203. A Pricing Bilevel Hub Location Problem with Vehicle Based Costs
Invited abstract in session TD-1: Hub location and service network design, stream Mobility, Transportation, and Traffic.
Thursday, 14:30-16:00Room: Audimax
Authors (first author is the speaker)
| 1. | Nele Pommerening
|
| Institute of Transport Logistics, TU Dortmund University | |
| 2. | Maja Hügging
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| TU Dortmund University | |
| 3. | Christoph Buchheim
|
| Fakultät für Mathematik, Technische Universität Dortmund | |
| 4. | Uwe Clausen
|
| Director, Fraunhofer-Institute for Materialflow and Logistics (IML) |
Abstract
In this contribution we consider a bilevel variant of the well-known single allocation hub location problem involving vehicle capacities in the cost function.
It is not surprising that this problem inherits its NP-hardness from the classical hub location problem.
Here, the bilevel structure is set up as follows:
The leader is a logistic service provider who aims to maximize her profit, while the customers (the follower) want to ship their transport goods.
First, the leader decides where to build the hubs and sets a price per unit of transport good for every transportation route.
After this, every customer decides based on his budget whether to book the shipment or not.
Every customer has an individual budget and always books the transport, if he can afford it.
The leader knows the budget of all customers and has to maximize her profit, which is the price the customers have to pay minus the costs caused by the required transport vehicles.
As usual, the transportation costs between the hubs are discounted.
The advantage of considering vehicle costs is that they commonly arise in practical applications.
However, they do not rise linearly in the transport volume.
In a recent publication we dealt with the latter bilevel problem with linear costs, deriving a Lagrangian Decomposition into two smaller problems (one is in P) leaving no duality gap.
Now, the same approach results in a duality gap for vehicle-based costs, even if all customers have uniform transport volume.
However, this can be repaired by including particular redundant constraints into the respective bilevel problem.
Keywords
- Graphs and Networks
- Logistics
- Mixed-Integer Programming
Status: accepted
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