approach to deal with multi-objective optimization problems from the viewpoint of system theory and method of probability theory, in which the new concept of "preferable probability" is introduced to formulate the methodology of PMOO. In PMOO, the evaluated attributes (objectives) of candidates are preliminarily divided into two basic types: beneficial attributes and unbeneficial attributes, and the corresponding quantitative evaluation method of partial preferable probability of each type of attribute is established. Furthermore, the total preferable probability of each candidate alternative is the product of partial preferable probabilities of all possible attributes, and the maximum value of the total preferable probability presents the overall optimization of the system. In the enterprise production management problem of three kinds of products, the objective function is to maximize the long-term profit target and minimize the investment amount, the discretization of Hua's "good lattice point" and uniform mixture design are applied to simplify the optimization process and data processing. Finally, a rational result is obtained.