A Survey of Recent Progress in the Asymptotic Analysis of Inventory Systems

It has long been recognized that many inventory models most relevant to practice are inherently high-dimensional, and hence generally believed to become computationally intractable as certain problem parameters grow large (suffering from the "curse of dimensionality"). In the last decade, asymptotic analysis has shown that in many interesting settings such problems can actually be well-approximated by much simpler optimization problems, leading to new algorithms and insights. In this survey, we review the state-of-the-art as regards applying asymptotic analysis to such challenging inventory problems. In addition to surveying the literature, we present a detailed introduction to the relevant tools and methodologies through three in-depth case studies in which asymptotic analysis has recently led to major progress: lost-sales models, dual-sourcing models, and Assemble-to-Order systems in the presence of large lead times.