Joint Replenishment Problems in Inventory and Distribution Systems: A Review of Models, Constraints, and Algorithms

Mengru Wang

doi:10.62051/ijgem.v10n5.13

Authors

Mengru Wang

DOI:

https://doi.org/10.62051/ijgem.v10n5.13

Keywords:

Joint replenishment problem, Joint replenishment and delivery, Heuristic algorithms, Reinforcement learning

Abstract

The joint replenishment problem (JRP) examines replenishment cycles, order quantities, and coordinated execution decisions for multiple items that share ordering costs or operational resources. As inventory management becomes increasingly connected with distribution networks, JRP has moved beyond static cost minimization and has been extended to stochastic demand, dynamic demand, resource constraints, joint replenishment and delivery, inventory routing, vendor-managed inventory, and learning-based optimization. This paper provides a narrative review of representative studies on JRP and related integrated inventory-distribution problems. The review is organized around four themes: relaxation of modeling assumptions, incorporation of operational constraints, expansion of decision boundaries, and evolution of algorithmic paradigms. It compares the decision scope of JRP, JRD, IRP, and S&OP-related models, and discusses the applicability of heuristics, metaheuristics, mathematical programming, approximation algorithms, and reinforcement learning. The review suggests that JRP research is shifting from replenishment-cycle selection under a single cost objective toward integrated supply chain decision-making under uncertain demand, limited resources, distribution coordination, and multi-objective performance requirements.

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