Blockchain technology is booming up the digital world in recent days and thus paved a way for creating separate blockchain network for various industries. This technology is characterized by its distributed, decentralized, and immutable ledger system which serves as a fundamental platform for managing smart contract transactions (SCTs). However, these self-executing codes implemented using blockchains undergo sequential validation within a block which introduces performance bottlenecks. In response, this paper introduces a framework called the Multi-Bin Parallel Scheduler (MBPS) designed for parallelizing blockchain smart contract transactions to leverage the capabilities of multicore systems. Our proposed framework facilitates concurrent execution of SCTs, enhancing performance by allowing non-conflicting transactions to be processed simultaneously while preserving deterministic order. The framework comprises of three vital stages: conflict detection, bin creation and execution. We conducted an evaluation of our MBPS framework in Hyperledger Sawtooth v1.2.6, revealing substantial performance enhancements compared to existing parallel SCT execution frameworks across various smart contract applications. This research contributes to the ongoing optimization efforts in blockchain technology demonstrating its potential for scalability and efficiency in real-world scenarios.