A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions

Fuente: arXiv
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Autori principali: Ata, Barış, van Eekelen, Wouter, Zhong, Yuan
Natura: Preprint
Pubblicazione: 2025
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author Ata, Barış
van Eekelen, Wouter
Zhong, Yuan
author_facet Ata, Barış
van Eekelen, Wouter
Zhong, Yuan
contents 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 control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions -- that is, 50 stock-keeping units (SKUs).
format Preprint
id arxiv_https___arxiv_org_abs_2511_11830
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions
Ata, Barış
van Eekelen, Wouter
Zhong, Yuan
Optimization and Control
Machine Learning
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 control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions -- that is, 50 stock-keeping units (SKUs).
title A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions
topic Optimization and Control
Machine Learning
url https://arxiv.org/abs/2511.11830