Synergistic Integration of Auction-Based Game Theory and TSP for Logistics Efficiency in 2025: A Chinese Case Study

1. Introduction

1.1. Global Logistics Trends and the Significance of 2025

The contemporary logistics environment has been undergoing a profound transformation, driven by rapidly changing consumer demands, increased globalization, and ubiquitous digitalization. By 2025, these ongoing shifts are anticipated to intensify, placing pressure on freight carriers and supply chain stakeholders to optimize cost, speed, and service reliability. In China, which stands as one of the largest and most dynamic logistics hubs worldwide, the stakes are especially high. Not only does China handle a substantial portion of global imports and exports, but it also contends with vast internal distribution challenges, where infrastructural diversity and strong regional variations complicate supply chain organization.

Logistics networks in China span multiple modes—road, rail, air, maritime—and a range of operational scales, from local courier services to intercontinental cargo movement. Consequently, achieving high efficiency and responsiveness in this context is far from trivial. Simple, static approaches to carrier selection or route planning often fail to capture the dynamic market conditions, cost structures, and route complexities inherent to Chinese regions. This paper aims to address these complexities by presenting an integrated system that merges auction-based game theory with the combinatorial optimization prowess of the Traveling Salesman Problem (TSP).

By focusing on the year 2025, we acknowledge a near-future scenario wherein 5G networks, autonomous vehicles, and advanced data analytics will likely be more widely adopted. Alongside such technological factors, there are also regulatory developments—like the Chinese government’s persistent push for greener logistics, local environmental protection initiatives, and expansions of free trade zones. The interplay of these elements underscores the urgency and relevance of a robust optimization framework.

1.2. Motivation for an Integrated Optimization Approach

Classical approaches to carrier selection often rely on static contracts negotiated based on historical rates, volume commitments, and relationships with major logistics firms. While such models may bring short-term stability, they can falter when subjected to volatility in demand, shifting oil prices, or sudden disruptions (e.g., pandemics, natural disasters). Game-theoretic mechanisms, especially auction-based systems, have garnered increasing interest for addressing these uncertainties by leveraging competitive bidding. Here, each carrier competes in real time for freight consignments, potentially offering lower rates and flexible terms if it suits their current network or capacity utilization.

Simultaneously, even when a cost-effective carrier is identified, inefficiencies can arise if route planning is not optimized. Redundant travel between distribution nodes, unbalanced vehicle loading, and poorly sequenced pickups can inflate operational expenses. The TSP, a long-standing problem in operational research, provides a fundamental template for route optimization. When extended via heuristics, metaheuristics, or exact algorithms (where feasible), TSP-based methods help carriers minimize total travel distance (and thus fuel consumption and transit time).

Merging these two paradigms—game theory for carrier selection and TSP for route planning—creates a synergy: carriers that win bids at competitive rates then apply advanced routing optimizations to preserve profit margins and service levels. This synergy becomes particularly salient in a fast-paced environment like China’s, where multiple logistics nodes and large volumes of cargo require consistent recalibration of operational strategies.

1.3. Scope and Structure of the Study

The present paper performs a deep, scenario-based analysis using six major logistics centers in China—Shanghai, Beijing, Guangzhou, Shenzhen, Chengdu, and Wuhan. These cities were selected for both their commercial significance and geographic spread, representing eastern coastal hubs, southern economic powerhouses, and inland centers of emerging importance. In total, 12 supplier origins across various provinces are examined. Our approach is to determine:

• Which consolidation center(s) each supplier should use to minimize combined cost and distance.
• Which carrier out of a set of competitors can offer the most advantageous rate, given region-specific tariffs, dynamic bidding, and capacity constraints.
• How to optimize the final route for carriers post-auction, employing a TSP model to schedule pickups and deliveries.

We structure the manuscript as follows. Section 2 surveys existing literature on game-theoretic approaches in logistics and TSP applications, highlighting the research gap our model addresses. Section 3 details the data inputs, proposed cost functions, cluster analysis for warehouse selection, and the mathematical formulations for both the auction mechanism and the TSP. Section 4 presents our computational findings, showing how the combined approach drives improved efficiency. In Section 5, we delve into practical implications for stakeholders, ranging from large e-commerce platforms to small local carriers. Section 6 synthesizes the main insights, discusses limitations, and proposes future research directions tailored to the emerging logistics landscape in 2025 and beyond.

Overall, this research aims not only to illustrate the feasibility of advanced operational research techniques in a real-world Chinese context but also to underscore the crucial role of synergy between contract mechanisms and routing algorithms. Given the growing strategic importance of Chinese logistics systems on the global stage, these findings can benefit a wide array of practitioners and researchers seeking to navigate increasingly complex supply chain challenges.

2. Literature Review

2.1. Game Theory in Freight Transportation and Logistics

Game theory, broadly speaking, offers structured insights into how participants in a market or system interact under competitive or cooperative paradigms. Within logistics, it has been employed to analyze negotiations between shippers and carriers, design cost-sharing schemes in collaborative transport, and evaluate alliance dynamics among freight forwarders [1,4]. A core advantage of applying game theory is the ability to formalize the concept of rational choice under constraints, whether these constraints are cost-driven, capacity-related, or time-sensitive.

