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This paper studies a continuous-review backlogged inventory model considered by Helmes et al. (2015) but with discontinuous quantity-dependent setup cost for each order. In particular, the setup cost is characterized by a two-step function…

Optimization and Control · Mathematics 2020-09-03 Fen Xu , Dacheng Yao , Hanqin Zhang

We study periodic review stochastic inventory control in the data-driven setting where the retailer makes ordering decisions based only on historical demand observations without any knowledge of the probability distribution of the demand.…

Statistics Theory · Mathematics 2021-11-05 Xun Zhang , Zhisheng Ye , William B. Haskell

In this article, we investigate a dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the…

Optimization and Control · Mathematics 2024-08-06 Subrata Golui , Chandan Pal , Manikandan R. , Abhay Sobhanan

In this paper we study a continuous time stochastic inventory model for a commodity traded in the spot market and whose supply purchase is affected by price and demand uncertainty. A firm aims at meeting a random demand of the commodity at…

Optimization and Control · Mathematics 2015-06-12 Maria B. Chiarolla , Giorgio Ferrari , Gabriele Stabile

In this paper, we consider an infinite horizon, continuous-review, stochastic inventory system in which cumulative customers' demand is price-dependent and is modeled as a Brownian motion. Excess demand is backlogged. The revenue is earned…

Optimization and Control · Mathematics 2018-07-12 Dacheng Yao

We consider an inventory system in which inventory level fluctuates as a Brownian motion in the absence of control. The inventory continuously accumulates cost at a rate that is a general convex function of the inventory level, which can be…

Optimization and Control · Mathematics 2014-01-21 Jim Dai , Dacheng Yao

In this paper, we present long-awaited algorithmic advances toward the efficient construction of near-optimal replenishment policies for a true inventory management classic, the economic warehouse lot scheduling problem. While this paradigm…

Data Structures and Algorithms · Computer Science 2026-01-23 Danny Segev

In classic adversarial online resource allocation problems such as AdWords, customers arrive online while products are given offline with a fixed initial inventory. To ensure revenue guarantees under uncertainty, the decision maker must…

Data Structures and Algorithms · Computer Science 2025-11-21 Yiding Feng , Rad Niazadeh , Amin Saberi

We consider a stochastic inventory control problem under censored demands, lost sales, and positive lead times. This is a fundamental problem in inventory management, with significant literature establishing near-optimality of a simple…

Machine Learning · Computer Science 2019-05-14 Shipra Agrawal , Randy Jia

Inventory models with lost sales and large lead times have traditionally been considered intractable due to the curse of dimensionality. Recently, Goldberg and co-authors laid the foundations for a new approach to solving these models, by…

Probability · Mathematics 2016-04-21 Linwei Xin , David A. Goldberg

The continuous-review (s,S) inventory model is a cornerstone of stochastic inventory theory, yet its analysis becomes analytically intractable when dealing with non-Markovian systems. In such systems, evaluating long-run performance…

Machine Learning · Computer Science 2026-01-21 Eliran Sherzer , Yonit Barron

We consider a general class of high-volume, fast-moving production-inventory systems based on both lost-sales and backorder inventory models. Such systems require a fundamental understanding of the asymptotic behavior of key performance…

Optimization and Control · Mathematics 2015-01-29 Yingdong Lu , Mark S. Squillante , David D. Yao

We consider an inventory system whose state is modeled by a L\'{e}vy process. There are two types of costs--the running costs and the inventory control costs. The running costs (also known as the holding/penalty costs) are incurred…

Optimization and Control · Mathematics 2016-09-02 Jinbiao Wu , Haolin Feng , Dacheng Yao

A high-tech manufacturer often produces products that consist of many modules. These modules are either sourced from one of its suppliers or produced in-house. In this paper we study an assembly system in which one module is sourced from a…

Optimization and Control · Mathematics 2021-05-20 Mirjam S Meijer , Willem van Jaarsveld , Ton de Kok

We consider the classical discrete time lost-sales model under stationary continuous demand and linear holding and penalty costs and positive constant lead time. To date the optimal policy structure is only known implicitly by solving…

Optimization and Control · Mathematics 2024-10-21 Ton de Kok , Mirjam S. Meijer

Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and retailing limited-time availability products. In this paper, we consider a set of sequential…

Optimization and Control · Mathematics 2022-09-09 Yoon Lee , Yonatan Mintz , Anil Aswani , Zuo-Jun Max Shen , Cong Yang

We study the cyclic inventory routing problem that involves joint decisions on vehicle routing and inventory replenishment on an infinite, cyclic horizon. It considers a single warehouse and a set of geographically dispersed retailers. We…

Optimization and Control · Mathematics 2026-05-07 Menglei Jia , Albert H. Schrotenboer , Ahmadreza Marandi , Feng Chen

We consider a distribution warehouse where both the inbound inventory replenishment and outbound dispatch decisions are subject to fixed (as well as per-unit) transportation charges and demand is stochastic. In order to realize scale…

Optimization and Control · Mathematics 2020-12-07 Bo Wei , Sila Cetinkaya , Daren B. H. Cline

We consider a two-product inventory system with independent Poisson demands, limited joint storage capacity and partial demand substitution. Replenishment is performed simultaneously for both products and the replenishment time may be fixed…

Optimization and Control · Mathematics 2015-10-20 Apostolos N. Burnetas , Odysseas Kanavetas

In this paper we address the problem of learning and backtesting inventory control policies in the presence of general arrival dynamics -- which we term as a quantity-over-time arrivals model (QOT). We also allow for order quantities to be…

Machine Learning · Computer Science 2024-01-23 Sohrab Andaz , Carson Eisenach , Dhruv Madeka , Kari Torkkola , Randy Jia , Dean Foster , Sham Kakade