Some APX-completeness results for cubic graphs
Theoretical Computer Science
Control Message Aggregation in Group Communication Protocols
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Competitive analysis of organization networks or multicast acknowledgement: how much to wait?
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
A constant approximation algorithm for the one-warehouse multi-retailer problem
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Primal-Dual Algorithms for Deterministic Inventory Problems
Mathematics of Operations Research
Online make-to-order joint replenishment model: primal dual competitive algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Latency-constrained aggregation in sensor networks
ACM Transactions on Algorithms (TALG)
Improved approximation algorithm for the one-warehouse multi-retailer problem
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
Computational complexity of uncapacitated multi-echelon production planning problems
Operations Research Letters
ACM SIGACT News
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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 over time from a supplier to retailers. Over time, in response to demands at the retailers, the supplier sends shipments, via a warehouse, to the retailers. The objective is to schedule shipments to minimize the sum of shipping costs and retailers' waiting costs. We study the approximability of JRP with deadlines, where instead of waiting costs the retailers impose strict deadlines. We study the integrality gap of the standard linear-program (LP) relaxation, giving a lower bound of 1.207, and an upper bound and approximation ratio of 1.574. The best previous upper bound and approximation ratio was 1.667; no lower bound was previously published. For the special case when all demand periods are of equal length we give an upper bound of 1.5, a lower bound of 1.2, and show APX-hardness.