［Purposes］Two-agent scheduling problem with fixed time windows was studied. ［Methods］The jobs of the first agent might be preemptive.The objective function is the total weighted late work or the total weighted early work on a single machine, and the objective function is the total completion time on two parallel machines.The second agent is arranged to be processed in a fixed time window.The objective is to find a scheduling scheme to make the objective function value of the first agent as small as possible when the second agent objective is feasible. ［Findings］The scheduling algorithm of fixed time windows job loss problem on single machine was designed, and the corresponding algorithm was also designed for the total completion time of two parallel machines. ［Conclusions］It is proved that the designed algorithms are polynomial time solvable, and the optimality of the algorithms is proved.