The share of renewable energy sources (RESs)-based generation within contemporary power systems has expanded substantially in recent years, driven by environmental concerns and policy incentives to promote clean and sustainable electricity generation. However, the inherently variable and difficult-to-predict behavior of renewable generation, with a particular emphasis on wind-based resources, introduces substantial operational challenges for system operators that require effective flexibility resources. This paper addresses these challenges by formulating a network-constrained unit commitment (NCUC) model that incorporates mobile-based battery energy storage systems (MBESSs) and price-based demand response program (DRP) as key flexibility resources. A time–space network is employed to optimize the charging, discharging, and transportation schedules of MBESSs. Moreover, a new version of the information gap decision theory (IGDT) method is developed to handle wind power uncertainty more accurately. Unlike the conventional IGDT approach, the proposed method introduces a time-varying uncertainty radius, effectively capturing the dynamic and variable behavior of wind power. The model is formularized as a mixed-integer linear programming (MILP) problem and tested on a six-bus power system integrated with a three-station railway network. Simulation outcomes demonstrate that the proposed framework completely eliminates load shedding and wind power curtailment. Furthermore, compared to the conventional IGDT, the proposed novel method can provide different levels of uncertainty for each interval of the scheduling horizon.