A circumscribed ellipsoid method for multiobjective programming and applications to robust optimization

The purpose of this research is to propose an innovative methodology that solves practical business planning problems efficiently. Business planning models are typically prone to be complex and large-scale by nature. The new method proposed herein employs two main approaches to these inevitable conditions. The first approach is to build the basic model relatively simple with respect to its original structure. Then the method incorporates any additional information into the model framework by an interactive way in multiobjective optimization. The second approach is to employ an ellipsoid interior point algorithm in order to improve computational efficiency.; By utilizing parametric decomposition theory in multi-objective programming for the first approach, the method provides several alternative nondominated optimal solutions. In this way, intangible information which is normally difficult to formulate can be added into the model to satisfy the decision maker through the decision-making process. The interior point algorithm developed in this research for the second approach is an extension of a series of ellipsoid algorithms for multiobjective programming. The algorithms trace their origin to an ellipsoid method developed in the early 1980s. The proposed method is distinguished from the previous algorithms by several new concepts which include a linearization at the analytic center and an approximate efficient point with equivalent satisfactory levels of each objective function.; Two application examples were chosen from financial and production planning problems, and their robustness to cope with the uncertain business environment was discussed. The efficiency of the method was tested by codes written on Lotus 1-2-3 and GWBASIC software. The attempt to use microcomputers has also confirmed a better interface between the decision maker and the computer. Although the method was originally designed to solve a particular type of business planning problem, it is also applicable to various problems in other fields as well.