Order Lot Sizing: Insights from a Lattice-Gas Type Model

Efficient inventory management and material supply planning are critical aspects for the successful operation of companies in highly competitive and dynamic environments. Determining the order lot size emerges as a key strategic decision that directly influences operational efficiency, associated costs, and responsiveness. For this reason, in this work, we propose the use of well-established tools from physics, particularly in the field of statistical mechanics, to analyze a complex system such as material requirements and, specifically, the dimensioning of order lot sizes. The result is a novel approach to the order lot-sizing problem, where ordering options are mapped to states in a classical lattice-gas problem. From this perspective, we demonstrate how studying the main thermodynamic functions associated with the lattice gas offers valuable insights for optimizing the selection of order lot sizes. Of particular interest is the analysis of the configurational entropy as a function of surface coverage (or its equivalent, the number of orders over the planning horizon), whose minima provide relevant information for the management of material supply.