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978-3-8439-0538-1, Reihe Mathematik
Combinatorial Exchanges in Freight Logistics
203 Seiten, Dissertation Technische Universität Kaiserslautern (2011), Softcover, A5
In this thesis the author presents various aspects of modeling a combinatorial exchange for cooperating freight carriers. The main topics are the mathematical modeling, the development of a bidding assistance, and investigating the different possibilities to share the profit amongst participants.
The mathematical model enables the daily exchange of requests for transportation between the participating carriers by means of a decentralized auction mechanism. By using a combinatorial exchange, more complex trades are enabled than with a standard auction; by dividing up the auction in four separate phases which all participants go through in a synchronous manner, the complexity for participants is greatly reduced.
Various aspects of how to share the resulting profit between the participants are investigated. This is an important topic, since the profit sharing can keep the carriers from participating if they do not consider it to be fair. Three important game theoretic properties of profit sharing mechanisms are introduced which are crucial for the practical operation of a combinatorial exchange platform. It is then explored what degrees of freedom are still left when requiring the three properties. A monetary flow network is introduced to model the payments between participants. It is shown that a profit distribution is representable in the flow network if and only if it satisfies the three desired properties.
A novel approach is presented how to share the profit between participants. It scales down the payments of the Vickrey-Clarke-Groves mechanism to regain the core property while maximizing the minimum used scaling factor over all participants. It is shown that this approximates the Shapley Value linearly in the number of bundles.
To support freight carriers with the complex and tedious task of formulating bundle offers in the auction, a bidding assistance module is developed. First, it is shown how to approximate a bundle’s chance to be successful in the auction, then a two-stage procedure is introduced, which employs a Mixed Integer Program to model dependencies between bundles and vehicles.
Finally, a wide range of computational results is presented, both for generated test data and for real-world data of a German freight carrier. The savings achieved with the combinatorial exchange are compared to bilateral trade and to a centralized optimization procedure.