Traditionally Electric Multiple Unit (EMU) requirements for High-Speed Railway (HSR) are determined through a rigorous sequential process manually that can lead to sub-optimal EMU circulation plans. In response to the inherent complexities and inefficiencies of this sequential approach, this paper presents a coordinated approach that integrates timetable and EMU circulation planning through feedback links. The proposed approach explores application of adjustable departure time windows in the initial timetable to minimize the number of EMUs needed for the entire timetable. The study considers two types of EMU usage methods i.e. fixed routing and flexible routing. An Integer Linear Programming (ILP) model incorporating train operation constraints is devised and solved over CPLEX commercial solver. To solve the NP-Hard problem efficiently, an iterative local search algorithm inspired by TABU search principles is introduced. Comparative analysis between ILP and the algorithm is carried out, validating their applicability. The model and algorithm are validated against the real case data of Beijing-Tianjin HSR. The findings demonstrate the efficacy of the proposed approach in addressing optimization challenges in coordinated circulation planning. The proposed algorithm is demonstrated to be capable of returning high-quality solutions swiftly, especially in scenarios involving time windows, where exact solutions by commercial solvers are time-consuming.