Joint Optimization of Delivery Time, Quality, and Cost for Complex Product Supply Chain Networks Based on Symmetry Analysis

Products with complex structures are structurally intricate and involve multiple professional fields and engineering construction elements, making it difficult for a single contractor to independently develop and manufacture such complex structural products. Therefore, during the research, development, and production of complex products, collaboration between manufacturers and suppliers is essential to ensure the smooth completion of projects. In this process, a complex supply chain network is often formed to achieve collaborative cooperation among all project participants. Within such a complex supply chain network, issues such as delayed delivery, poor product quality, or low resource utilization by any participant may trigger the bullwhip effect. This, in turn, can negatively impact the delivery cycle, product cost, and quality of the entire complex product, causing it to lose favorable competitive positions such as quality advantages and delivery advantages in fierce market competition. Therefore, this paper firstly explores the mechanism of complex product manufacturing and the supply network of complex product manufacturing, in order to grasp the inherent structure of complex product manufacturing with a focus on identifying symmetrical properties among supply chain nodes. Secondly, a complex product supply chain network model is constructed with the Graphical Evaluation and Review Technique (GERT), incorporating symmetry constraints to reflect balanced resource allocation and mutual dependencies among symmetrical nodes. Then, from the perspective of supply chain, we focus on identifying the shortcomings of supply chain suppliers and optimizing the management cost of the whole supply chain in order to improve the quality of complex products, delivery level, and cost saving level. This study constructs a Restricted Grey GERT (RG-GERT) network model with constrained outputs, integrates moment-generating functions and Mason’s Formula to derive transfer functions, and employs a hybrid algorithm (genetic algorithm combined with non-linear programming) to solve the multi-objective optimization problem (MOOP) for joint optimization of delivery time, quality, and cost. Empirical analysis is conducted using simulated data from Y Company’s aerospace equipment supply chain, covering interval parameters such as delivery time [5–30 days], cost [40,000–640,000 CNY], and quality [0.85–1.0], validated with industry-specific constraints. Empirical analysis using Y Company’s aerospace supply chain data shows that the model achieves a maximum customer satisfaction of 0.96, with resource utilization efficiency of inefficient suppliers improved by 15–20% (p < 0.05) after secondary optimization. Key contributions include (1) integrating symmetry analysis to simplify network modeling; (2) extending GERT with grey parameters for non-probabilistic uncertainty; (3) developing a two-stage optimization framework linking customer satisfaction and resource efficiency.