Abstract: Aiming at the scheduling problems of the single machine and two parallel machines,a model of scheduling problems with learning effect and an availability constraint is established.In the model,the machines have learning effect.By the learning effect,the processing time of jobs is defined as the function of their positions in a sequence,and the jobs to be processed on the same machine,Their actual processing time is gradually reduced along with the order of their positions.Moreover,the machine could be unavailable for a specified period of time by periodic machine maintenance activity.That the objective function is to minimize the total completion time of single machine problems and two parallel machines problems is considered.A dynamic programming algorithm is provided for the machine maintenance in the common case at any time,and the validity of the algorithm is also illustrated by an example.A polynomial algorithm is given for the maintenance before the use of the machine in the special case.