While undertaking the transformation and upgrading of global industries, China has gradually become a world manufacturing power. After the rapid development and scale expansion, China′s manufacturing industry has faced an unreasonable supply-side structure, an imbalance between supply and demand, and a low utilization of manufacturing resources. To improve these problems, the central government has encouraged and supported the development of third-party sharing platforms for manufacturing enterprises in the 14th Five-Year Plan, Made in China 2025, and other national policy documents. The third-party shared platforms match the supply and demand of capacity by providing matching services, such as matchmaking and docking, to support capacity sharing among manufacturers. In doing so, manufacturers with insufficient capacity can find partners, while manufacturers with surplus capacity can share surplus capacity. In practice, manufacturers often possess multiple periods of demand information due to the possible receipt of production orders in advance. To match partners on time and reduce production risks, manufacturers may submit demand information to the platform in advance. From the perspective of the platform, knowing the demand information of multiple periods beforehand optimizes the matching decision and allows more manufacturers be matched successfully. Thus, the reputation and income of the platform are improved. Therefore, the platform will encourage manufacturers to submit the demand information in advance. In this context, the platform is facing a cross-period capacity-matching problem. It not only needs to match the capacity supply and demand in the current period but also needs to decide whether to meet the manufacturer′s demand in advance. As a result, the matching work of the platform becomes increasingly complex. When manufacturers have cross-period capacity demand, studying the capacity matching of the third-party shared manufacturing platform is of great practical significance for the development of the platform.Motivated by the above practice, this study focuses on multiple manufacturers with insufficient capacity, multiple manufacturers with surplus capacity and a third-party shared manufacturing platform, in which the platform provides matching services for them and charges transaction commissions from manufacturers with surplus capacity. When the capacity demand is met in advance, considering the impact of capacity price and quantity on the matching strategy, we formulate a bi-level multi-objective optimization model with the objective functions of maximizing the matching rate and commission income. The lower-level model optimizes the matching strategy for the current period, and the upper-level model decides whether to meet the manufacturer′s demand for the next period in advance. To solve this bi-level multi-objective optimization model, the weight method is adopted to convert the multi-objective model into a single-objective model. Then, a two-stage solving algorithm (GA-HSSA) is designed to solve it. In the first stage, we adopt the greedy algorithm to generate the initial solution of the model. In the second stage, we combine the random search algorithm (RSA) and directed search algorithm (DSA) to design a hybrid strategy search algorithm (HSSA) to optimize the initial solution generated by the greedy algorithm.To verify the feasibility and effectiveness of the matching model and algorithm proposed in this study, we constructed small-sized, medium-sized, and large-sized instances in the numerical simulation. Then, we compared the results with the optimization solver CPLEX and the greedy algorithm. In addition, we also analyzed the advantages and disadvantages of the directional search algorithm, random search algorithm and hybrid strategy search algorithm through numerical experiments. Further, we performed a sensitivity analysis of the parameters, thus verifying that the algorithm designed in this study (GA-HSSA) is robust.The numerical experiments obtain the following results. 1) Compared with the optimization solver CPLEX, GA-HSSA outperforms CPLEX in terms of computational effectiveness and efficiency. Moreover, GA-HSSA can find the valid solution of large-sized instances within an acceptable time, while CPLEX runs for 12h without finding a feasible solution. Thus, the feasibility and effectiveness of the algorithm designed in this study are verified. 2) HSSA can match more than 92% of manufacturers with suitable partners and significantly improve the quality of the solutions generated by the greedy algorithm, optimizing the lower-level objective function by 14% to 52% and the upper-level objective function by 0% to 31%. 3) Compared with the DSA and RSA, the optimization ability of HSSA is stronger than that of DSA and RSA. In addition, the stability analysis of algorithms shows that HSSA improves the solution while maintaining stability. 4) The parameter sensitivity analysis reveals that the algorithm proposed in this study (GA-HSSA) has good robustness.This research considers several key factors in the actual matching process of third-party shared manufacturing platforms, such as capacity price and demand and supply quantity. It further investigates the impact of met demand in advance on the manufacturers and the matching work of the platform. By constructing a multi-objective matching model and designing a two-stage matching algorithm, the cross-period matching problem of third-party shared manufacturing platforms is studied. The matching model and algorithm designed in this study enrich existing research on the capacity matching of third-party shared manufacturing platforms. Moreover, we provide reference methods for third-party shared manufacturing platforms to solve cross-period capacity matching problems.