The Uncertainty Of The Deterministic Method And Its Application Of The Optimization Problem

The classical mathematical programming theories and methods, including linear programming, non-linear programming, objective programming, dynamic programming, deal with all information from the real problems by deterministic models. However, in almost all real problems from engineering technology and management, such as the decision-making problem for supply chain management, there exist a lot uncertainties for some reasons. For these uncertainties, this dissertation addresses the construction of optimization models and the efficient algorithms for the different practical problems. It mainly consists of the following parts.Firstly, we introduced some relevant concepts for uncertainties. After giving a review on the recent advances in stochastic programming and fuzzy programming, we also summed up the main problems to be solved.Secondly, we studied the cost minimization problem for multi-products production and transportation with stochastic production capacity of supplier, stochastic sales amount and stochastic unit transportation costs. Stochastic optimization model for this problem was constructed. It can give scheme to determine the amount of deliveries from each supplier to each of the sales by minimizing total cost of transportation with a fixed confidence level. From the numerical experiments of the proposed algorithm, the effects of different confidence levels on the transportation costs were reported.Thirdly, a fuzzy linear programming model was constructed for the portfolio management problem with one risk-free security under the condition that the return and the risk are fuzzy. Based on introducing the concepts of superiority degree and inferiority degree of triangular fuzzy number, we describe the attention degrees of investors to the return of investment and to the risk. Then, we can also determine the optimal investment ratio among some securities under the fuzzy situation.Finally, based on the measures of the possibilities, the necessity and the credibility, we established the profit maximization models for transportation company. In three cases, called optimistic, pessimistic and compromising, the transportation company obtains different profits. These models can reflect the preference of the decision-maker compared with the existing methods.