Nowadays, the demand of “personalization” and “multiple varieties and small batch production” in machining is increasing dramatically. The great challenges of scheduling are brought about by the high flexibility of production and the necessity of equipment maintenance, and the scheduling problems are more complex due to the deteriorating effect of the production process. In order to solve the single machine scheduling problem with step-deteriorating jobs and fixed periodic maintenance strategy, the processing time was described by the piecewise linear function. Based on the properties of the periodic maintenance and the flexible periodic maintenance, two scheduling models were established respectively to minimize the tardiness penalties and maintenance cost. According to the numerical experiments and parameter analysis, the key factors and non-key factors of maintenance decision were determined. The result shows that flexible periodic maintenance has no idle time between adjacent batches. The objective function value increases step by step with the increase of ratio, which can realize “adaptive” adjustment of cost and has significant advantages over fixed cycle maintenance. The construction of a joint scheduling model of production and maintenance can realize the comparison of the advantages and disadvantages of maintenance strategies and the joint decision of production and maintenance, and reduce the operating cost of enterprise production and maintenance.