Optimization Approaches for the (r,Q) Inventory Policy

Abstract

This thesis presents a comprehensive investigation into the performance and generalizability of optimization approaches for the single-echelon (r, Q) inventory management policy under stochastic demand, specifically focusing on demand characterized by a Poisson distribution. The research integrates both classical optimization techniques and advanced metaheuristic methods, with a particular emphasis on Genetic Programming (GP), to assess the effectiveness of various heuristics. The study systematically compares the performance of these approaches in terms of both accuracy and computational efficiency using two well-known datasets. To rigorously evaluate the generalizability of the heuristics, an extensive random dataset of 10,000 instances, drawn from a vast population of approximately 24 billion instances, was generated and employed in this study. Our findings reveal that the exact solution provided by the Federgruen-Zheng Algorithm consistently outperforms hybrid heuristics in terms of computational efficiency, confirming its reliability in smaller datasets where precise solutions are critical. Additionally, the extended Cooperative Coevolutionary Genetic Programming (eCCGP) heuristic proposed by Lopes et al. emerges as the most efficient in terms of runtime, achieving a remarkable balance between speed and accuracy, with an optimality error gap of only 1%. This performance makes the eCCGP heuristic particularly suitable for real-time inventory management systems, especially in scenarios involving large datasets where computational speed is paramount. The implications of this study are significant for both theoretical research and practical applications, suggesting that while exact solution, i.e., the Federgruen-Zheng Algorithm is ideal for smaller datasets, the eCCGP heuristic provides a scalable and efficient alternative for larger, more complex datasets without substantial sacrifices in accuracy. These insights contribute to the ongoing development of more effective inventory management strategies in environments characterized by stochastic demand.