This research project belongs to the intersection of mathematics, operations research and theoretical computer science. It mainly studies new sequencing problems such as online sequencing, network sequencing, batch sequencing and agent sequencing, establishes mathematical models of the problems, analyzes the complexity and solvability of the problems, designs efficient optimal algorithms, approximate algorithms or online algorithms, analyzes the performance ratio or competition ratio of the algorithms or conducts numerical simulations. The main scientific contributions of the project are: (1) Regarding online scheduling, pioneering research has been carried out on online single machine and parallel machine minimization of completion time sum problems, online batch machine scheduling problems, and online flow job scheduling problems, and the lower bound of the problem has been proposed., the optimal algorithm has been designed, and the conjecture proposed by Professor Stougie in 1995 has been successfully solved; in-depth discoveries and applications have been made in research methods such as waiting strategies, minimum counterexample and gap techniques. (2)Conducted research on network sequencing, a cutting-edge field of combination optimization research in China, and achieved breakthrough research results. This paper studies the network sequencing and routing problem with regular objective functions on linear networks, basically and thoroughly solves its complexity classification, and designs an efficient approximation algorithm. It proves that the two-machine pipeline problem on a tree network is NP difficult, thus solving Averbakh and Berman's conjecture; It proves that the important conclusion that there is an optimal solution to the two-machine pipeline problem on a general network has the same order; and gives the best approximation algorithm at present for several network sequencing problems. (3)The earliest research on batch machine sequencing was carried out in China, which solved the complexity classification of batch machine sequencing problems with unlimited capacity, and solved the complexity of the basic problem of minimizing the maximum completion time when workpieces have ready time constraints. For the first time, the lower bound of the competition ratio of online algorithms is given. In terms of online algorithm research for the maximum completion time problem of multiple batch processors without capacity constraints, the first optimal algorithm is given. (4)The project team is one of the earliest groups in China to conduct research on agent scheduling. In terms of parallel machine two-agent scheduling, the FPTAS algorithm was proposed for the situation where the schedule length of one agent is a constraint and the schedule length of the other agent is minimized or the sum of the completion time. The best approximation algorithm is obtained by minimizing the schedule length of two agents at the same time; For the multi-agent maximum completion time problem on two parallel machines, an approximate algorithm with the best performance ratio is designed, and the performance ratio is proved to be tight. The original innovative research results of the project team are mainly published in important international professional academic journals such as the Journal of Scheduling, Operations Research Letters, Discrete Applied Mathematics, Networks, European Journal of Operational Research, Annals of Operations Research, Theoretical Computer Science, etc. 54 papers published by the project team as the first author or corresponding author were included in the SCI database. The total number of citations in the core collection of Web of Science was 485. The number of citations in the core collection of Web of Science of 8 representative papers was 185, of which the number of citations in SCI was 163.