<p>The serverless computing model frees developers from operational and management tasks, allowing them to focus solely on business logic. This paper addresses the computationally challenging function-container-virtual machine (VM) scheduling problem, especially under stringent deadline constraints. We propose a two-stage holistic scheduling framework called <i>DCRDA</i> targeting deadline-constrained function scheduling. In the first stage, the function-to-container scheduling is modeled as a one-to-one matching game and solved using the classical Deferred Acceptance Algorithm (DAA). The second stage addresses the container-to-VM assignment, modeled as a many-to-one matching problem, and solved using a variant of the DAA, the Revised-Deferred Acceptance Algorithm (RDA), to account for heterogeneous resource demands. Since matching-based strategies require agent preferences, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) ranking mechanism is employed to prioritize alternatives based on execution time, deadlines, and resource demands. The primary goal of <i>DCRDA</i> is to maximize the success ratio (SR), defined as the ratio of functions executed within the deadline to the total functions. Extensive test-bed validations over commercial providers such as <i>Amazon EC2</i> show that the proposed framework significantly improves the success ratio compared to baseline approaches.</p>