90C06 Large-scale problems
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We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, the crews of the tours have to be scheduled. Thus, we developed a personalized crew rostering model. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The paper focuses first on different requirements for the rostering and how they can be modeled in detail. The second focus is on a bicriterion analysis of the planning problem to find the balance between the control quality and the roster acceptance. On the one hand the tour planning is a profit maximization problem and on the other hand the rostering should be made in a employee friendly way. Finally, computational results on real-world instances show the practicability of our method.
A Case Study of Joint Online Truck Scheduling and Inventory Management for Multiple Warehouses
(2005)
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.