Order Lot Sizing: Insights from Lattice Gas-Type Model

Abstract

In this study, we introduce a novel interdisciplinary framework that applies concepts from statistical physics, specifically lattice-gas models, to the classical order lot-sizing problem in supply chain management. Traditional methods often rely on heuristic or deterministic approaches, which may fail to capture the inherently probabilistic and dynamic nature of decision-making across multiple periods. Drawing on structural parallels between inventory decisions and adsorption phenomena in physical systems, we constructed a mapping that represented order placements as particles on a lattice, governed by an energy function analogous to thermodynamic potentials. This formulation allowed us to employ analytical tools from statistical mechanics to identify optimal ordering strategies via the minimization of a free energy functional. Our approach not only sheds new light on the structural characteristics of optimal planning but also introduces the concept of configurational entropy as a measure of decision variability and robustness. Numerical simulations and analytical approximations demonstrate the efficacy of the lattice gas model in capturing key features of the problem and suggest promising avenues for extending the framework to more complex settings, including multi-item systems and time-varying demand. This work represents a significant step toward bridging physical sciences with supply chain optimization, offering a robust theoretical foundation for both future research and practical applications.