This paper addresses the complex issue of resource-constrained scheduling, an NP-complete problem that spans critical areas including chip design and high-performance computing. Traditional scheduling methods often stumble over scalability and applicability challenges. We propose a novel approach through a differentiable combinatorial scheduling framework, utilizing the Gumbel-Softmax differentiable sampling technique. This innovation allows for a fully differentiable formulation of linear programming-based scheduling, extending its application to a broader range of LP formulations. To encode inequality constraints for scheduling tasks, we introduce the constrained Gumbel-Softmax technique, which adeptly encodes arbitrary inequality constraints. Consequently, our method facilitates efficient, scalable optimization via gradient descent, without the need for extensive data. Comparative evaluations on both synthetic and real-world benchmarks highlight our framework's capability to significantly enhance scheduling runtime efficiency, surpassing state-of-the-art solutions offered by commercial solvers such as CPLEX and Gurobi.