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A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses

Fakultät für Mathematik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
Vorarlberg University of Applied Sciences, A-6850 Dornbirn, Austria
helmberg{at}mathematik.tu-chemnitz.de
stefan.roehl{at}fhv.at

For a real-world problem—transporting pallets between warehouses 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 five to 12 minutes for up to three warehouses and 40,000 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.

Subject classifications: convex relaxation; integer programming; stochastic demand; network models; large-scale problems; bundle method; logistics; vehicle routing.
History: Received February 2005; revision received April 2006; accepted July 2006.