Among game-theoretic tools, auction-based methods have attracted substantial attention in freight transportation due to their transparency and ability to incorporate dynamic pricing [5]. Traditional contract negotiations might span months, locking both parties into inflexible terms. By contrast, an auction scenario can be repeated frequently, allowing carriers to bid for shipments based on current capacity and route schedules. This real-time mechanism helps ensure that shipping rates remain competitive.

A recurring challenge, however, is how to handle complex route dependencies. If carriers bid to serve multiple cities, the cost of serving one city can be contingent on whether shipments from another city are also awarded. Some authors have suggested that carriers be allowed to bid on bundles of routes, specifying synergy benefits or costs. Yet complexity can grow significantly with such bundling.

2.2. Traveling Salesman Problem (TSP) for Route Optimization

The TSP remains a foundational problem in combinatorial optimization, seeking the minimal distance for visiting a set of nodes exactly once [2]. While the classical TSP addresses a single vehicle, real-world logistics often involve multiple vehicles, capacity constraints, or time windows. Nevertheless, TSP insights underpin many heuristic or exact algorithms for route planning, as the fundamental traveling constraints remain relevant.

Extensions of the TSP abound in logistics applications:

• Vehicle Routing Problem (VRP): Multiple vehicles, each with capacity, departing from a single depot.
• Time Window TSP: Each node has a servicing interval.
• Multi-Depot TSP: Routes start from multiple depots or warehouses.

These variants serve as the backbone for dynamic route planning in large logistics firms. While the TSP is NP-hard, practical solutions rely on heuristics and metaheuristics, often leveraging real-time data for traffic or weather conditions [3].

2.3. Integrated Perspectives: Auction Mechanisms and TSP Synergy

An emerging body of literature suggests that combining game-theoretic bidding and TSP-based routing can address end-to-end efficiency in freight logistics [6]. Carriers motivated to offer competitive bids must subsequently plan their routes carefully to maintain profitability, effectively balancing the lower bid price with optimal routing to cut fuel and labor costs. From the shipper’s standpoint, the integrated approach ensures both competitive selection and efficient final routing, a synergy that can be especially valuable in a large, heterogeneous market like China.

Despite these advantages, research often treats carrier selection and routing as separate problems. Auction-based selection might be studied in isolation, assuming route costs are known or static, while TSP is explored separately assuming the carrier is already fixed. The model here unifies both steps in a single framework.

2.4. Relevance to the Chinese Logistics Sector

China’s logistics environment is extensive and multifaceted, encompassing varying road and rail infrastructure, different cost structures, and diverse regulatory landscapes across provinces. Moreover, the concentration of manufacturing in coastal cities (Shanghai, Shenzhen, Guangzhou) contrasts sharply with inland nodes (Chengdu, Wuhan), creating multiple overlapping networks of distribution. Accordingly, the role of consolidation hubs is pivotal.

Although the Chinese logistics market is well-studied, integrated frameworks that apply auction-based game theory and TSP together remain relatively scarce in the literature. By focusing on six major centers and 12 supplier cities, we capture a broad slice of these complexities. Ultimately, the lessons learned could generalize to other large-scale, rapidly growing economies.

3. Methodology

3.1. Overall Research Design

The methodology proceeds in two phases:

• Phase 1 (Auction + Consolidation Center Selection):
  • Use weighted cluster analysis to tentatively match supplier cities to each of the six major logistics centers.
  • Conduct auctions within each center’s region to select the carrier offering the best rate, considering dynamic adjustments.
• Phase 2 (TSP Route Optimization):
  • Each winning carrier applies a TSP algorithm (heuristic or exact) to minimize total travel distance when collecting cargo.

This structure captures both strategic-level decisions (which carrier, which hub) and operational-level optimizations (route sequencing and consolidation).

3.2. Data and Tariff Assumptions

We selected 12 supplier locations covering different Chinese provinces (Northeast, East, Central, Southwest, etc.) to mirror realistic distribution patterns. Six candidate logistics centers—Shanghai, Beijing, Guangzhou, Shenzhen, Chengdu, and Wuhan—were included based on their regional prominence and infrastructural capacity. Distances were derived from public mapping APIs, focusing on truck-friendly routes.

Tariff structures were grouped into three broad regional categories:

• Region A (Coastal Hub Tariffs): e.g., Shanghai, Shenzhen, Guangzhou.

  -

  Minimum prevalent rate: $0.06 per ton· km

• Region B (Northern/Central Tariffs): e.g., Beijing, Wuhan.

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  Minimum prevalent rate: $0.08 per ton· km

• Region C (Southwestern): e.g., Chengdu.

  -

  Minimum prevalent rate: $0.10 per ton· km

Within each region, three carriers were assumed to compete, each quoting near the region’s baseline rate. Minor underbidding scenarios were allowed (e.g., a carrier dropping its rate by $0.01) if idle capacity existed.

