Abstract: This paper considers the scheduling problem under linear deterioration. It is assumed that the deterioration function is a linear function. Optimal algorithms are presented respectively for single machine scheduling problems of minimizing the makespan, weighted sum of completion times, maximum lateness and maximum cost. For two-machine flow shop scheduling problem to minimize the makespan, it is proved that the optimal schedule can be obtained by Johnson's rule. If the processing times of operations are equal for each job, flow shop scheduling problems can be transformed into single machine scheduling problems.