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

Abstract

I t 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: lostsales models, dual-sourcing models, and Assemble-to-Order systems in the presence of large lead times.

Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

“…Second, this paper is related to the growing literature on asymptotic analysis of simple heuristics for complex inventory systems. We refer to Goldberg et al (2021) for a detailed review on this topic. In particular, there have been extensive studies on lost-sales non-perishable inventory systems with lead times, including asymptotic analysis of base-stock policies with large unit penalty costs or high service-level requirements (Reiman 2004, Bijvank et al 2014, Arts et al 2015, Wei et al 2021, and constant-order or capped base-stock policies with large lead times (Goldberg et al 2016, Xin and Goldberg 2016, Bu et al 2020, Xin 2021b.…”

Time‐average stochastic control based on a singular local Lévy model for environmental project planning under habit formation

“…Subsequently, the Hamilton-Jacobi-Bellman (HJB) equation of this control problem and its discounted version also referred to as Abel limit [46] are formally obtained. The latter is used for computing the HJB equation based on a vanishing-discount method: a methodology to approximate a time-average control problem as a small-discount control problem [47][48][49]. Ratcheting problems as extreme cases of the habit formation are also investigated as they are tractable non-ergodic cases.…”

Solving Inventory Management Problems with Inventory-dynamics-informed Neural Networks

“…When lead times differ more than one period, the optimal policy is state-dependent, as it depends on the vector of pipeline orders in a non-trivial way (Whittemore and Saunders 1977). As the difference between the supplier lead times grows larger, the problem becomes computationally intractable because of the associated "curse of dimensionality" (Powell 2007, Goldberg et al 2021. Most of the literature has therefore focused on the development of heuristic policies, such as the single index (SI) (Scheller-Wolf et al 2007), dual index (DI) (Veeraraghavan and Scheller-Wolf 2008), capped dual index (CDI) (Sun and Van Mieghem 2019), vector-base-stock (Sheopuri et al 2010, Hua et al 2015, (VBS) and tailored-based surge (TBS) (Allon and Van Mieghem 2010, Xin and Goldberg 2018, Chen and Shi 2019 policies.…”

“…Dual sourcing can be extended in multiple other directions, such as having endogenous stochastic lead times (Song et al 2017), multi-source systems (Song et al 2021), non-stationary demand, and supplier capacities (Boute et al 2021a). A comprehensive overview of dual-sourcing models is presented in Xin and Van Mieghem (2021), while Goldberg et al (2021) provide a review of asymptotic analysis in inventory control problems and show how it can be applied to dual-sourcing models.…”