A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Facility location with Service Installation Costs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Asymmetric k-center is log* n-hard to approximate
Journal of the ACM (JACM)
On dependent randomized rounding algorithms
Operations Research Letters
Online make-to-order joint replenishment model: primal dual competitive algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Cost Allocation for Joint Replenishment Models
Operations Research
Primal-dual schema for capacitated covering problems
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
A simple and fast 2-approximation algorithm for the one-warehouse multi-retailers problem
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On the power of lookahead in online lot-sizing
Operations Research Letters
An efficient polynomial-time approximation scheme for the joint replenishment problem
IPCO'13 Proceedings of the 16th international conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for the joint replenishment problem with deadlines
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We consider several classical models in deterministic inventory theory: the single-item lot-sizing problem, the joint replenishment problem, and the multistage assembly problem. These inventory models have been studied extensively, and play a fundamental role in broader planning issues, such as the management of supply chains. For each of these problems, we wish to balance the cost of maintaining surplus inventory for future demand against the cost of replenishing inventory more frequently. For example, in the joint replenishment problem, demand for several commodities is specified over a discrete finite planning horizon, the cost of maintaining inventory is linear in the number of units held, but the cost incurred for ordering a commodity is independent of the size of the order; furthermore, there is an additional fixed cost incurred each time a nonempty subset of commodities is ordered. The goal is to find a policy that satisfies all demands on time and minimizes the overall holding and ordering cost. We shall give a novel primal-dual framework for designing algorithms for these models that significantly improve known results in several ways: the performance guarantees for the quality of the solutions improve on or match previously known results; the performance guarantees hold under much more general assumptions about the structure of the costs, and the algorithms and their analysis are significantly simpler than previous known results. Finally, our primal-dual framework departs from the structure of previously studied primal-dual approximation algorithms in significant ways, and we believe that our approach may find applications in other settings. More specifically, we provide 2-approximation algorithms for the joint replenishment problem and for the assembly problem, and solve the single-item lot-sizing problem to optimality. The results for the joint replenishment and the lot-sizing problems also hold for their generalizations with back orders allowed. As a byproduct of our work, we prove known and new upper bounds on the integrality gap of some linear-programming (LP) relaxations of the abovementioned problems.