This paper addresses a single machine scheduling problem in which the actual job processing times are determined by resource allocation function, its position in a sequence and a rate-modifying activity simultaneously. We discuss two objective functions with two resource allocation functions under the consideration of a rate-modifying activity. We show that the problems are solvable in O(n4) time for a linear resource allocation function and are solvable in O(n2logn) time for a convex resource allocation function.