1538. Optimal Pricing in a Bilevel Hub Location Problem
Invited abstract in session MB-15: Location problems, stream Combinatorial Optimization.
Monday, 10:30-12:00Room: Esther Simpson 1.08
Authors (first author is the speaker)
| 1. | Nele Pommerening
|
| Institute of Transport Logistics, TU Dortmund University | |
| 2. | Uwe Clausen
|
| Director, Fraunhofer-Institute for Materialflow and Logistics (IML) | |
| 3. | Christoph Buchheim
|
| Fakultät für Mathematik, Technische Universität Dortmund | |
| 4. | Maja Hügging
|
| TU Dortmund University |
Abstract
We study a bilevel variant of the hub location problem in which a logistic-service provider (the leader) builds a logistical network and offers several options of shipment service at different quality and at different prices. These shipment options can represent different delivery speed or features like real-time tracking. The shipment costs for the leader increase with the quality of the service. Based on their available budgets and the prices appointed by the leader, customers (the follower) then decide whether they order one of the shipment options. A customer will always order the 'best' shipment option they can afford.
Because of the reciprocal interference of the two decision-makers, the leader has to take into account the customers' reaction when maximizing the profit, i.e. the costs of transport via the established network subtracted from the generated revenue.
Due to the complexity of classical hub location problems, our bilevel problem is NP-hard. Our langrangian decomposition approach yields a tractable customers' decision problem and an NP-hard prize-collecting hub location problem. We specify lagrangian multipliers and prove their optimality, showing that they leave no duality gap. As a by-product, we obtain a polynomial-time reduction of our bilevel problem to the more compact (single-level) prize-collecting problem which may offer a significant advantage with respect to the required computational effort compared to standard single-level reformulations.
Keywords
- Transportation
- Graphs and Networks
- Programming, Mixed-Integer
Status: accepted
Back to the list of papers