Study On Fuzzy Optimization Methods For Production And Financial Investment Problem

The production and financial investment planning problem is an integrated decisions in both production capacity and financial products of a profit-maximising company. In this process, the uncertain factors in the global market environment is closely related with the final profits of the company. Two main uncertain factors that the decision makers often consider are currency exchange rates and the market demands. However, these two uncertain factors usually present fuzziness,so we study the production and financial investment planning problem in a fuzzy environment.In this thesis, we consider a new production and financial investment planning problem with fuzzy currency exchange rate and market demands, and a two-stage fuzzy programming method is used to model our problem. We discuss the investment planning problem under two situations: the currency exchange rate is uncertain but demands are determinisic and both of them are uncertainty. Using the LebesgueStieltjes integral to measure the benefits of the company, we derive the analytical form about the optimal value function in the second stage. In order to solve the proposed model, we derive the equivalent programming problems in different feasible regions. Based on the characteristics of the equivalent models, we employ the domain decomposition method to solve them. Finally, we conduct two numerical experiments to demonstrate the applicability of the proposed model and solution approaches.In this thesis, the main new work can be summarized as the following four aspects:(1) Two production and financial investment planning problems are modeled under uncertain currency exchange rate, uncertain demands and currency exchange rate;(2) We derive the the analytical form about the optimal value function in the second stage of the proposed models;(3) Under di?erent feasible regions, we derive the equivalent programming models when uncertain currency exchange rate and the demands follow the triangular distributions;(4) According to the characteristics of the models, two feasible domain decomposition methods are presented to solve the obtained equivalent models, and the numerical experiments are provided to illustrate the applicability of the proposed model and solution approaches.