Abstract
Collaboration has been one of the important trends in vehicle routing. A typical mechanism to enable carrier collaboration is to use combinatorial auctions, where requests are not traded individually but are combined into bundles. Previous literature on carrier collaboration has focused on issues such as bundle formation or winner determination, typically assuming truthfulness of all agents and absence of any strategic behavior. This article considers the interdependencies and problems that arise from bidders acting as buyers and sellers of requests at the same time. From standard auction theory, desirable properties of exchange mechanisms are identified as efficiency, incentive compatibility, individual rationality, and budget balance. It is shown that these desirable properties cannot be fulfilled at the same time. In particular, the properties efficiency and incentive compatibility induce that budget balance is violated, that is, an outside subsidy is required. We propose two incentive compatible exchange mechanisms. One is more closely related to the classical VCG approach, while the other one uses a more complicated concept for computing payments to participants. A numerical study investigates how frequently desired properties are violated. We show that both mechanisms can be acceptable in practical situations, but none of them can satisfy all desired properties.
Highlights
Collaborative relationships have been recently identified by Speranza [57] to be one of the big trends in transportation
The difference between Z∗ and Zm0 reflects the marginal effect of removing several bidders, and not just one bidder. This leads to the familiar problem of team production in economics [5]: If changes in output cannot be allocated to the activities of specific team members, on the one hand incentive considerations require each team member to receive the full marginal output, which on the other hand means that incentive payments exceed total output and the system cannot be budget balance (BB)
We first consider the case of an additive cost structure: Proposition 1 If the cost function is additive, and bidders bid for all combinations of requests, the VCG mechanism will not generate a positive net payment for the auctioneer. (We remark that in this setting, it is not really necessary to perform a combinatorial auction, each request could be auctioned off by itself.)
Summary
Collaborative relationships have been recently identified by Speranza [57] to be one of the big trends in transportation. The carriers are willing to exchange their requests with their competitors, aiming for an increase in efficiency and sustainability They do so using combinatorial auction-based mechanisms, where we assume that carries determine their bids based on their marginal costs for the traded requests. A buyer’s marginal costs for performing a given request herself (and the maximum cost at which the request should be outsourced) may depend both on whether other requests are outsourced or not, as well as on the requests insourced and executed for other carriers These complex interactions make the problem difficult and present specific challenges for the design of an adequate mechanism that we will explore in this article.
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