An O(T log T) Algorithm for the Dynamic Lot Size Problem with Limited Storage and Linear Costs
Computational Optimization and Applications
Dynamic Lot Sizing with Batch Ordering and Truckload Discounts
Operations Research
A bilinear reduction based algorithm for solving capacitated multi-item dynamic pricing problems
Computers and Operations Research
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Mathematics of Operations Research
Fast generation of production schedules on a single machine
EUROCAST'07 Proceedings of the 11th international conference on Computer aided systems theory
Primal-dual schema for capacitated covering problems
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Lot-sizing with non-stationary cumulative capacities
Operations Research Letters
Allocating procurement to capacitated suppliers with concave quantity discounts
Operations Research Letters
A polynomial algorithm for a lot-sizing problem with backlogging, outsourcing and limited inventory
Computers and Industrial Engineering
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NP-hard cases of the single-item capacitated lot-sizing problem have been the topic of extensive research and continue to receive considerable attention. However, surprisingly few theoretical results have been published on approximation methods for these problems. To the best of our knowledge, until now no polynomial approximation method is known that produces solutions with a relative deviation from optimality that is bounded by a constant. In this paper we show that such methods do exist by presenting an even stronger result: the existence of fully polynomial approximation schemes. The approximation scheme is first developed for a quite general model, which has concave backlogging and production cost functions and arbitrary (monotone) holding cost functions. Subsequently we discuss important special cases of the model and extensions of the approximation scheme to even more general models.