A Shadow Simplex Method for Infinite Linear Programs
Operations Research
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
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We establish a duality theory for a broad class of deterministic inventory control problems on continuous spaces that includes the classical joint replenishment problem and inventory routing. Using this theory, we establish the existence of an optimal policy, which has been an open question. We show how a primal-dual pair of infinite dimensional linear programs encode both cyclic and noncyclic schedules, and provide various results regarding cyclic schedules, including an example showing that they need not be optimal.