Approximate Dynamic Programming for Lateral Transshipments with a Concave Cost Function

Inventory management in modern retail is persistently challenged by the mismatch between supply and customer demand, a problem that leads to costly overstocks and lost sales from stockouts. This issue persists despite sophisticated forecasting tools, primarily due to the inherent uncertainty and volatility of consumer behavior. Lateral transshipment—the practice of moving inventory between locations at the same supply chain echelon—has emerged as a key strategy to enhance flexibility and mitigate these imbalances by creating a pooled inventory resource. This thesis develops and analyzes a reactive transshipment policy tailored for multi-location retail networks that manage products with short selling seasons and highly uncertain demand based on the paper “Approximate Dynamic Programming for Lateral Transshipment Problems in Multi‑Location Inventory Systems” by Joern Meissner and Olga V. Senicheva. In their paper Meissner and Senicheva address the computational complexity of this problem, known as the "curse of dimensionality," by implementing an approximate dynamic programming (ADP) framework to find high-quality, feasible solutions where exact optimization is intractable. The primary contribution of this work is an extension to the existing model: the incorporation of economies of scale into the transshipment cost structure. This is achieved by introducing a concave cost function, a departure from the linear cost assumptions commonly found in the literature. This enhancement creates a more realistic but non-convex optimization problem, necessitating a novel formulation to be solved effectively. The performance of the proposed ADP model is benchmarked against other established reactive transshipment policies to validate its effectiveness.