The pharmaceutical supply chain is a critical component of the healthcare system, ensuring the safe production, distribution, and delivery of medicines. However, existing systems face challenges such as counterfeit drugs, lack of transparency, inefficient tracking, and the improper disposal of expired drugs. Traditional supply chain models use centralised databases, which are prone to security vulnerabilities, limited traceability, and inefficiencies in resource allocation. This paper proposes a blockchain-based pharmaceutical supply chain management system using Ethereum, integrating smart contracts, zero-knowledge proofs (ZKPs), and decentralised identifiers (DIDs) to enhance security, privacy, and transparency. A key aspect of the proposed system is the inclusion of secure digital prescriptions, utilizing verifiable credentials (VCs) and ZKPs to prevent prescription fraud while maintaining patient confidentiality. Additionally, various resource allocation algorithms are analysed to optimise pharmaceutical distribution, with the Hungarian algorithm identified as the most efficient in minimizing cost and ensuring equitable drug distribution. The proposed framework enhances traceability, prevents counterfeit drugs, and ensures secure digital prescription management, addressing key weaknesses of the conventional supply chain systems. Our findings indicate that blockchain technology when combined with cryptographic techniques, can significantly improve the security and efficiency of pharmaceutical supply chains, making them less susceptible to frauds and operational inefficiencies.