A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses
Please always quote using this URN: urn:nbn:de:0297-zib-8454
- 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.
Author: | Christoph Helmberg, Stefan Röhl |
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Document Type: | ZIB-Report |
Tag: | bundle method; convex relaxation; integer programming; large scale problems; logistics; network models; stochastic demand; vehicle routing |
MSC-Classification: | 90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B05 Inventory, storage, reservoirs |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Bxx Operations research and management science / 90B06 Transportation, logistics | |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C06 Large-scale problems | |
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C90 Applications of mathematical programming | |
Date of first Publication: | 2005/01/25 |
Series (Serial Number): | ZIB-Report (05-11) |
ZIB-Reportnumber: | 05-11 |
Published in: | Appeared in: Operations Research 55 (2007) 733-752 |