A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions
arXiv:2511.11830v2 Announce Type: replace-cross Abstract: 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
The increasing complexity and scale of supply chains, combined with advances in AI and computational methods, make this an opportune time for developing more sophisticated optimization techniques.
Improving the efficiency of stochastic replenishment problems has direct implications for reducing costs, optimizing inventory, and enhancing resilience across numerous industries facing high-dimensional challenges.
This method offers a new approach to complex inventory management, potentially leading to more adaptive and data-driven supply chain operations than traditional models.
- · Logistics and supply chain companies
- · E-commerce retailers
- · Manufacturing sectors
- · AI/ML solution providers
- · Companies relying on static inventory models
- · Operations research firms without AI expertise
Companies can optimize inventory levels more effectively, reducing waste and improving product availability.
Enhanced supply chain efficiency could lead to lower consumer prices and more robust global logistics networks.
The widespread adoption of such methods might further centralize supply chain planning in AI-driven systems, impacting human decision-making roles.
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Read at arXiv cs.LG