Within the context of Software-Defined Networking (SDN), the problem of resource allocation for a set of incoming Virtual Network Functions (VNF) service requests has been the focus of many studies. In this paper, a new optimization model has been developed to find the near to optimal mapping and scheduling for the incoming VNF service requests. This model while considering delay, aims to achieve three objectives functions, namely, minimizing the transmission delays occurring in every link, minimizing the processing capacity for every Virtual Machine (VM) and minimizing the processing delay at every VM. The resultant problem is formulated as a multi-objective optimization problem and the developed solution is based on a multi-objective evolutionary algorithm utilizing the decomposition algorithm. Simulation results illustrate that the resulting algorithm is scalable while considering delay and it outperforms the genetic bandwidth link allocation (GA-BA) and genetic non-bandwidth link allocation (GA-NBA) algorithms.