The Periodic Joint Replenishment Problem Is Strongly 𝒩𝒫-Hard

Tamar Cohen-Hillel · Liron Yedidsion

23 citations0/0 files storedMathematics of Operations Research

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Supply Chain and Inventory Management Complexity and Algorithms in Graphs Scheduling and Optimization Algorithms

Abstract

In this paper, we study the long-standing open question regarding the computational complexity of one of the core problems in supply chains management, the periodic joint replenishment problem. This problem has received a lot of attention over the years, and many heuristic and approximation algorithms have been suggested. However, in spite of the vast effort, the complexity of the problem remains unresolved. In this paper, we provide a proof that the problem is indeed strongly 𝒩𝒫-hard.

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References

2000Foundations of Inventory Management 2019Production and Operations Analysis 198598%-Effective Integer-Ratio Lot-Sizing for One-Warehouse Multi-Retailer Systems 2007A review of the joint replenishment problem literature: 1989–2005 1989Computational complexity of uncapacitated multi-echelon production planning problems 1976A Simple Method of Determining Order Quantities in Joint Replenishments Under Deterministic Demand 1989Joint replenishment inventory control: Deterministic and stochastic models 1985The Joint Replenishment Problem with a Powers-of-Two Restriction

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2023Adaptive inventory replenishment using structured reinforcement learning by exploiting a policy structure 2020Efficient methods for stochastic joint replenishment and delivery problem 2020An integrated algorithm for solving multi-customer joint replenishment problem with districting consideration

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