The Study On The Properties And Application Of Two-Stage Random Fuzzy Programming

The generalized assignment problem (GAP) is concerned with finding the total costs or efficiency optimal assignment schedule of m tasks to n agents such that each task is assigned to exactly one agent, while the total resource capacity of each agent is not exceeded. However, in real-world problems, we often face a hybrid uncertain environment where both randomness and fuzziness coexist. In this thesis, we employ random fuzzy theory to study the generalized assignment problem in random fuzzy decision making systems.First of all, this thesis discusses the properties of the feasible set and the objec-tive function for two-stage random fuzzy programming with recourse problem. Then we study the expected value of perfect information (EVPI) and the value of the ran-dom fuzzy solution (VRFS). Finally, we employ random fuzzy theory to study the generalized assignment problem, and build a kind of generalized assignment model. We use approximation approach to converting the original optimization model to an approximating problem, calculate the value of recourse function, and demonstrate the convergence about the objective function of the approximating two-stage GAP model to that of the original two-stage GAP one. Furthermore, we design a hy-brid PSO algorithm to solve the proposed GAP model and present one application example to illustrate the effectiveness of the algorithm.The main work of this thesis includes the following four aspects:(â…°) the prop-erties of the feasible set and the objective function for two-stage random fuzzy programming with recourse problem are discussed;â…±) the expected value of perfect information and the value of the random fuzzy solution are established; (â…²) the ap-plication of random fuzzy theory to generalized assignment problem is considered, and a kind of two-stage random fuzzy generalized assignment problem models is presented; and (â…³) a hybrid PSO algorithm is designed and one numerical example is given to demonstrate the effectiveness of the designed algorithm.