Single machine scheduling problem with slake due date assignment is studied. The actual processing time of a job is determined by deterioration effects, convex resource allocation and a rate-modifying activity on the machine. The problem is to determine the optimal job sequence, the optimal position of the rate-modifying activity, the optimal common flow allowance and the amount of resource allocation such that the two constrained optimization objective cost functions are minimized. One is the weighted penalties for the sum of earliness, tardiness, common flow allowance and maximum completion time subject to an upper bound on the total resource cost, the other is minimizing the total resource cost subject to an upper bound on the total penalty cost. Transform the two problems into assignment problems. When the rate-modifying activity is located in different positions, select the optimal solution such that minimizes the objective function. It is proved that these problems remain polynomial solvable under the proposed algorithms and the time complexity are O(n4), where n is the number of jobs. Numerical examples show that the proposed algorithms are effective.