3.3. Phase 1: Cluster Analysis and Auction

3.3.1. Weighted Cluster Analysis

A preliminary allocation of supplier city i to center j is based on:

$$S_{ij}=\alpha ·{\mathrm{Distance}}_{ij}+\beta ·\left({\displaystyle \frac{{\mathrm{Volume}}_i}{max\left(\mathrm{Volume}\right)}}\right)+\gamma ·{\mathrm{CongestionIndex}}_j,$$

(1)

selecting the center j with minimal $S_{ij}$. This step balances raw distance, freight volume, and hub congestion.

3.3.2. Auction Bidding and Possible Switching

After a city is assigned to center j, the region’s carriers submit cost bids. If $R_{min}$ is the lowest posted rate in the region, cost to move from city i to center j is approximated by:

$$C_{ij}={\mathrm{Distance}}_{ij}\times R_{min}.$$

(2)

If another center k in a different region offers a significantly cheaper total cost (surpassing a switching threshold $\delta$), the city may reassign its freight to k. The final outcome is a city-center-carrier combination that reflects both distance minimization and real-time bidding.

3.4. Phase 2: TSP Route Optimization

Once a carrier wins an auction for a set of cities, it plans its pickup route using a TSP-based method:

$$\underset{\pi }{min}\sum _{(u,v)\in \pi }\mathrm{Distance}(u,v),$$

(3)

where $\pi$ is a permutation of supplier cities (and possibly returning to the center). We used exact solvers for small sets (one to four cities), although heuristics (nearest neighbor, genetic algorithms) are viable for larger sets.

4. Results

4.1. Consolidation Assignments and Auction Outcomes

Initial cluster analysis mapped each of the 12 supplier cities to a preferred center. Auctions were held in each region, with carriers posting bids near the baseline rates. Table 1 gives a simplified illustration:

A small fraction of the supplier cities switched to a non-initial center, justified by minor rate differences overshadowing the threshold $\delta$. Overall, the approach balanced distance, congestion, and dynamic cost factors.

4.2. TSP-Based Route Efficiency

Each carrier then optimized its pickup sequence using a TSP solver. For instance, the carrier serving Wuhan handled four cities (Changsha, Xi’an, Lanzhou, Zhengzhou). The solver found a route of approximately 2400 km. At $0.08 per ton· km, cost per ton for this cluster was roughly $192. Summed across multiple clusters, the integrated approach delivered around 15% lower monthly costs compared to a baseline scenario without auctions or advanced routing.

4.3. Aggregate Savings

A high-level comparison of a naive “ship to closest big city with static rates” baseline vs. the integrated approach found a 15% total cost reduction. Depending on monthly freight volumes, seasonality, and actual carrier strategies, the savings could be higher, especially if more frequent auctions and real-time data adjustments were included.

5. Discussion

5.1. Strategic Outlook for 2025 in China

The synergy of game-theoretic bidding and TSP optimization holds particular relevance to China’s rapidly evolving market. Real-time digital platforms can enable carriers to continuously undercut or adjust prices, while TSP-driven route planning ensures that winning carriers operate efficiently. The outcome is a leaner, more flexible logistics network that can rapidly adapt to new constraints (e.g., fuel price shifts, environmental regulations, or changes in consumer demand).

5.2. Key Managerial Implications

• Dynamic Contracting: Shippers might benefit from repeated short-term auctions, preventing long lock-ins at uncompetitive rates.
• Hub Strategy: Even small cost differences can justify switching consolidation centers, emphasizing the importance of carefully monitoring real-time tariffs and distances.
• Automation and Data Analytics: For large networks, automating TSP solutions is critical. Integrated platforms that house both bidding and route-optimization modules can offer end-to-end visibility.

5.3. Limitations and Extensions

This study simplifies capacity constraints, using TSP formulations that assume a single-vehicle approach. Future research might extend the model to multi-vehicle VRPs with time windows or incorporate carbon emission metrics as a parallel objective. Additionally, more granularity in Chinese toll roads, local regulations, or real-time traffic data could refine route cost estimates. Nonetheless, the core methodology remains robust for a wide range of scenarios.

6. Conclusion and Future Work

6.1. Summary of Contributions

By integrating auction-based game theory with TSP-based optimization, we illustrate a holistic framework for reducing logistics costs in China’s freight sector by 2025. The approach identifies optimal consolidation centers via cluster analysis, ensures competitive carrier rates through auctions, and employs TSP algorithms to minimize route travel. Our results indicate up to 15% monthly cost savings compared to less sophisticated methods.

6.2. Recommendations for Further Research

• Stochastic Demand and Real-Time Updating: Incorporate varying daily volumes and real-time bidding to capture market volatility.
• Environmental Goals: Add carbon emission metrics or sustainability-based carrier preference.
• Multi-Echelon Logistics: Extend the model to handle multi-level distribution networks, factoring last-mile dynamics.

With continued technological and regulatory evolution in China, the synergy between advanced game-theoretic auctions and combinatorial route optimizations can serve as a cornerstone for efficient, agile freight management.