Research On Multi-objective Fuzzy Resource-constrained Project Scheduling

The resource-constrained project scheduling problem (RCPSP) is to schedule the activities such that resource and precedence constraints are satisfied while optimizing some managerial objective. RCPSP is not only rich in theory, but also widely used in practice. But for now, for these problems, the determined time is the precondition. But in the practical problems, working hours for each task in the project is uncertain. In this case, many scholars set the fuzzy theory to the resource-constrained project scheduling problem, therefore, Fuzzy resource-constrained project scheduling problem will be formed.In this paper, we study the RCPSP which based on the duration uncertain time. In this project scheduling problem, the duration of the activities and completion in the project are fuzzy numbers, which are fuzzy duration and fuzzy completion date. For this fuzzy resource-constrained project scheduling problem, the main efforts of this paper are as follows.(1) On the basis of the classical resource-constrained project scheduling,, Research uncertain activity duration. Applied summation of fuzzy number and Comparison of fuzzy numbers to Fuzzy resource-constrained project scheduling problem, and then use three-point fuzzy numbers to represent the work start time and completion time, Then, The two weak comparison method are introduced, Integral value method and the probability distribution. Firstly, research the fuzzy resource-constrained project scheduling problem; with Fuzzy minimum total duration of project scheduling objective function for the project, For this kind of problem, Design a genetic algorithm. The genetic algorithm based on the form of a task linked list encoding. Finally, using example to validate the algorithm.(2) On the basis of the single-objective fuzzy resource-constrained project scheduling problem, Design a fuzzy scheduling rules, And analysis of the objective function, Converted The total duration of the project to triangular fuzzy numbers in fuzzy mathematics membership function, Translated it into customer satisfaction, using maximum Satisfaction To represent the minimum total duration of the project; Another objective function is the average activities of the project’s delay, the smaller Average activity delays, the higher and the degree of Resource utilization. To study of the two objective functions in this paper have important practical significance.(3) From the above research, translate Two different dimensions of the objective function into a unified dimensionless, Create a model of multi-objective fuzzy resource-constrained project scheduling problem. Finally, to solve this problem, Designed a genetic algorithm based on the form of a task linked list encoding. Compare the size of two fuzzy numbers with Probability distribution method, Compare genetic algorithm in this paper with that which coded based on priority values. For this problem, carried out a numerical example, the numerical results show that, the genetic algorithm in this paper is better than the related algorithms in the literature. In solving multi-objective fuzzy resource-constrained project scheduling problem, the genetic algorithm showed a larger advantage.