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

Goldberg, David A.; Reiman, Martin I.; Wang, Qiong

doi:10.1111/poms.13339

Cited by 31 publications

(14 citation statements)

References 220 publications

(532 reference statements)

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“…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.…”

Section: Literature Reviewmentioning

confidence: 99%

Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

Gong

Chao

2023

Management Science

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We consider periodic review perishable inventory systems with a fixed product lifetime. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty, and outdating cost. The optimal policy for these systems is notoriously complex and computationally intractable because of the curse of dimensionality. Hence, various heuristic replenishment policies are proposed in the literature, including the base-stock policy, which raises the total inventory level to a constant in each review period. Whereas various studies show near-optimal numerical performances of base-stock policies in the classic system with zero replenishment lead time and a first-in-first-out issuance policy, the results on their theoretical performances are very limited. In this paper, we first focus on this classic system and show that a simple base-stock policy is asymptotically optimal when any one of the product lifetime, demand population size, unit penalty cost, and unit outdating cost becomes large; moreover, its optimality gap converges to zero exponentially fast in the first two parameters. We then study two important extensions. For a system under a last-in-first-out or even an arbitrary issuance policy, we prove that a simple base-stock policy is asymptotically optimal with large product lifetime, large unit penalty costs, and large unit outdating costs, and for a backlogging system with positive lead times, we prove that our results continue to hold with large product lifetime, large demand population sizes, and large unit outdating costs. Finally, we provide a numerical study to demonstrate the performances of base-stock policies in these systems. This paper was accepted by Victor Martinez de Albéniz, operations management.

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Section: Literature Reviewmentioning

confidence: 99%

Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

Gong

Chao

2023

Management Science

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“…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.…”

Section: Objective and Contributionmentioning

confidence: 99%

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

Yoshioka

Tsujimura

Hamagami

et al. 2023

Math Methods in App Sciences

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This study applies the theory of stochastic control to an environmental project planning to counteract against the sediment starvation problem in river environments. This can be considered as a time-average inventory problem to time-discretely control a continuous-time system driven by a non-smooth jump process under habit formation disturbing project implementation. The system is modeled such that the sediment storage dynamics are physically consistent with certain experimental results. Further, the habit formation is modeled as simple linear dynamics and serves as a constraint related to the replenishment amount of the sediment. We show that the time-average control problem is not necessarily ergodic. Consequently, the effective Hamiltonian may become a non-constant. Thereafter, ratcheting cases as extreme cases of the irreversible habit formation are considered, owing to them being unique exactly solvable non-ergodic control problems. The optimality equation associated with a regularized and hence well-defined control problem is verified. Furthermore, a finite difference scheme is examined against the exactly solvable case and then applied to more complicated cases.

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“…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.…”

Section: Inventory Management With Dual Sourcingmentioning

confidence: 99%

“…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.…”

Section: Inventory Management With Dual Sourcingmentioning

confidence: 99%

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

Böttcher¹,

Asikis²,

Fragkos³

2022

Preprint

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A key challenge in inventory management is to identify policies that optimally replenish inventory from multiple suppliers. To solve such optimization problems, inventory managers need to decide what quantities to order from each supplier, given the on-hand inventory and outstanding orders, so that the expected backlogging, holding, and sourcing costs are jointly minimized. Inventory management problems have been studied extensively for over 60 years, and yet even basic dual sourcing problems, in which orders from an expensive supplier arrive faster than orders from a regular supplier, remain intractable in their general form.In this work, we approach dual sourcing from a neural-network-based optimization lens. By incorporating inventory dynamics into the design of neural networks, we are able to learn near-optimal policies of commonly used instances within a few minutes of CPU time on a regular personal computer. To demonstrate the versatility of inventory-dynamics-informed neural networks, we show that they are able to control inventory dynamics with empirical demand distributions that are challenging to tackle effectively using alternative, state-of-the-art approaches.

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

Cited by 31 publications

References 220 publications

Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems

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

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

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