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The Joint Replenishment Problem (JRP) is a fundamental optimization problem in supply-chain management, concerned with optimizing the flow of goods from a supplier to retailers. Over time, in response to demands at the retailers, the…

Data Structures and Algorithms · Computer Science 2015-12-04 Marcin Bienkowski , Jaroslaw Byrka , Marek Chrobak , Neil Dobbs , Tomasz Nowicki , Maxim Sviridenko , Grzegorz Swirszcz , Neal E. Young

The Joint Replenishment Problem (JRP) is a classical inventory management problem, that aims to model the trade-off between coordinating orders for multiple commodities (and their cost) with holding costs incurred by meeting demand in…

Data Structures and Algorithms · Computer Science 2026-02-13 David Shmoys , Varun Suriyanarayana , Seeun William Umboh

In this paper we consider a combination of the joint replenishment problem (JRP) and single machine scheduling with release dates. There is a single machine and one or more item types. Each job has a release date, a positive processing…

Data Structures and Algorithms · Computer Science 2022-03-03 Péter Györgyi , Tamás Kis , Tímea Tamási , József Békési

This paper addresses the single-item single-stocking location non-stationary stochastic lot-sizing problem under a reorder point -- order quantity control strategy. The reorder points and order quantities are chosen at the beginning of the…

Optimization and Control · Mathematics 2022-03-08 Xiyuan Ma , Roberto Rossi , Thomas Welsh Archibald

The (R, s, S) is a stochastic inventory control policy widely used by practitioners. In an inventory system managed according to this policy, the inventory is reviewed at instant R; if the observed inventory position is lower than the…

Optimization and Control · Mathematics 2023-09-26 Andrea Visentin , Steven Prestwich , Roberto Rossi , S. Armagan Tarim

We study an online generalization of the classic Joint Replenishment Problem (JRP) that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning systems. A retailer places orders to a supplier…

Data Structures and Algorithms · Computer Science 2024-10-25 Benjamin Moseley , Aidin Niaparast , R. Ravi

In their seminal paper Moseley, Niaparast, and Ravi introduced the Joint Replenishment Problem (JRP) with holding and backlog costs that models the trade-off between ordering costs, holding costs, and backlog costs in supply chain planning…

Data Structures and Algorithms · Computer Science 2025-07-23 Yossi Azar , Shahar Lewkowicz

The Joint Replenishment Problem (JRP) deals with optimizing shipments of goods from a supplier to retailers through a shared warehouse. Each shipment involves transporting goods from the supplier to the warehouse, at a fixed cost C,…

Data Structures and Algorithms · Computer Science 2013-07-10 Marcin Bienkowski , Jaroslaw Byrka , Marek Chrobak , Łukasz Jeż , Jiří Sgall

In this paper, we develop mixed integer linear programming models to compute near-optimal policy parameters for the non-stationary stochastic lot sizing problem under Bookbinder and Tan's static-dynamic uncertainty strategy. Our models…

Optimization and Control · Mathematics 2014-09-18 Roberto Rossi , Onur A. Kilic , S. Armagan Tarim

We consider a discrete-time formulation for a class of high-dimensional stochastic joint replenishment problems. First, we approximate the problem by a continuous-time impulse control problem. Exploiting connections among the impulse…

Optimization and Control · Mathematics 2026-05-29 Barış Ata , Wouter van Eekelen , Yuan Zhong

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

This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product from suppliers and sells it to a market while facing non-stationary demands. In each period, the…

Optimization and Control · Mathematics 2021-08-13 Zhen Chen , Roberto Rossi

The joint replenishment problem (JRP) is a classical inventory management problem. We consider a natural generalization with outliers, where we are allowed to reject (that is, not service) a subset of demand points. In this paper, we are…

Data Structures and Algorithms · Computer Science 2023-08-10 Varun Suriyanarayana , Varun Sivashankar , Siddharth Gollapudi , David Shmoys

A well-know control policy in stochastic inventory control is the (R, s, S) policy, in which inventory is raised to an order-up-to-level S at a review instant R whenever it falls below reorder-level s. To date, little or no work has been…

Optimization and Control · Mathematics 2022-03-08 Andrea Visentin , Steven Prestwich , Roberto Rossi , S. Armagan Tarim

The Replenishment Storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system where each item has a given reorder size and cycle length. The reorders can only take place at…

Data Structures and Algorithms · Computer Science 2020-10-06 Dorit S. Hochbaum , Xu Rao

The main contribution of this paper resides in developing a new algorithmic approach for addressing the continuous-time joint replenishment problem, termed $\Psi$-pairwise alignment. The latter mechanism, through which we synchronize…

Data Structures and Algorithms · Computer Science 2023-02-21 Danny Segev

The primary objective of this work is to revisit and revitalize one of the most fundamental models in deterministic inventory management, the continuous-time joint replenishment problem. Our main contribution consists of resolving several…

Data Structures and Algorithms · Computer Science 2024-08-13 Danny Segev

There is a growing interest in using electric vehicles (EVs) and drones for many applications. However, battery-oriented issues, including range anxiety and battery degradation, impede adoption. Battery swap stations are one alternative to…

Optimization and Control · Mathematics 2022-01-11 Amin Asadi , Sarah Nurre Pinkley

This paper explores continuous-time and state-space optimal stopping problems from a reinforcement learning perspective. We begin by formulating the stopping problem using randomized stopping times, where the decision maker's control is…

Optimization and Control · Mathematics 2026-03-12 Jodi Dianetti , Giorgio Ferrari , Renyuan Xu

While dynamic policies have historically formed the foundation of most influential papers dedicated to the joint replenishment problem, we are still facing profound gaps in our structural understanding of optimal such policies as well as in…

Data Structures and Algorithms · Computer Science 2025-06-24 Danny Segev
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