A Study on the Feasibility of Implementing the Bellman Equation Algorithm in a Discrete Model with PL/SQL (Oracle)

Proceedings of the Scientific Conference "Problems of Informatics and Modeling (PIM-2025). This study explores the implementation of the Bellman equation, a fundamental dynamic programming algorithm, for solving the discrete optimal investment problem using PL/SQL within an Oracle database. The primary objective was to develop a solution capable of handling large datasets by performing all computations directly within the database management system, thereby leveraging its processing power and minimizing data transfer overheads. The research involved a comparative analysis of two methods: a brute-force algorithm implemented with a recursive SQL query and the Bellman equation algorithm realized in PL/SQL. Experimental results clearly demonstrated the superior efficiency of the Bellman equation approach. While the execution time for the brute-force method increased exponentially with the number of investment objects, becoming impractical for complex scenarios, the Bellman equation algorithm's runtime grew almost linearly. The findings confirm that applying the Bellman recurrence relation significantly reduces the computational complexity of the discrete optimization task. The successful implementation in PL/SQL proves its effectiveness for processing substantial data volumes, with performance limited only by server hardware capacity. This work establishes a foundation for further research in integrating dynamic programming and reinforcement learning methods for economic process modeling.