We give new approximation algorithms for the submodular joint replenishment problem and the inventory routing problem, using an iterative rounding approach. In both problems, we are given a set of N items and a discrete time horizon of T days in which given demands for the items must be satisfied. Ordering a set of items incurs a cost according to a set function, with properties depending on the problem under consideration. Demand for an item at time t can be satisfied by an order on any day prior to t, but a holding cost is charged for storing the items during the intermediate period; the goal is to minimize the sum of the ordering and holding cost. Our approximation factor for both problems is O(loglogmin(N,T)); this improves exponentially on the previous best results.
@article{arxiv.1912.00101,
title = {Improved Approximation Algorithms for Inventory Problems},
author = {Thomas Bosman and Neil Olver},
journal= {arXiv preprint arXiv:1912.00101},
year = {2019}
}