@misc{HelmbergRoehl2005, author = {Helmberg, Christoph and R{\"o}hl, Stefan}, title = {A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8454}, number = {05-11}, year = {2005}, abstract = {For a real world problem --- transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand --- we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost function that is based on minimizing the expected number of pallets that still need transportation. For speed, the convex relaxation is solved approximately by a bundle approach yielding an online schedule in 5 to 12 minutes for up to 3 warehouses and 40000 articles; in contrast, computation times of state of the art LP-solvers are prohibitive for online application. In extensive numerical experiments on a real world data stream, the approximate solutions exhibit negligible loss in quality; in long term simulations the proposed method reduces the average number of pallets needing transportation due to short term demand to less than half the number observed in the data stream.}, language = {en} }