This paper studied a single machine scheduling with a slack due-date and a maintenance activity which is deteriorating and resource-dependent, where the actual processing time of the job depends on whether it is processed before or after the maintenance activity. The due-date of the job is the sum of its actual processing time and the slack variable (i.e., the common flow allowance). The objective of this problem is to determine the sequence of the jobs, the location of the maintenance activity, the value of the slack variable, and the resources consumed by the maintenance activity to minimize the total cost of the earliness, tardiness, slack due-date and resource consumption. For a given sequence, the value of slack variable is the starting processing time of some job in the sequence, through the cases to discuss the location of the maintenance activity, the objective function is transformed into a function which is only related to the sequence of the jobs and the resources respectively. The minimum value of the objective function is obtained by transforming it into an assignment problem or using the vector matching rule. Finally, the corresponding algorithm is given and we prove that the problem is polynomially solvable.