Research on dynamic programming method of complex product design task combining fuzzy set theory and greedy algorithm

During the product design process, the design team faces issues such as unreasonable allocation of resources and time, the sequence of task execution, and project delays caused by external factors affecting designers and tasks. Firstly, historical design case execution times are used as reference times, and fuzzy set theory is applied to quantify the execution times of tasks by designers of different skill levels. Secondly, a multi-level design structure matrix is constructed to obtain the relationships between tasks, and a topological hierarchy sorting method is utilized to determine the execution sequence of tasks. Finally, a state transition matrix is employed to analyze the execution status of design tasks, and a greedy algorithm is combined to generate an optimal allocation scheme under the constraints of task sequence and duration, which can be dynamically adjusted and redistributed when design resources change. The research results indicate that, using a certain model of cabin-type products from Company J as an example, a design task execution time matrix and a directed acyclic graph have been successfully constructed, and the optimization of task allocation has been achieved through the greedy algorithm.