Properties of bundle valuations in carrier collaboration

Area of Science:

• Operations Research
• Algorithmic Game Theory
• Logistics and Supply Chain Management

Background:

• Combinatorial auctions are crucial for efficient resource allocation in logistics, enabling carrier collaboration.
• Economic literature offers innovative auction mechanisms, but their practical application hinges on bidder valuation assumptions.
• The Traveling Salesman Problem (TSP) is a fundamental logistics challenge often used to derive bidder valuations.

Purpose of the Study:

• To computationally assess the validity of bidder valuation assumptions in combinatorial auctions for logistics.
• To analyze the extent to which valuations derived from a TSP satisfy requirements of existing auction mechanisms.
• To investigate the pattern and impact of valuation violations across different carriers and route calculation methods.

Main Methods:

• Conducted computational experiments using valuations derived from a simplified logistics problem (Traveling Salesman Problem).
• Analyzed bidder valuations against fundamental requirements of combinatorial auction mechanisms.
• Examined the consistency of valuation violations across multiple carriers and compared exact vs. approximated route length calculations.

Main Results:

• Found that bidder valuations derived from the TSP typically violate even basic assumptions of combinatorial auction mechanisms.
• Determined that these valuation violations affect only a limited subset of possible request bundles.
• Observed that violations do not exhibit a consistent pattern across different carriers and are robust to exact vs. approximated route lengths.

Conclusions:

• Despite common violations of theoretical assumptions, combinatorial auction mechanisms show potential for practical application in logistics.
• The limited impact of valuation violations suggests that current auction designs may still yield efficient allocations in many real-world scenarios.
• Further research can explore robust auction designs that accommodate typical valuation patterns in logistics.